In Richard Connell’s short story “The Most Dangerous Game,” does Zaroff give a fair chance to his human opponents?

On his remote island off the coast of South America the sociopathic General Zaroff hunts men for sport. He has grown tired of hunting animals because he has grown too expert in his chosen passion so he hunts men who become stranded on the island, which has the nickname "Ship-Trap." After revealing his diabolical pastime to Rainsford during their dinner conversation, Zaroff notes that the men he hunts are treated quite well before they are...

On his remote island off the coast of South America the sociopathic General Zaroff hunts men for sport. He has grown tired of hunting animals because he has grown too expert in his chosen passion so he hunts men who become stranded on the island, which has the nickname "Ship-Trap." After revealing his diabolical pastime to Rainsford during their dinner conversation, Zaroff notes that the men he hunts are treated quite well before they are released into the jungle:

"I treat these visitors with every consideration. They get plenty of good food and exercise. They get into splendid physical condition."

Along with this the general provides them with food, a good hunting knife, and gives them a three hours' head start before releasing them. Afterward he sets off after them with "a pistol of the smallest caