In chapter twelve of The Lightning Thief, what conflict did Grover face?

In chapter 12, Grover faces a conflict between his desire to find Pan and his responsibilities to Annabeth and Percy.

The text tells us that Grover's main goal is to look for the god Pan. However, in order to do that, he must prove his mettle as a keeper. In the book, a keeper is one who safeguards those who need protection. For his part, Grover has already failed twice as a keeper. He failed...

In chapter 12, Grover faces a conflict between his desire to find Pan and his responsibilities to Annabeth and Percy.

The text tells us that Grover's main goal is to look for the god Pan. However, in order to do that, he must prove his mettle as a keeper. In the book, a keeper is one who safeguards those who need protection. For his part, Grover has already failed twice as a keeper. He failed to secure Thalia's safety many years ago, and he also failed to bring Percy safely to Camp Half-Blood.

In order to earn his searcher's license, Grover must make sure that both Percy and Annabeth return safely from their mission. Essentially, every satyr must earn the right to become a searcher for Pan. However, not all satyrs succeed in earning this privilege, however. As a result, Grover is conflicted. His real desire is to search for the God of Wild Places and to wake him up from his sleep. Grover believes that the return of Pan will restore the earth to its former pristine glory.

However, he must make sure that he is not distracted by his inclinations. In other words, he must make sure that Annabeth and Percy are his first priority, rather than Pan.

Scout calls Dill a “pocket Merlin.” This is an allusion to what legend?

The legend in question is that of King Arthur and the Knights of the Round Table. One of the most memorable characters in that epic tale is Merlin the wizard.

It is summertime in Maycomb and that means playtime for the kids, with lots of opportunities for getting into all kinds of scrapes and crazy adventures. Scout and Jem are pretty imaginative when it comes to thinking up new ways to occupy themselves during those...

The legend in question is that of King Arthur and the Knights of the Round Table. One of the most memorable characters in that epic tale is Merlin the wizard.

It is summertime in Maycomb and that means playtime for the kids, with lots of opportunities for getting into all kinds of scrapes and crazy adventures. Scout and Jem are pretty imaginative when it comes to thinking up new ways to occupy themselves during those long, hot summer months, but Dill is in a different class all of his own:

Thus we came to know Dill as a pocket Merlin, whose head teemed with eccentric plans, strange longings and quaint fancies.

So says Scout. The boy clearly has a rich, imaginative fantasy world, the kind of thing that most children would find themselves being drawn to immediately. Scout's reference to "pocket Merlin" also highlights Dill's somewhat diminutive stature. He is one year older than Scout, yet she still towers over him. But what little Dill lacks in height, he more than makes up for in personality and imagination.

How is A Moveable Feast by Ernest Hemingway representative of the Lost Generation? What are the specific examples in the text?

Hemingway tells the story in A Moveable Feast of how Gertrude Stein came up with the term "the Lost Generation."

She had some ignition trouble with the old Model T Ford she then drove and the young man who worked in the garage and had served in the last year of the war had not been adept, or perhaps had not broken the priority of other vehicles, in repairing Miss Stein’s Ford. Anyway he had not been sérieux and had been corrected severely by the patron of the garage after Miss Stein’s protest. The patron had said to him, “You are all a génération perdue.” “That’s what you are. That’s what you all are,” Miss Stein said. “All of you young people who served in the war. You are a lost generation.”

It's telling that the phrase originates from Stein's dissatisfaction with having to wait for her car to be fixed, with her personal requirements for service, and it is characteristic that she effortlessly conflates this petty annoyance with the spirit of an entire generation. It was the sort of generalization that Hemingway was purposely trying to remove from his writing. Stein meant that the generation that had served in the First World War, and in particular the set of expatriate artists she entertained in her Paris apartment, were disoriented, or wandering aimlessly. I don't think Hemingway agreed, exactly. Hemingway's memoir, on the one hand, tells the story of his wanderings in Paris in the 20s, but on the other, it tells the story of how he came to master the craft of writing. Hemingway writes about wandering, but (at least in his memoir) there is a destination, which is his becoming a great writer.

Examples abound. Take, for instance, the beginning of the book, chapter one, "A Good Café on the Place St.-Michel." In this chapter Hemingway describes the squalor of the his neighborhood in Paris, the bad cafe with its "sour smell of drunkenness" and his freezing room at the top of the hotel, and his daily appraisal of the state of other chimneys on the street to determine if it was worthwhile to spend money on firewood that day. These details, which speak to his poverty, underline his commitment to his craft. In that first chapter, he tells about writing in a cafe, his engagement with the story he was writing (a story about Michigan), and about how a girl who comes to the cafe offers some inspiration. As Hemingway writes, he thinks of her:

I’ve seen you, beauty, and you belong to me now, whoever you are waiting for and if I never see you again, I thought. You belong to me and all Paris belongs to me and I belong to this notebook and this pencil. Then I went back to writing and I entered far into the story and was lost in it. I was writing it now and it was not writing itself and I did not look up nor know anything about the time nor think where I was nor order any more rum St. James. I was tired of rum St. James without thinking about it. Then the story was finished and I was very tired. I read the last paragraph and then I looked up and looked for the girl and she had gone. I hope she’s gone with a good man, I thought. But I felt sad.

The passage suggests that, if Hemingway is lost, he is lost in the act of creation. The Paris Hemingway knew was an incredibly fertile place for artists and intellectuals -- his comment, "All Paris belongs to me" -- is an expression of the artistic freedom he feels. And there is a sense in the writing of nostalgia or a longing for past times -- Hemingway at the end of his life, remembering the start of his journey, perhaps wishing he could be "lost" again.

How is morality explored in Will's dream vision? His pilgrimage is a quest for salvation and the justness of society, but how exactly are these...

Great question! It is true that the beginning of the prologue uses the tower and the dungeon as representations of Heaven and Hell. On an even deeper level, the tower represents God's Truth and the dungeon is filled with prisoners who represent the damned souls that occupy Hell. The prologue further expounds upon the ways in which Will's dream are connected to his quest for morality and justification.

The world between the tower and the...

Great question! It is true that the beginning of the prologue uses the tower and the dungeon as representations of Heaven and Hell. On an even deeper level, the tower represents God's Truth and the dungeon is filled with prisoners who represent the damned souls that occupy Hell. The prologue further expounds upon the ways in which Will's dream are connected to his quest for morality and justification.

The world between the tower and the dungeon represents mortal life, which determines where all living souls will end up. Will is urged by a woman who goes by the name of Holy Church to obtain the Truth found in the tower, but he faces many obstacles in pursuit of this moral goal. Holy Church warns him that his soul's salvation rests on following Truth and that the dungeon is full of all Wrong in the world. The dungeon is also associated in the text with Satan. After this initial warning, Will witnesses a marriage arrangement between Lady Mede, who represents Reward, and False. This setup is a representation of the false reward that comes with choosing Wrong. Instead, the king of London suggests that Lady Mede should marry Conscience. This sparks a moral debate on whether Reward is a matter of falsehood or good conscience.

Lady Mede is the primary source of conflict between Theology and Holy Church as well, and this conflict is the catalyst for Will's journey. Later in the text, the moral themes presented in the prologue gain more depth. As Will receives a second vision or dream, he preaches to others in an effort to compel them to repent of their sins. On another level, the prologue explores the nature of morality as it relates to the different social classes. In the beginning of Will's vision, he sees beggars, noblemen, clergy, and workers all engaged in their normal duties. While their lives are different, the moral conflicts they face all lead to the same eternal consequences. All major aspects of Will's visions are connected to morality in similar ways. The different people he meets represent either aspects of humankind (the king of London, for example) or a moral dilemma (the marriage conundrum between Lady Mede, Conscience and False.)

How is ambition important to the play, Macbeth, written by Shakespeare? What quotations support the theme of ambition.

It is ambition that initially prompts Macbeth to plot the murder of King Duncan.  Although it doesn't seem that he's ever dreamed of being the king before, when the Weird Sisters tell him that he will become king, Macbeth begins to dream of it.  Although he is incredulous initially, when the sisters' first apparent prediction, that he will become Thane of Cawdor, comes to fruition, he starts to believe it might be possible for him...

It is ambition that initially prompts Macbeth to plot the murder of King Duncan.  Although it doesn't seem that he's ever dreamed of being the king before, when the Weird Sisters tell him that he will become king, Macbeth begins to dream of it.  Although he is incredulous initially, when the sisters' first apparent prediction, that he will become Thane of Cawdor, comes to fruition, he starts to believe it might be possible for him to become king after all.  Then, when Duncan names his older son, Malcolm, Prince of Cumberland and his heir to the crown, Macbeth considers how fervently he now aspires to rule the country, saying, "Stars, hide your fires; / Let not light see my black and deep desires" (1.4.57-58).  He wants the stars to go dark so that no one will be able to look at him and see his new ambition for the throne.

Later, Macbeth recounts all the reasons he has not to go forward with the plan to kill Duncan, and there are many.  However, he has one reason to stick to the plan: his "Vaulting ambition" (1.7.28).  This ambition, then, is what has fueled his machinations so far. 

What were the destructive effects of Mt. Pinatubo eruption?

The destructive effects of the Mt. Pinatubos eruption were enormous and far-reaching.  Tons of volcanic ash heaped immeasurable harm to houses, rice paddies, fields, and the two military bases in the Philippines.  The ash, when combined with rain, produced mud flows that buried houses and cars.  Fields and rice paddies that were covered by igneous rock formations when the volcano erupted are still being recovered to this day.

Any time a volcano actively erupts, there...

The destructive effects of the Mt. Pinatubos eruption were enormous and far-reaching.  Tons of volcanic ash heaped immeasurable harm to houses, rice paddies, fields, and the two military bases in the Philippines.  The ash, when combined with rain, produced mud flows that buried houses and cars.  Fields and rice paddies that were covered by igneous rock formations when the volcano erupted are still being recovered to this day.

Any time a volcano actively erupts, there are several concerns that must be considered by scientists and emergency responders to preserve lives and property.  Mt. Pinatubos eruption was forecast in 1991, so it gave geologists time to warn the people, who made their homes in and around the volcano, to evacuate.  Over 5,000 lives were saved by scientists' ability to predict the eruption along with the preservation of a quarter-billion dollars in property.  Air traffic was diverted around the Philippines so as to avert air crash disasters.  The second largest modern day volcanic eruption had its day of destruction yet was not as catastrophically destructive as it might have been.

why did hughes title the story, thank you maam?

A grateful and now respectful Roger wants to say more than his mere "thank you" to Mrs. Luella Bates Washington Jones as she closes the door after taking him to her home and feeding him, but he does not have time. This phrase of "thank you m'am" is used by Langston Hughes as the title, perhaps, because it expresses the gratitude Roger feels toward this kind and generous woman who has effected a change in...

A grateful and now respectful Roger wants to say more than his mere "thank you" to Mrs. Luella Bates Washington Jones as she closes the door after taking him to her home and feeding him, but he does not have time. This phrase of "thank you m'am" is used by Langston Hughes as the title, perhaps, because it expresses the gratitude Roger feels toward this kind and generous woman who has effected a change in him.

After all, it is thanks to Mrs. Jones that Roger has not been arrested for stealing her purse; it is thanks to her that he has cleaned his face and had a hot meal. And it is thanks to her that Roger has been taught how wrong it is to steal from others as he is reprimanded physically and verbally by Mrs. Jones. Roger has felt the love of a woman with a large heart who has recognized a neglected boy in need of love and direction. The generous Mrs. Jones has given all these things to Roger. As she sends Roger on his way, he turns to thank her for her kindness and for disciplining him. But he feels awkward and embarrassed in his shame for his earlier actions toward this big-hearted woman. 

The boy wanted to say something else other than “Thank you, m’am” to Mrs. Luella Bates Washington Jones, but he couldn’t do so as he turned at the barren stoop and looked back at the large woman in the door.

As Roger departs, the reader has the sense that Mrs. Jones has brought about a change in this young man.

In "Thank You, M'am," where do you see a turning point for Roger in terms of his character?

There are two turning points for Roger's character in "Thank You, M'am." The first is where Roger chooses to stay with Mrs. Jones and wash his face as told to do: "Roger looked at the door—looked at the woman—looked at the door—and went to the sink." The second turning point provides the resolution of the story where, when Mrs. Jones and he are both overcome with emotion, he can manage only to say "Thank...

There are two turning points for Roger's character in "Thank You, M'am." The first is where Roger chooses to stay with Mrs. Jones and wash his face as told to do: "Roger looked at the door—looked at the woman—looked at the door—and went to the sink." The second turning point provides the resolution of the story where, when Mrs. Jones and he are both overcome with emotion, he can manage only to say "Thank you" as she ushers him out onto her "barren stoop" and the street.

"Good-night! Behave yourself, boy!" she said, looking out into the street.

The boy wanted to say something else other than "Thank you, m’am" to Mrs. Luella Bates Washington Jones, but he couldn’t do so as he turned at the barren stoop and looked back at the large woman in the door.

At the first turning point for Roger's character, Roger rejects running out the open door and instead chooses trusting Mrs. Jones and accepting her offer to share her meal with him. He turns from petty theft and fear and toward Mrs. Jones's compassion and care. It's as though he is thinking—or feeling—that he wishes he were her son and that she would teach him "right from wrong" and that she would make sure he had a clean face and meals to eat.

He looked as if he were fourteen or fifteen, frail and willow-wild, in tennis shoes and blue jeans.

The woman said, "You ought to be my son. I would teach you right from wrong. Least I can do right now is to wash your face. Are you hungry?"

At the second turning point for Roger's character—following their supper during which Mrs. Jones tells him about her job in the late-night "hotel beauty-shop" and during which she says, "Eat some more, son"—Roger comes to understand the meaning of Mrs. Jones's remark that he could have asked her for those "blue suede shoes" instead of snatching her "pocketbook." Puzzled at first ("M'am?"), he comes to learn about understanding, generosity, and compassion when she gives from the little she has. Because Mrs. Jones hands him ten dollars for "some blue suede shoes," he wants to say something heartfelt and grateful, but all he can manage is a quiet "Thank you." He turns from feeling alone and turns to feeling like part of a shared life.

"Now, here, take this ten dollars and buy yourself some blue suede shoes. And next time, do not make the mistake of latching onto my pocketbook nor nobody else’s—"

What is the full quotation about "bad mother" in Hamlet?

Your question apparently refers to the exchange between Hamlet and his mother in Act III, Scene 4, right after Hamlet kills Polonius, who was hiding behind the arras. Gertrude is horrified. She says,

O, what a rash and bloody deed is this!

Hamlet responds,

A bloody deed. Almost as bad, good mother,As kill a king, and marry with his brother.

Hamlet is testing Gertrude. He wants to see how she reacts, whether she will give...

Your question apparently refers to the exchange between Hamlet and his mother in Act III, Scene 4, right after Hamlet kills Polonius, who was hiding behind the arras. Gertrude is horrified. She says,

O, what a rash and bloody deed is this!

Hamlet responds,

A bloody deed. Almost as bad, good mother,
As kill a king, and marry with his brother.

Hamlet is testing Gertrude. He wants to see how she reacts, whether she will give herself away with a guilty expression or even confess. He still suspects she was somehow involved in his father's murder. She may not have been an accomplice, but she may have known either that Claudius intended to commit the crime or else have known he was guilty of committing the crime after her husband's dead body was discovered in the garden. Gertrude's reaction seems to indicate she is innocent of any kind of complicity in the murder. She simply asks,

As kill a king?

Gertrude doesn't understand. She still believes her son is insane. Her further utterances suggest she is innocent of any wrongdoing except for marrying Claudius without observing a decent period of mourning for her dead husband and perhaps for what Hamlet considers an incestuous marriage. Here are two examples of her dialogue which suggest her innocence of any complicity in her late husband's death:

What have I done, that thou darest wag thy tongue
In noise so rude against me?

Ay me, what act,
That roars so loud and thunders in the index?

Hamlet must be convinced. Throughout the scene, he focuses on his mother's guilt in marrying an inferior man like Claudius and doing it so precipitously. He reduces his mother to tears. He will not attempt to convince her that Claudius killed her former husband, and he does not attempt to get her to conspire with him against Claudius. She will remain loyal to her new husband, as shown when Laertes storms into the castle at the head of a mob in Act IV, Scene 5 and threatens to start a rebellion. She will keep Hamlet's secret that he is not mad, though, and it is possible that she keeps her promise not to engage in any more lovemaking with Claudius.

How is sexual orientation a continuum?

Sexual orientation can be viewed as a continuum because people's preferences can lie on a continuous spectrum between exclusively heterosexual and exclusively homosexual. Understanding sexuality as a continuum is useful because it acknowledges that people can experience attraction to different genders in varying amounts, and allows for the fluidity of sexuality that some people can experience. Fluidity of sexuality refers to the concept that people's attraction to certain genders can fluctuate throughout their lifetimes based...

Sexual orientation can be viewed as a continuum because people's preferences can lie on a continuous spectrum between exclusively heterosexual and exclusively homosexual. Understanding sexuality as a continuum is useful because it acknowledges that people can experience attraction to different genders in varying amounts, and allows for the fluidity of sexuality that some people can experience. Fluidity of sexuality refers to the concept that people's attraction to certain genders can fluctuate throughout their lifetimes based on changing feelings or circumstances.

Alfred Kinsey's studies of sexuality were significant in developing this concept because Kinsey acknowledged that bisexual people could be attracted to different genders to varying degrees. The Kinsey scale is an example of a sexual continuum; it ranks people's level of attraction to different genders by asking them to assess themselves on a scale from 0 to 6, with 0 being exclusively heterosexual and 6 being exclusively homosexual. Scholars have added more nuance and room for fluidity to Kinsey's scale since his studies in the 1940s, but his work was formative to the modern understanding of sexuality as a continuum.

How did Jefferson and Hamilton's ideas influence government policy?

Jefferson and Hamilton each had competing visions of what they wanted the United States to be. Jefferson's ideal was of a republic with weak Federal government (in domestic but not foreign affairs). The new nation would be based upon a largely agrarian economy. Jefferson, as a gentleman farmer himself, not surprisingly came to champion rural economic interests against a rising tide of commercial and industrial expansion.

But his passionate commitment to this ideal wasn't simply self-interested; it was also deeply principled. Jefferson believed that landowners such as himself formed the bedrock of any successful system of republican government. Those who owned land had a greater, deeper connection to the soil; this meant, among other things, that their economic interests were more stable than those of merchants and businessmen. As landowners had more of a stake in society, they would be the ones relied upon to exercise the limited powers of government wisely, instead of sacrificing the common good for their own narrow self-interest.

The best way of preserving this republican ideal was by strongly supporting states' rights. The republican spirit was born out of a war against what the Founding Fathers regarded as the tyranny of the British. The last thing Jefferson wanted to see was the establishment of a remote, centralized government of the United States, essentially re-constituting the spirit of British rule on American soil.

Hamilton's vision was almost diametrically opposite to Jefferson's. He saw America's future as a commercial, trading nation, opening itself up to the world's markets. He wanted the establishment of what we would today call a capitalist economy. Hamilton, unlike Jefferson, was a firm advocate of merchants' and financiers' interests. This strongly influenced his views on the function of central government.

In order for the United States to become the economic powerhouse he envisaged, it was necessary, thought Hamilton, for the power of the Federal government to become more powerful, more centralized. Hamilton advocated the establishment of a Federal Bank that would provide much-needed credit to the growing commercial and mercantile sectors of the economy as well as redeeming debt. This would ensure, it was believed, that the United States would become a trusted trade and business partner in the international marketplace. Centralization of government was a necessary condition of America's future prosperity.

These competing conceptions clashed in Jefferson's and Hamilton's radically different ideas of constitutional interpretation. As a strict constructionist, Jefferson vehemently opposed the establishment of a Federal Bank, not just because it could damage rural interests, but also because it wasn't expressly authorized by the Constitution.

Hamilton's approach was more flexible. By contrast to Jefferson, he saw the Constitution as giving implied authority to Congress to put into action powers that were indeed explicitly granted by the Constitution, such as the power of government to raise taxes and borrow money.

The differences between these two giants of American history have lived on ever since. We can see, for example, how the respective positions of the Union and Confederacy of the Civil War were greatly influenced by Hamilton and Jefferson. Hamilton's vision lives on today in the shape of the world's largest economy and sole remaining superpower, in which the power of Federal government has expanded beyond anything anyone in Hamilton's era could possibly have envisaged.

However, the spirit of Jefferson and his radical republicanism is far from dead. So long as Federal government continues its seemingly never-ending expansion there will be those who will evoke Jeffersonian principles in recalling Americans back to the principles on which their republic was built.

What is Eckles's reaction to the Tyrannosaurus?

While Eckels initially brushes off the idea that the Tyrannosaurus rex could panic him, when he sees it in all its huge immensity, he is badly frightened. It is so tall he thinks it could eat the moon. He believes it will be impossible to shoot and kill it. His rifle suddenly seems like a toy cap gun. He tells the others they were all fools to come. When the creature lunges at them at...

While Eckels initially brushes off the idea that the Tyrannosaurus rex could panic him, when he sees it in all its huge immensity, he is badly frightened. It is so tall he thinks it could eat the moon. He believes it will be impossible to shoot and kill it. His rifle suddenly seems like a toy cap gun. He tells the others they were all fools to come. When the creature lunges at them at high speed with a terrible scream, Eckel goes numb with panic. He fears dying, so he does what he was strictly forbidden to do: unable to think clearly, he steps off the path and heads, "not knowing it," into the prehistoric jungle to get away from the dinosaur. This moment of benumbed fright has dire consequences for human history, as it changes the future. 

In City of Bones by Cassandra Clare, what rune does Clary Fray draw, indicating that her sight is returning?

This question makes an assumption that Clary’s returning Sight is attached to a rune, when in fact her Sight (capitalized to indicate the ability to see demons and cloaked Shadowhunters) is a natural part of her. Since she'd been a child, Clary’s mother had been hiring the warlock Magnus Bane to suppress Clary’s Sight; however, the spell tended to wear off every two years and need to be renewed. Clary discovers her regained ability right...

This question makes an assumption that Clary’s returning Sight is attached to a rune, when in fact her Sight (capitalized to indicate the ability to see demons and cloaked Shadowhunters) is a natural part of her. Since she'd been a child, Clary’s mother had been hiring the warlock Magnus Bane to suppress Clary’s Sight; however, the spell tended to wear off every two years and need to be renewed. Clary discovers her regained ability right in chapter one when she confronts Jace Wayland for bumping into her and ends up witnessing the destruction of her first demon.

Traditionally, the first rune a Shadowhunter receives is the “Voyance” rune, which either awakens or strengthens the Shadowhunter’s ability to See demons. But Clary Sees just fine without it.

In fact, the first rune that Clary receives is a “Hiding” rune, drawn on her wrist by Jace during a fight with Raveners in chapter four. The fact that the rune on her skin doesn’t burn her or drive her insane is proof, or at least a strong indication, that Clary has Shadowhunter blood.

Clary doesn’t actually draw her first rune until late in the book. Jace is imprisoned by the Inquisitor and, with Alec’s help, Clary launches a rescue. She uses the “Open” rune to blow the cell door off its hinges.

How does Swift use irony in Gulliver's Travels?

Irony occurs when there is some discrepancy between what we expect and what the reality is. We do not really expect Gulliver to end up in locations where human beings are so very different, physically, than the way we are or he is.  First, he arrives in Lilliput, where the humans are only about six inches tall. Then he gets stranded on Brobdingnag, where he is dwarfed by the natives' giant size. Ultimately, he travels...

Irony occurs when there is some discrepancy between what we expect and what the reality is. We do not really expect Gulliver to end up in locations where human beings are so very different, physically, than the way we are or he is.  First, he arrives in Lilliput, where the humans are only about six inches tall. Then he gets stranded on Brobdingnag, where he is dwarfed by the natives' giant size. Ultimately, he travels to Houyhnhmland, where horses are civilized and run the society, and humanlike creatures are called Yahoos. They are totally uncivilized and used like livestock by the Houyhnhnms. We would certainly be unlikely to expect to see a society where the horses are in charge and use people like we use horses.

Further, Swift employs irony in Gulliver's third voyage to Lagado. There, he sees scholars and intellectuals working on such experiments as trying to extract sunshine from a cucumber or reanimate a dead dog by placing a bellows in his anus and pumping him full of air. We would hardly expect to see such absolutely ridiculous experiments being conducted by people who are like the most highly educated, the most intelligent among us.

In the end, Gulliver decides that the Houyhnhnms really are the master race, agreeing with them about the dirtiness and stupidity of humans. When he returns home, he cannot stand the smell of his wife and children, and he generally finds everyone he once thought so wonderful absolutely disgusting. After Gulliver has spent so long defending his home country, customs, and government to so many individuals, against so much criticism, we would not expect him to turn on his countrymen and women the way he does. This, too, is ironic.

Why was the audience at the final oratorical competition stunned by Stargirl's performance? How do you know they approved?

Susan (Stargirl) was one of the last finalists to speak at the final oratorical competition. The audience was stunned by Stargirl's performance because it was so unlike that of the typical teenage orator.

First, Stargirl began her speech by executing a pirouette, curtsying, and waving to the audience. This was highly unusual; most contestants were nervous and behaved accordingly. Then, Stargirl began her oratorical speech in a similarly informal way. She chatted, instead of giving...

Susan (Stargirl) was one of the last finalists to speak at the final oratorical competition. The audience was stunned by Stargirl's performance because it was so unlike that of the typical teenage orator.

First, Stargirl began her speech by executing a pirouette, curtsying, and waving to the audience. This was highly unusual; most contestants were nervous and behaved accordingly. Then, Stargirl began her oratorical speech in a similarly informal way. She chatted, instead of giving a formal opening statement. 

Stargirl proceeded with the rest of her speech in the same vein. Towards the end of her speech, she dropped her voice to a whisper. The audience strained to hear her last words. Cleverly, Stargirl concluded her speech with ten seconds of pure silence before returning abruptly to her seat. The audience members were so impressed with Stargirl's unconventional performance that they rose to their feet shouting, clapping, and whistling. Their exuberant response shows that they clearly approved of Stargirl's performance.

Can I have a detailed analysis (tone, themes, language, imagery, and style) of the poem "Requiem" by Robert Louis Stevenson?

Tone

I would say that the poet's tone is accepting and even reflective. The poet is glad he lived, but he's ready to die. He's rather philosophical about his death. Dying isn't a morbid subject for him, and he voices no fear of it. He readily asks for a grave to be dug for him, and he assures his listener that he already has a will written out. In other words, he's put his house in order, and he's ready to leave the world of the living.

Themes

The main themes of this poem are the inevitability of death and death as a respite at the end of an eventful life. In the poem, the poet calls the grave a "home" for seafaring sailor and roaming hunter alike. The last lines of the poem imply that the grave willingly accepts all who choose to lie in it.

Language

The poet uses alliteration (starry sky) to make a strange request: he wants his grave to be dug under the night sky. He doesn't say why; perhaps he feels that his request is appropriate because he will soon be enveloped in darkness in the grave.

In the poem, the rhyme scheme is aaab cccb; the poem is written in two quatrains.

Under/ the wide/ and star/ry sky/

Dig the/ grave and/ let me/ lie:

Glad did/ I live/ and glad/ly die,

And I laid/ me down with/ a will.

The above is the first stanza, and it is an interesting one. We have four poetic feet in the first three lines, so this would make the lines tetrameters. The last line has three feet, so this would make it a trimeter. The tetrameters appear to be a mixture of trochaic (accented followed with unaccented words) and iambic (unaccented followed with accented words). Meanwhile, the trimeter or last line can be said to be anapestic (unaccented/unaccented/accented) with iambic (unaccented/accented) thrown in towards the end. The second stanza is similarly structured.

In the last stanza, the poet uses repetition (through the word "home") to reinforce the idea of the grave as his final resting place.

Imagery

In this poem, the "wide and starry sky" imagery alerts us to a sense of freedom and space. The poet wants to be buried under this wide expanse; under the sky, his grave will be his "home." He will be free from all responsibilities and earthly burdens.

Style

As mentioned, the poem consists of two quatrains. It is rustic in style. In the last stanza, the poet characterizes himself as a sailor "home from the sea" and a hunter "home from the hill." He has traveled far and worked hard; it is time for the last stage of his life: death. To understand all that style encompasses in poetry, please refer to

Where does Ichabod Crane live? Why does he need to be able to have all of his belongings in a small bundle?

Ichabod Crane, a school teacher in the fictional town of Sleepy Hollow, is the main character in the short story "The Legend of Sleepy Hollow" by Washington Irving. In the short story, Irving describes Crane as being a "huge feeder," meaning he has a big appetite. Since his job as a teacher does not pay well and is barely enough to provide him with enough food for the day, he does not have a...

Ichabod Crane, a school teacher in the fictional town of Sleepy Hollow, is the main character in the short story "The Legend of Sleepy Hollow" by Washington Irving. In the short story, Irving describes Crane as being a "huge feeder," meaning he has a big appetite. Since his job as a teacher does not pay well and is barely enough to provide him with enough food for the day, he does not have a permanent residence. Instead, Ichabod lodges at various farmers' houses. These farmers are the families of the students Ichabod instructs at his schoolhouse. Each week, Ichabod packs up his belongings and lodges at a different farmer's home. Due to the fact that Ichabod must move around so frequently, he must keep his belongings small enough to tie up in a "cotton handkerchief" so he can move on to the next place. 

According to Nat, what is odd about winter so far this year? What do you think the description of the cold and black ground early in the story...

In the opening paragraphs of "The Birds," Nat notices that the winter is so far quite different than that of previous years. The birds are more "restless," for example, and appear to be unsatisfied, even when they feed. In addition, there are more birds than usual, a fact which is supported by the observations of the farmer, Mr Trigg.

After the attack on Nat's house, Du Maurier describes the cold ground and how it has...

In the opening paragraphs of "The Birds," Nat notices that the winter is so far quite different than that of previous years. The birds are more "restless," for example, and appear to be unsatisfied, even when they feed. In addition, there are more birds than usual, a fact which is supported by the observations of the farmer, Mr Trigg.

After the attack on Nat's house, Du Maurier describes the cold ground and how it has the "hard, black look of frost." This, perhaps, foreshadows Nat's attempt to bury the dead birds which have attacked his family. The ground is too hard to dig, however, and Nat is forced to take the birds to the beach. While he is there, he sees the gulls riding the waves and realises that the birds will return to attack his home. He must now take action to safeguard his home so that his family is protected. 

Did the painting of murals in US Post office pose controversy during the Great Depression?

The Great Depression was the worst economic disaster of the 20th century. In an effort to inject money into the economy, President Franklin Delano Roosevelt created the New Deal. This economic recovery plan created a variety of jobs across the nation. For the most part, the jobs generated much needed income for millions of American workers without any controversy. Occasionally, however, controversy did occur.

The massive building projects of the New Deal included construction of...

The Great Depression was the worst economic disaster of the 20th century. In an effort to inject money into the economy, President Franklin Delano Roosevelt created the New Deal. This economic recovery plan created a variety of jobs across the nation. For the most part, the jobs generated much needed income for millions of American workers without any controversy. Occasionally, however, controversy did occur.

The massive building projects of the New Deal included construction of new postal facilities in thousands of cities and towns across the country. Artists were commissioned to paint 12' by 5' murals on the walls of these newly constructed buildings. These murals were to depict day to day life in the area served by the local post office in a traditional Americana setting.

Often, the artists hired to paint these murals came from out of state. This led to distrust among the local population of these outsiders. Sensitivities were particularly high in regard to stereotyping the local population, especially in the rural south. In places like my home state of Arkansas, where residents had long been represented as backwards and illiterate by most of the rest of the nation, the murals were subject to significant criticism. 

No region wants to have less attractive portions of its culture permanently on display as a constant reminder of those shortcomings. As a result, an unintentional controversy did ensue over the painting of murals on U.S. Postal Facilities during the Great Depression.

What is the point of view of the story of "The Lottery"?

The point of view of "The Lottery" is the third person point of view.  

A third person point of view places the narrator outside of the events happening in the story.  The narrator obviously knows characters and things that are happening, but a third person narrator means that the story's narrator is not a character within the story.  More specifically, the narrator of "The Lottery" is narrating from the third person objective point of...

The point of view of "The Lottery" is the third person point of view.  

A third person point of view places the narrator outside of the events happening in the story.  The narrator obviously knows characters and things that are happening, but a third person narrator means that the story's narrator is not a character within the story.  More specifically, the narrator of "The Lottery" is narrating from the third person objective point of view.  This allows the narrator to jump from person to person and group to group.  Readers are allowed to listen in on various conversations as if we are eavesdropping on everybody.  

The fact that the narrator is only capable of eavesdropping on people is why this story's point of view is third person objective and not third person omniscient.  An omniscient narrator is privy to the internal thoughts of characters, and the narrator of "The Lottery" never indicates that knowledge. That's a good thing for this story too.  If readers knew the thoughts of the characters, the final shocking moments of the story wouldn't be as shocking.  

One natural effect of the third person narration is that readers feel a bit of distance from the events happening in the story.  We feel invested to a certain extent, but we also know that the events (good or bad) are always happening to somebody else.  That distance is important for this story.  While readers are appalled at the realistic feel of the lottery, we can at least take comfort that the people are not our personal friends.  It's not my town's tradition.  It's their town's tradition.  I've often wondered what this story might be like from the first person perspective.  I don't think the ending would be as shocking, because a character narrator would likely give away his/her apprehension about the lottery system.  

`int (3-x) / (3x^2-2x-1) dx` Use partial fractions to find the indefinite integral

`int(3-x)/(3x^2-2x-1)dx`

Let's use partial fraction decomposition on the integrand,

`(3-x)/(3x^2-2x-1)=(3-x)/(3x^2+x-3x-1)`

`=(3-x)/(x(3x+1)-1(3x+1))`

`=(3-x)/((3x+1)(x-1))`

Now form the partial fractions using the denominator,

`(3-x)/((3x+1)(x-1))=A/(3x+1)+B/(x-1)`

Multiply equation by the denominator `(3x+1)(x-1)`

`=>(3-x)=A(x-1)+B(3x+1)`

`=>3-x=Ax-A+3Bx+B`

`=>3-x=(A+3B)x+(-A+B)`

comparing the coefficients of the like terms,

`A+3B=-1`   ----------------(1)

`-A+B=3`      ----------------(2)

Now let's solve the above equations to get A and B,

Add the equations 1 and 2,

`4B=-1+3`

`4B=2`

`B=2/4`

`B=1/2`

Plug in the value of B in equation 1,

`A+3(1/2)=-1`

`A+3/2=-1`

`A=-1-3/2`

...

`int(3-x)/(3x^2-2x-1)dx`

Let's use partial fraction decomposition on the integrand,

`(3-x)/(3x^2-2x-1)=(3-x)/(3x^2+x-3x-1)`

`=(3-x)/(x(3x+1)-1(3x+1))`

`=(3-x)/((3x+1)(x-1))`

Now form the partial fractions using the denominator,

`(3-x)/((3x+1)(x-1))=A/(3x+1)+B/(x-1)`

Multiply equation by the denominator `(3x+1)(x-1)`

`=>(3-x)=A(x-1)+B(3x+1)`

`=>3-x=Ax-A+3Bx+B`

`=>3-x=(A+3B)x+(-A+B)`

comparing the coefficients of the like terms,

`A+3B=-1`   ----------------(1)

`-A+B=3`      ----------------(2)

Now let's solve the above equations to get A and B,

Add the equations 1 and 2,

`4B=-1+3`

`4B=2`

`B=2/4`

`B=1/2`

Plug in the value of B in equation 1,

`A+3(1/2)=-1`

`A+3/2=-1`

`A=-1-3/2`

`A=-5/2`

Plug in the value of A and B in the partial fraction template,

`=(-5/2)/(3x+1)+(1/2)/(x-1)`

`=-5/(2(3x+1))+1/(2(x-1))`

So, `int(3-x)/(3x^2-2x-1)dx=int(-5/(2(3x+1))+1/(2(x-1)))dx`

Apply the sum rule,

`=int-5/(2(3x+1))dx+int1/(2(x-1))dx`

Take the constant out,

`=-5/2int1/(3x+1)dx+1/2int1/(x-1)dx`

Now let's evaluate both the above integrals separately,

`int1/(3x+1)dx`

Apply integral substitution:`u=3x+1`

`=>du=3dx`

`=int1/u(du)/3`

Take the constant out,

`=1/3int1/udu`

Use the common integral:`int1/xdx=ln|x|`

`=1/3ln|u|`

Substitute back `u=3x+1`

`=1/3ln|3x+1|`

Now evaluate the second integral.

`int1/(x-1)dx`

Apply integral substitution: `u=x-1`

`du=1dx`

`=int1/udu`

Use the common integral:`int1/xdx=ln|x|`

`=ln|u|`

Substitute back `u=x-1`

`=ln|x-1|`

`int(3-x)/(3x^2-2x-1)dx=-5/2(1/3ln|3x+1|)+1/2ln|x-1|` 

Simplify and add a constant C to the solution,

`=-5/6ln|3x+1|+1/2ln|x-1|+C`

Who is the speaker of the italicized portions in Gary D. Schmidt's novel Trouble?

Multiple chapters of Gary D. Schmidt's novel Trouble end with paragraphs written in italics. The speaker in those italicized portions is still the same third-person-limited narrator relaying the whole story; however, the narrator's focus switches in those sections from Henry to Chay Chouan.Like all third-person narrators, a third-person-limited narrator is not a character of the story and instead relays the story as an observer, using third-person pronouns such as he and she. However,...

Multiple chapters of Gary D. Schmidt's novel Trouble end with paragraphs written in italics. The speaker in those italicized portions is still the same third-person-limited narrator relaying the whole story; however, the narrator's focus switches in those sections from Henry to Chay Chouan.

Like all third-person narrators, a third-person-limited narrator is not a character of the story and instead relays the story as an observer, using third-person pronouns such as he and she. However, whereas a third-person omniscient narrator will get into the heads of every single character in the story, a third-person limited narrator will only focus on getting inside the head of one character. In Schmidt's story, the narrator focuses on getting inside Henry Smith's head. We can tell because Henry is the focus of every single scene; plus, the narrator relays only the thoughts and feelings of Henry through the narration. Numerous examples can be found throughout the book, but one example of the narrator relaying Henry's thoughts and feelings in the narrative text can be found at the end of Chapter 12, after Henry has had his first meal with his brother's killer:

He looked across at Chay. Who had murdered his brother, Franklin. And he felt anger rise in him and sour the chowder in his stomach. (p. 165)

In contrast, if we learn the thoughts and feelings of other characters, it is because they speak them aloud.

However, in the italicized parts, the narrator relays the thoughts and feelings of Chay, which we can also tell at the end of Chapter 12 when the speaker reflects, "But why would anyone eat a chowder?," immediately after Chay had refused to order clam chowder in the chowder house. Through these italicized parts, we learn multiple details about Chay's backstory such as what happened to his pet dog and why, that there was a girl with him in the truck when he accidentally hit Franklin, and that Chay was the one who set on fire the boarding house owned by Chay's own father.

How did the Battle of Bunker Hill affect American history?

The Battle of Bunker Hill in 1775 ended in defeat for the American Revolutionary forces. Yet, in time, it came to take on the appearance of a Pyrrhic victory for the British. Despite losing the battle, the Americans were nonetheless able to inflict quite serious losses upon the British. Strategically, Bunker Hill was undoubtedly a setback for the colonists, but it showed that their method of fighting could potentially cause huge damage to British troops...

The Battle of Bunker Hill in 1775 ended in defeat for the American Revolutionary forces. Yet, in time, it came to take on the appearance of a Pyrrhic victory for the British. Despite losing the battle, the Americans were nonetheless able to inflict quite serious losses upon the British. Strategically, Bunker Hill was undoubtedly a setback for the colonists, but it showed that their method of fighting could potentially cause huge damage to British troops and their morale. The mood of the British in the aftermath of the battle was succinctly summed up by one of their generals named Henry Clinton:

A few more such victories would have shortly put an end to British dominion in America.

It was now abundantly clear to both sides that the war would be long, bloody, and hard. The British soldiers were paid to fight and had no connection with this strange and distant land. The Americans, however, were fighting on home soil for a cause in which they passionately believed. Nearly two decades before the French Revolutionary Army achieved a stunning victory at Valmy, the Americans had already harnessed the power of revolutionary fervor in the heat of battle. They were not successful this time, but the genie of revolutionary consciousness was now out of the bottle. There was very little that the British could do to put it back in again.

One of the twins happily asks John if Linda is dead. What does John do to the child?

After a date with Lenina that ends with John shoving her and forcing her to hide in a bathroom, John is notified by phone that his mother has overdosed on soma. Soma is a drug that people take every day, as encouraged by the World Controllers. This tragedy marks the end of Linda and John's enjoyment of the decadent world they find themselves in. When John arrives at the hospital, he is horrified to find...

After a date with Lenina that ends with John shoving her and forcing her to hide in a bathroom, John is notified by phone that his mother has overdosed on soma. Soma is a drug that people take every day, as encouraged by the World Controllers. This tragedy marks the end of Linda and John's enjoyment of the decadent world they find themselves in. When John arrives at the hospital, he is horrified to find his mother in a soma-stupor. It becomes clear that she is dying and he collapses to grieve at her bedside, recalling his childhood memories of her. This visceral reaction causes the nurses in the ward to believe that John has gone mad and worry that he will disturb a group of Delta twins who are there on a death tour. The children observe John's grief with distant curiosity before coming into the room to disturb him.

As John continues to cry over his mother's near-lifeless body, the children crowd around him to observe her death as if it is a spectacle for their entertainment. John is repulsed by the fact that they are eating eclairs, seemingly unaffected by the death and suffering that surrounds them. This is, in fact, the purpose of the death training that is used to condition the fear of death out of all citizens from a young age. One of the twins remarks that he thinks Linda is fat, which offends an already unstable John. Adding to his anger, Linda talks about Popé in her sleep. When one of the twins casually asks, "Is she dead?" after Linda has been silent for a while, John shoves him to the ground in a violent display that further shocks everyone in the ward. John's reaction is the result of all the anger that began accumulating on his date with Lenina. In a literary sense, it is the culmination of his growing distaste for society and its decadence as well as the apathy it instills. The child is merely a scapegoat for John's disgust with society in general, a construct he feels powerless to overcome.

What is the point of view of the story "Miss Brill?

The story "Miss Brill" is narrated from a third person omniscient point of view. 

This point of view consists on a narrator who detaches emotionally and personally from the story. This way, the narrator is capable of telling facts and events from a number of different perspectives, without affecting the action. 

Just because a story is being told from a third person omniscient point of view does not mean that the narrator does not expose the innermost feelings of the main character. 

In the story "Miss Brill', it is evident that the narrator is quite aware of her emotions. From the choice of words, the narrator creates a tone in the narrative that elicits moods of loneliness, longing, and sadness. 

The main character, who is a lonely, aging expatriate living in Paris as an English teacher, depends on her Sunday afternoons in the park to make her life more livable. She does this by going people-watching, and by creating scenarios in her mind using the people that she sees.

She also seems to display an uncanny amount of affection toward an old necklet in the likeness of a fox, which she speaks to as if it were a living thing. She calls it her "little rogue", and she feels as if this piece of clothing is an actual companion. Keep in mind, that she does not do this the way someone with a mental illness would; she does not directly engage in discourse with this inanimate object. She simply pretends that it is more than just a necklet, and so she carries on this way. 

The author is able to describe the emotions that run deep within Miss Brill. On this particular day, something ominous is present in the air, which makes her feel strange, and out of the ordinary. Mansfield describes the emotion as 

a the chill from a glass of iced water before you sip.

Moreover, Mansfield enters the psyche of Miss Brill, and tells the audience everything that she is thinking of during her people-watching experiment. We learn that Miss Brill feels, for a rare time, as if she were an actual part of the world; a world created in her imagination. In this world of hers, the people in the park are actually actors in a play, and Miss Brill is in it. So emotional is Miss Brill at this prospect, that she even cries of joy. 

All of these feelings are entirely personal to Miss Brill, but the third person omniscient narrator is able to know them and relate them to the reader. 

Therefore, while the narrator speaks in third person, detached, and with objectivity, it is still possible to see inside the mind of Miss Brill and learn everything that she is going through. This is an effective narrative technique because it allows us to make our own conclusions since the narrator is neither condemning, nor condoning the actions of the main character, which may lead to bias. 

What best describes the political divide between North and South during the Election of 1860?

The political divide between the North and the South in the election of 1860 can best be described by looking at the issue of slavery. In the election of 1860, the Democratic Party split over the issue of slavery. The Northern Democrats nominated Stephen Douglas. Because of the stance Douglas took regarding slavery in the Lincoln-Douglas debates in 1858, the Southern Democrats couldn’t support his nomination. The Southern Democrats believed Douglas wanted to end slavery...

The political divide between the North and the South in the election of 1860 can best be described by looking at the issue of slavery. In the election of 1860, the Democratic Party split over the issue of slavery. The Northern Democrats nominated Stephen Douglas. Because of the stance Douglas took regarding slavery in the Lincoln-Douglas debates in 1858, the Southern Democrats couldn’t support his nomination. The Southern Democrats believed Douglas wanted to end slavery based on his comments in those debates. Therefore, the Southern Democrats nominated John C. Breckinridge as their candidate.

The Republicans nominated Abraham Lincoln as their candidate. While Lincoln was against slavery, he wasn’t prepared to end it where it already existed. In the election of 1860, Lincoln won. However, he didn’t win any southern states. Slavery clearly exemplified the political divide that existed between the North and the South in the election of 1860.

I just need help. How did Alice Walker bring heritage awareness in the short story?

Alice Walker increases our awareness of the concept of heritage by juxtaposing Dee's idea of heritage with Mama and Maggie's.

For Mama and Maggie, heritage is something alive, something present. It is using the butter churn with pieces whittled by uncles; it's sitting on the benches dad made that have "rump prints" from years and years of use; it's using the quilts made by aunts and grandmothers; most of all, it's knowing the stories of...

Alice Walker increases our awareness of the concept of heritage by juxtaposing Dee's idea of heritage with Mama and Maggie's.

For Mama and Maggie, heritage is something alive, something present. It is using the butter churn with pieces whittled by uncles; it's sitting on the benches dad made that have "rump prints" from years and years of use; it's using the quilts made by aunts and grandmothers; most of all, it's knowing the stories of all of these people and keeping them alive through the use of these items.

For Dee, on the other hand, heritage is something you hang on the wall; it's something distant and past, something to be preserved and not used.

When Mama tells Dee that she has promised the quilts to Maggie, Dee is horrified because she thinks Maggie will be "backward" and put them to "everyday use." Mama doesn't understand why Dee would hang a quilt on the wall or why she would insult Maggie for using what was made to be a blanket as a blanket. The conflict here comes from the fact that Dee has a very different, somewhat shallow, idea of what heritage is and means.

`lim_(x->oo) x^3/e^(x/2)` Evaluate the limit, using L’Hôpital’s Rule if necessary.

Given to solve,

`lim_(x->oo) x^3/(e^(x/2))`

as `x->oo` then the `x^3/(e^(x/2))=oo/oo` form

so upon applying the L 'Hopital rule we get the solution as follows,

as for the general equation it is as follows

`lim_(x->a) f(x)/g(x) is = 0/0` or `(+-oo)/(+-oo)` then by using the L'Hopital Rule we get  the solution with the  below form.

`lim_(x->a) (f'(x))/(g'(x))`

so , now evaluating

`lim_(x->oo) (x^3)/(e^(x/2))`

=`lim_(x->oo) ((x^3)')/((e^(x/2))')`

= `lim_(x->oo) (3x^2)/((e^(x/2))(1/2))`

again `(3x^2)/((e^(x/2))(1/2))` is of the form `oo/oo`...

Given to solve,

`lim_(x->oo) x^3/(e^(x/2))`

as `x->oo` then the `x^3/(e^(x/2))=oo/oo` form

so upon applying the L 'Hopital rule we get the solution as follows,

as for the general equation it is as follows

`lim_(x->a) f(x)/g(x) is = 0/0` or `(+-oo)/(+-oo)` then by using the L'Hopital Rule we get  the solution with the  below form.

`lim_(x->a) (f'(x))/(g'(x))`

so , now evaluating

`lim_(x->oo) (x^3)/(e^(x/2))`

=`lim_(x->oo) ((x^3)')/((e^(x/2))')`

= `lim_(x->oo) (3x^2)/((e^(x/2))(1/2))`

again `(3x^2)/((e^(x/2))(1/2))` is of the form `oo/oo` so , applying the L'Hopital Rule we get

= `lim_(x->oo) (3x^2)/((e^(x/2))(1/2))`

= `lim_(x->oo) ((3x^2)')/(((e^(x/2))(1/2))')`

=`lim_(x->oo) ((6x))/(((e^(x/2))(1/2)(1/2)))`

=`lim_(x->oo) ((6x))/(((e^(x/2))(1/4)))`

again `((6x))/(((e^(x/2))(1/4))) ` is of the form `oo/oo` so , applying the L'Hopital Rule we get

=`lim_(x->oo) ((6x))/(((e^(x/2))(1/4)))`

=`lim_(x->oo) ((6x)')/(((e^(x/2))(1/4))')`

=`lim_(x->oo) ((6))/(((e^(x/2))(1/4)(1/2)))`

=`lim_(x->oo) ((6))/(((e^(x/2))(1/8)))`

=`lim_(x->oo) ((6*8))/(((e^(x/2))))`

=`lim_(x->oo) ((48))/(((e^(x/2))))`

upon plugging the value of `x= oo`

 we get

=`lim_(x->oo) ((48))/(((e^((oo)/2))))`

=`lim_(x->oo) ((48))/(oo)`

What is the difference between specific and latent heat?

Specific heat and latent heat are intensive material properties. Intensive properties are properties of a material which don't vary depending on the amount of mass present. For example, if a block of lead is cut into two pieces, the specific heat and latent heat of the two pieces will be the same as that of the original large block.

Specific heat is the amount of energy needed to raise the temperature of a mass by...

Specific heat and latent heat are intensive material properties. Intensive properties are properties of a material which don't vary depending on the amount of mass present. For example, if a block of lead is cut into two pieces, the specific heat and latent heat of the two pieces will be the same as that of the original large block.

Specific heat is the amount of energy needed to raise the temperature of a mass by one degree Celsius. Specific heat is expressed in units of energy per unit mass per degree. The equation for specific heat (c) is

`c = (DeltaQ)/(m*DeltaT)`   

where `DeltaQ` is the energy required for the change in temperature, m is the mass, and `DeltaT` is the change in temperature.

Latent heat is the amount of energy needed to change the physical state of a certain mass. For example, the amount of heat needed to change water from a liquid to a gas is called the latent heat of vaporization. Latent heat is expressed in units of energy per unit mass. The equation for latent heat (L) is

`L = Q / m` 

where Q is the required energy and m is the mass. It is important to note that changes in physical state occur at constant temperature. Furthermore, specific latent heat is the energy needed to change the physical state of 1 kg of a particular substance.

In "Sinners in the Hands of an Angry God" how does the tone change from vexed to relatable ?

The majority of Edwards's sermon has a vexed, or perhaps troubled, tone as the Puritan minister preaches at length about God's displeasure with sinners. Edwards uses words such as "destruction" and phrases such as "cast into hell" to describe the condition of those who are out of favor with God. Edwards also uses imagery to emphasize the horrors that await those who will not be saved; they are "as great heaps of light chaff before...

The majority of Edwards's sermon has a vexed, or perhaps troubled, tone as the Puritan minister preaches at length about God's displeasure with sinners. Edwards uses words such as "destruction" and phrases such as "cast into hell" to describe the condition of those who are out of favor with God. Edwards also uses imagery to emphasize the horrors that await those who will not be saved; they are "as great heaps of light chaff before the whirlwind" and will be cast into hell where "the furnace is now hot, ready to receive them."

Late in the sermon Edwards modifies his tone to urge people who desire salvation to change their ways. He speaks of an "extraordinary opportunity" on a day "wherein Christ has thrown the door of mercy wide open," waiting to receive them and wash away their sin. Edwards describes those who "are now in a happy state, with their hearts filled with love to him who has loved them" in profound contrast to how he berates his listeners for the majority of the sermon. Perhaps, then, the congregation who heard the sermon found this part of his message something that they could relate to; there was still time for them to do something to help themselves avoid damnation. 

How has America changed as a result of immigration?

America has changed significantly as a result of immigration.  The first Europeans were immigrants, but after the nation's founding, immigration increased.  Immigrants brought their own cultural traditions and religions.  Parts of the United States that were settled by the Irish tended to have many Catholic Churches, while places settled by the Scots had many Presbyterian parishes.  Immigrants brought their own words, dialects, and different languages.  The Germans who settled in Pennsylvania before the Revolutionary War...

America has changed significantly as a result of immigration.  The first Europeans were immigrants, but after the nation's founding, immigration increased.  Immigrants brought their own cultural traditions and religions.  Parts of the United States that were settled by the Irish tended to have many Catholic Churches, while places settled by the Scots had many Presbyterian parishes.  Immigrants brought their own words, dialects, and different languages.  The Germans who settled in Pennsylvania before the Revolutionary War kept their own language by living in closely-knit communities and maintaining their own German communities.  As late as 1918, it was possible to find newspapers printed in many languages in most major cities in the United States; it was only with the crackdown against "hyphenated-Americans" that this trend stopped.  Immigrants also brought in their own recipes—without immigrants, one could not order sauerkraut, tamales, sushi, or borscht.  

Immigrants also provided a labor pool for the industrialists of the nineteenth century.  Many of the railroads and canals constructed before the Civil War were created by Irish and German immigrants.  Before 1900, immigrants tended to come from eastern and southern Europe.  In the twentieth century, more immigrants came from Mexico, Asia, and the Middle East.  Most of these workers filled the need for laborers.  

Why do sociologists find it important to differentiate between sex and gender? What importance does the differentiation have in modern society?

In sociology, sex refers to the biological characteristics that a society uses to categorize people as either male or female. For example, each of the sexes has specific genitalia. Other secondary characteristics that are acquired upon adolescence are the development of breasts and broadening of hips among girls and the deepening of voices among boys.

Gender, on the other hand, explains how societies identify and take care of the different sexes. This includes a cultural interpretation...

In sociology, sex refers to the biological characteristics that a society uses to categorize people as either male or female. For example, each of the sexes has specific genitalia. Other secondary characteristics that are acquired upon adolescence are the development of breasts and broadening of hips among girls and the deepening of voices among boys.

Gender, on the other hand, explains how societies identify and take care of the different sexes. This includes a cultural interpretation of the roles played by either sex in the society. It also looks at how the society influences our understanding of the sexes. It addresses what is seen as "male" or "female" behavior—aspects that are not defined by the male or female biology. It addresses questions such as "can a man wear a dress?" or "why do we have distinct names that separate boys from girls?”

The distinction between sex and gender is important, because sometimes a person’s sex may not align with his or her gender. There is pretty clear evidence that gender is socially constructed. Different societies can ascribe different behavior to a gender. For instance, while it is weird for men to wear dresses in certain societies, other societies in Africa, Asia, and the Middle East have a culture that encourages the wearing of dresses or even skirts among men.

In modern society, a distinction between sex and gender is also important because of changing gender roles, for instance in occupations. Women are increasingly taking up jobs that were previously considered "male jobs," (e.g., heavy truck driving, technology jobs or even politics). As such, the term "gender" rather than "sex" is used to remove traditional societal biases between the sexes.

How relevant is the encyclical Centesimus Annus today?

The encyclical Centesimus Annus is a letter prepared by Pope John Paul II and made publicly available. The aim of the letter was to inform Catholic social doctrine as it concerned the issue and threat posed by dictatorial communist regimes. At the time the letter was prepared, most territories under communism were going through social upheavals due to extreme human rights abuses. Individual freedoms and rights, including those of private ownership, were being infringed upon...

The encyclical Centesimus Annus is a letter prepared by Pope John Paul II and made publicly available. The aim of the letter was to inform Catholic social doctrine as it concerned the issue and threat posed by dictatorial communist regimes. At the time the letter was prepared, most territories under communism were going through social upheavals due to extreme human rights abuses. Individual freedoms and rights, including those of private ownership, were being infringed upon by different dictatorial regimes. Through his encyclical, Pope John Paul II called upon the different regimes to become agents of social and economic justice by protecting the rights of all its citizens.

Centesimus Annus remains relevant today because it seeks to improve the status of international human rights given some current regimes are still perpetrating human rights abuses. The letter also informs people of their responsibility to peacefully reject dictatorial regimes and practices. In addition, the letter outlines the responsibility of developed countries in assisting developing countries to improve the quality of life for their people.

What was the attitude of President Johnson toward the Reconstruction of the South?

Like Lincoln, Johnson wanted the former Confederate states brought back into the Union as quick as possible. Johnson did not insist on the Radicals "Ironclad Oath" which prohibited anyone who willingly helped the Confederacy from taking an active role in government.  Johnson realized that this would not only prohibit former Confederate bureaucrats from holding office, but it would also stop former soldiers of the Confederacy from playing an active role in Reconstruction.  Johnson, a resident...

Like Lincoln, Johnson wanted the former Confederate states brought back into the Union as quick as possible. Johnson did not insist on the Radicals "Ironclad Oath" which prohibited anyone who willingly helped the Confederacy from taking an active role in government.  Johnson realized that this would not only prohibit former Confederate bureaucrats from holding office, but it would also stop former soldiers of the Confederacy from playing an active role in Reconstruction.  Johnson, a resident of East Tennessee before the war and military governor of the state during the conflict, did not like the planter class because he felt as though they dragged the majority of Southerners into the Civil War.  Johnson also believed that the former slaves would be for the planters' interests because of the security provided under the slave system.  Johnson, while desiring free enterprise in the South, wanted to see a system where blacks would continue to work the former plantations for wages.  He saw black suffrage as a hindrance to Reconstruction because it would only cause whites in the South to hinder the Reconstruction process.  Johnson wanted the Reconstruction South to be ably maintained, even if this meant giving government positions to the planter class that he personally despised.  Johnson personally pardoned many former Confederate officials, much to the consternation of the Radicals in his own Cabinet and Congress.   

What are the advantages and disadvantages of being an office incumbent in Washington, DC? Which incumbent is more likely to win an...

There are many advantages to being an incumbent in Washington D.C.  This explains why the turnover rate of Congress is so small even though public approval of Congress is at an all-time low.  Many voters go to the polls and vote for familiar names--this gives the incumbent an advantage.  Incumbents also receive more money from the national party conventions.  Incumbents also have the experience of serving on Congressional committees.  It is also easier for a presidential incumbent to ask for donations; there is a space in one's income tax returns where one can make a donation to the president's campaign.  

There are also numerous disadvantages to being an incumbent.  A party that has fallen out of favor with the public, such as the Democrats in 2010, might lose congressional seats because of the public's overall dissatisfaction.  Political activists can also target incumbents as being ineffective, and social media allows for this news to spread before the member of Congress can explain his/her stance properly.  Also, scandals are more magnified on Capitol Hill than they would be in the private sector.  

It is easier for a presidential incumbent to be reelected.  If one looks at the track record, there has only been a single one-term president in the last thirty years, George H.W. Bush, who was defeated in 1992.  Presidents have more resources and more staff and other key party members who will give speeches on their behalf. Many states have fallen into patterns of either giving their votes to Republicans or Democrats consistently, leaving a handful of battleground states on which a sitting president can focus his/her resources.  Presidents receive a great deal of credit when things are going well for the country, and it seems as though it takes a national economic crisis or scandal for the party in power to be replaced in the Oval Office.  

What is an analysis of The Control of Nature?

The Control of Nature by journalist and nonfiction writer John McPhee was originally published in book form in 1989. It consists of three main sections, each of which initially appeared as a long essay in The New Yorker magazine. It is a work of creative nonfiction rather than a scientific study, distinguished by its lyrical and descriptive style. 

The inspiration and title for the book was an inscription on the engineering building at the University...

The Control of Nature by journalist and nonfiction writer John McPhee was originally published in book form in 1989. It consists of three main sections, each of which initially appeared as a long essay in The New Yorker magazine. It is a work of creative nonfiction rather than a scientific study, distinguished by its lyrical and descriptive style. 

The inspiration and title for the book was an inscription on the engineering building at the University of Wyoming reading "Strive on—the control of Nature is won, not given." Seeing the inscription gleaming in the sunlight made McPhee think about situations where humans were engaged in major struggles against nature. His three main sections are extended descriptions of three specific twentieth-century examples of this struggle, two in the United States and one in Iceland. The chapters blend historical information, interviews, and elaborate descriptions of people and places. 

The first case is the work of the Army Corps of Engineers on controlling the course of the Mississippi River. Had the ACE not intervened, the river would have shifted course to drain through what is now the Atchafalaya River. McPhee discusses the massive intervention at a location known as Old River to prevent the course of the river from shifting to preserve New Orleans, Baton Rouge, and commercial shipping. Written before the great floods of 1993 and Hurricane Katrina, this chapter warns about how these interventions might lead to massive flooding, identifying consequences that have now occurred.

The second section of the book discusses efforts to divert lava flows from a harbor after the January 1973 eruption of Eldfell in Iceland. This was achieved by spraying sea water on the lava to cool it down and solidify it. The islanders then creatively began to tap the hot interior of the lava for geothermal energy. In contrast to the ACE approach of controlling nature by brute force, the Icelandic experiment shows an example of how to work creatively with natural phenomena, turning what could have been a major disaster to their advantage.

The final section discusses how Los Angeles has built extremely expensive basins to catch debris from mudslides in order to preserve and continue to build luxury homes in areas prone to mudslides. 

Who is the main character, Sonny or the narrator? How would this story be different if it were told by Sonny?

The main character of "Sonny's Blues" is the narrator, who tries to come to terms with what has happened to his brother. At the outset of the story, after he hears that his brother has been arrested for selling heroin, the narrator says, "I couldn't believe it: but what I mean by that is that I couldn't find any room for it anywhere inside me." The story revolves around the narrator's attempt to make sense...

The main character of "Sonny's Blues" is the narrator, who tries to come to terms with what has happened to his brother. At the outset of the story, after he hears that his brother has been arrested for selling heroin, the narrator says, "I couldn't believe it: but what I mean by that is that I couldn't find any room for it anywhere inside me." The story revolves around the narrator's attempt to make sense of what has happened to his brother by going back into their past and then watching his brother play music, an experience that helps the narrator understand who his brother is and what he values.

If Sonny had told the story, it would have been very different. Instead of Sonny's brother trying to figure out Sonny, Sonny could have told his own tale of what happened. Sonny would've explained what drove him to do drugs and how the narrator, his brother, and his family had not understood him. He would have perhaps included other reasons why he turned to drugs. "Sonny's Blues" involves one character trying to unravel the psychological mysteries of another character; if Sonny had told the story, it would have involved less psychological mystery and would have been a more straightforward narrative. 

What are the risks that Tom is taking in "Contents of the Dead Man's Pocket?" What could be the consequences of his risk?

In “The Contents of the Dead Man’s Pocket,” Tom Benecke takes one major physical risk.  He takes a major risk when he chooses to go out on to the ledge and try to retrieve the paper that has blown out the window.  When he does this, he is risking death.

We could also say that Tom takes other risks in this story.  We could say that he is risking his marriage by being so involved...

In “The Contents of the Dead Man’s Pocket,” Tom Benecke takes one major physical risk.  He takes a major risk when he chooses to go out on to the ledge and try to retrieve the paper that has blown out the window.  When he does this, he is risking death.

We could also say that Tom takes other risks in this story.  We could say that he is risking his marriage by being so involved in his work.  At the beginning of the story, Tom is going to stay home and work while his wife goes out to the movie alone.  It is possible that his wife would get tired of being, in a sense, abandoned by her husband.  By working so hard to fulfill his career ambitions, Tom might be putting his marriage in danger.

While Tom might be risking his marriage by working too much, the real risk in this story is the risk to his life.  When the paper blows out the window, it lands on a ledge.  Tom estimates that the ledge is something like a foot wide.  As the story says,

The ledge, he saw, measuring it with his eye, was about as wide as the length of his shoe...

He thinks to himself that he would have no fear about walking on the ledge if it were a yard or so off the ground.  However, the ledge is actually somewhere around 100 feet off the ground as the Beneckes live on the 11th floor of their building.  A person who tries to inch along on a one-foot-wide ledge 100 feet off the ground is clearly risking their life.  They could easily slip and fall or be blown off the ledge.  Falling from the ledge would mean certain death because of how high up the ledge is.  This is the risk Tom takes.  He risks falling and dying in order to try to save the work he has done and, thereby, to advance his career.

What is so enjoyable about "The Pardoner's Tale" from The Canterbury Tales?

"The Pardoner's Tale" is enjoyable because both the prologue and the tale itself satirize human failings. In the prologue, the Pardoner, himself a greedy character who is open about his cupidity, relates how he defrauds his parishioners. While he preaches that greed is the root of evil, he also admits that "It's greed alone that makes me sermonize." He sells relics to make money, and he preaches to acquire money while watching others live in...

"The Pardoner's Tale" is enjoyable because both the prologue and the tale itself satirize human failings. In the prologue, the Pardoner, himself a greedy character who is open about his cupidity, relates how he defrauds his parishioners. While he preaches that greed is the root of evil, he also admits that "It's greed alone that makes me sermonize." He sells relics to make money, and he preaches to acquire money while watching others live in poverty.

In "The Pardoner's Tale," three unholy youths, condemned to death for their sins, hear while drinking in a pub that their friend, also drunk, was slain by a character named Death. They promise each other to slay Death--which is of course a fruitless and darkly funny task--and they wind up dying themselves. What kills them all is their own stupidity and greed, as two of them wait to slay the man who has gone for food and drink. After two of them slay the first man, they drink the wine that the other brought them (and that is poisoned). They all wind up dead, as by trying to meet Death, they wind up dead. The humor in this story comes from the tendency of people to think they can outwit death and from the way in which humans only wind up hurting themselves through their greed.

What is the most significant theme of the book Seven Myths of the Spanish Conquest by Matthew Restall.

The significant theme in the book Seven Myths of the Spanish Conquestby Restall is that the conquest is rooted in myth--not in the sense of the supernatural but in the sense that ideas and concepts related to the Spanish conquest were seeped in the culture and political agenda of the time. For example, in the first chapter, the author discusses the myth that the Spanish conquest was possible only through the actions of a...

The significant theme in the book Seven Myths of the Spanish Conquest by Restall is that the conquest is rooted in myth--not in the sense of the supernatural but in the sense that ideas and concepts related to the Spanish conquest were seeped in the culture and political agenda of the time. For example, in the first chapter, the author discusses the myth that the Spanish conquest was possible only through the actions of a few "great men." Instead, the author writes that the conquest was made possible through the actions of many Spaniards who were schooled in the ways of Spanish settlement and conquest. By contrasting myths of conquest with evidence from more modern sources, the author is not suggesting that history written a long time ago is myth while today's history is "true." Instead, the author writes that "a supposed reality built by researching archival sources can also generate its own myths" (page xvi). Therefore, even a modern search for sources and evidence can result in myths that arise from cultural conceptions rather than resulting in pure objectivity. 

How did the Homestead and Pacific Railroad Acts passed by the federal government help lead to the defeat of the numerous Native American nations in...

The Homestead Act and the Pacific Railway Act helped lead to the defeat of many Native American tribes in the West. When white Americans began to expand westward between 1820-1850, they encountered numerous Native American tribes east of the Mississippi River. Many white Americans viewed these tribes as obstacles to progress. As a result, the United States government forced these tribes to move to lands located west of the Mississippi River. Many Native Americans died...

The Homestead Act and the Pacific Railway Act helped lead to the defeat of many Native American tribes in the West. When white Americans began to expand westward between 1820-1850, they encountered numerous Native American tribes east of the Mississippi River. Many white Americans viewed these tribes as obstacles to progress. As a result, the United States government forced these tribes to move to lands located west of the Mississippi River. Many Native Americans died because of the horrible conditions they encountered as they were forced to move westward.

Once the Homestead Act was passed (which gave people 160 acres of western land basically for free if they lived on that land for five years), more Americans began to move the West. The Pacific Railway Act allowed for the construction of the transcontinental railroad, which also encouraged westward expansion. As people moved to the West, they again encountered the Native Americans. The Native Americans, in many instances, resisted the spread of white settlers onto their lands. Many battles ensued with many Native Americans being killed. Additionally, white settlers brought diseases to the West to which the Native Americans had no immunity. More Native Americans died. As white Americans moved westward, they also killed many buffalo which the Native Americans depended on. This also led to the death of some Native Americans. Many Native American tribes were weakened by these factors, which made it easier for them to be defeated in battle.

These laws, which encouraged westward expansion, significantly harmed many Native American tribes and led to their defeat in conflicts with the United States military.

Why does the political system in our country seem so dysfunctional ? I think it because of gridlock but I don't have any example. If you have one...

A major factor in the dysfunction in our political system is the effects of gerrymandering. Gerrymandering is a process where the political parties create districts that are safe for a given political party. As a result, a candidate knows he or she will be elected and reelected as long as the candidate supports the positions of the people who live in that district. The effect of this is that there are fewer politicians who are...

A major factor in the dysfunction in our political system is the effects of gerrymandering. Gerrymandering is a process where the political parties create districts that are safe for a given political party. As a result, a candidate knows he or she will be elected and reelected as long as the candidate supports the positions of the people who live in that district. The effect of this is that there are fewer politicians who are willing to compromise on a given issue, fearing it will prevent that person from being reelected. With fewer politicians in the middle of the political spectrum, we are seeing more extreme and polarized politics. As a result, it appears that little is getting done because, depending on the issue, one political party uses tactics to block a bill from become law.

A good example of this polarization is the difficulty in getting the Affordable Health Care law passed and the number of failed attempts to repeal it. Other examples include the lack of progress on passing a bill on immigration reform or the reauthorizing of the Elementary and Secondary Education Act. With few politicians in the middle of the political spectrum, there is little compromise occurring. Thus, when the President is from one party, and the other party controls the Congress, little gets done when neither Democrats nor Republicans are willing and/or able to compromise. This is why there is so much dissatisfaction with our political process, and the appearance of gridlock exists. It also explains why in some states, one party controls a majority of the seats in the state legislature even though they have received less than half of the total number of votes cast.

In the story "A Rose for Emily" what does Emily represent?

First, Miss Emily is a character, not just a representation of something else, as the story is not a fable or an allegory but a piece of realistic fiction. 

One major theme of the story is the relationship between the "old South" with its aristocratic ideals and social stratification and the "New South," which is much more modern and equal but in some ways more crassly commercial and not without prejudices of its own.

Miss...

First, Miss Emily is a character, not just a representation of something else, as the story is not a fable or an allegory but a piece of realistic fiction. 

One major theme of the story is the relationship between the "old South" with its aristocratic ideals and social stratification and the "New South," which is much more modern and equal but in some ways more crassly commercial and not without prejudices of its own.

Miss Emily comes from a wealthy family and has habits and assumptions based on a certain class structure that no longer exists. She is not really prepared to live in the "New South" and thus is a sort of misfit, but one whose pride in her background and traditions prevent her from reaching out to others in the town for help. While she is in many ways portrayed as a grotesque throwback, some readers also come to admire her indomitable will and ability not to be exploited by Homer.

She can be said to represent the Old Southern aristocracy and its traditions and values. 

How did German attacks on United States shipping change America's policy of neutrality?

Germany’s attacks on American shipping changed the policy of neutrality that the United States was following before it entered World War I. The United States remained neutral when World War I began. This meant the United States was allowed to trade with any country, including countries that were at war. When Germany began to sink American ships, the United States warned Germany to stop. In the Sussex Pledge, Germany agreed to stop sinking American ships....

Germany’s attacks on American shipping changed the policy of neutrality that the United States was following before it entered World War I. The United States remained neutral when World War I began. This meant the United States was allowed to trade with any country, including countries that were at war. When Germany began to sink American ships, the United States warned Germany to stop. In the Sussex Pledge, Germany agreed to stop sinking American ships. As a result, the United States remained neutral.

However, Germany broke this pledge in 1917. Germany began to sink American ships. As a result of this and other factors, the United States joined World War I on the side of the Allies. Germany believed that victory was near, and Germany was convinced it would win the war before the United States could become a major factor in the war. Germany terribly miscalculated based on this belief.

`f(x)=1/(1+x)^2` Use the binomial series to find the Maclaurin series for the function.

Recall binomial series  that is convergent when `|x|lt1` follows: 

`(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` 

  or         `(1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4-` ...

 For given function `f(x) =1/(1+x)^2` , we may  apply Law of Exponents: `1/x^n = x^(-n)` to rewrite it as:

`f(x) = (1+x)^(-2)`

This now resembles `(1+x)^k` for binomial series.  

By comparing "`(1+x)^k` " with "`(1+x)^(-2)` ", we have the corresponding values:

`x=x ` and `k = -2`...

Recall binomial series  that is convergent when `|x|lt1` follows: 

`(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` 

  or         `(1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4-` ...

 For given function `f(x) =1/(1+x)^2` , we may  apply Law of Exponents: `1/x^n = x^(-n)` to rewrite it as:

`f(x) = (1+x)^(-2)`

This now resembles `(1+x)^k` for binomial series.  

By comparing "`(1+x)^k` " with "`(1+x)^(-2)` ", we have the corresponding values:

`x=x ` and `k = -2` .

 Plug-in the values  on the formula for binomial series, we get:

`(1+x)^(-2)=sum_(n=0)^oo (-2(-2-1)(-2-2)...(-2-n+1))/(n!)x^n`

               `= 1 + (-2)x + (-2(-2-1))/(2!) x^2 + (-2(-2-1)(-2-2))/(3!)x^3 +(-2(-2-1)(-2-2)(-2-3))/(4!) x^4-` ...

             `= 1 -2x + 6/(2!) x^2 -24/(3!)x^3 +120/(4!)x^4-` ...

              `= 1- 2x +3x^2 -4x^3 +5x^4-` ...

              or  `sum_(n=0)^oo (-1)^n (n+1)x^n`

Therefore, the Maclaurin series  for  the function `f(x) =1/(1+x)^2` can be expressed as:

`1/(1+x)^2 =sum_(n=0)^oo (-1)^n (n+1)x^n`

or 

`1/(1+x)^2 =1- 2x +3x^2 -4x^3 +5x^4-` ...

How does Raymond's run contribute to the resolution of the story?

Raymond's having run alongside her on the other side of the fence reminds Squeaky of what she has revealed in the exposition as her duty to her family:

All I have to do in life is mind my brother Raymond....

Now, she "minds" her brother more closely and perceives potential in her brother that she has not noticed before; and, having done so, Squeaky abandons her preoccupation with herself, 

[A]nd I look over at Gretchen.......

Raymond's having run alongside her on the other side of the fence reminds Squeaky of what she has revealed in the exposition as her duty to her family:

All I have to do in life is mind my brother Raymond....

Now, she "minds" her brother more closely and perceives potential in her brother that she has not noticed before; and, having done so, Squeaky abandons her preoccupation with herself, 

[A]nd I look over at Gretchen.... And I smile. Cause she’s good, no doubt about it....And she nods to congratulate me and then she smiles. And I smile. We stand there with this big smile of respect between us.

Squeaky now has learned to find merits in others. As she acknowledges Raymond's talent, so, too, does she acknowledge that Gretchen is a real person on her own, who does not act as though she is better than someone else; nor does Gretchen have any personal motives for pretense. She is simply pleased and proud of Raymond's efforts, as well as those of Squeaky. Her genuine smile and gestures toward Squeaky convey her sincere feelings, feelings that Squeaky realizes are much the same as those she has herself toward Raymond. 

What does Faber say about Jesus and the controllers of society?

During a conversation with Montag, Faber makes an important comment about the role of Jesus in society:

Christ is one of the 'family' now. I often wonder if God recognizes His own son the way we've dressed him up, or is it dressed him down? He's a regular peppermint stick now, all sugar-crystal and saccharine when he isn't making veiled references to certain commercial products that every worshipper absolutely needs.

In other words, in Faber...

During a conversation with Montag, Faber makes an important comment about the role of Jesus in society:

Christ is one of the 'family' now. I often wonder if God recognizes His own son the way we've dressed him up, or is it dressed him down? He's a regular peppermint stick now, all sugar-crystal and saccharine when he isn't making veiled references to certain commercial products that every worshipper absolutely needs.

In other words, in Faber and Montag's society, the controllers of society have hijacked the image of Jesus to suit their own agenda. They have removed his association with morality and ethics and transformed him into a member of the "family," a figure of mindless entertainment who is projected on to parlour walls across the country, for women like Mildred to talk and listen to.

In doing this, Jesus is no longer recognisable ("I often wonder if God recognizes his own son") to those who remember life before the burning of the books. Gone are the true stories of Jesus, replaced with messages invented by the controllers to make him "sugar-crystal" and "saccharine," instead of human and flawed. These messages, devised by the controllers, lead people to buy things they don't really need and focus on entertainment, instead of asking deeper questions of themselves and society.

By doing this, the controllers have also cleverly eradicated the association between Jesus and the Bible. If people think that Jesus is one of the "family," they will be less inclined to want to read the original stories of his life in the Bible and, over time, will completely forget this book ever existed.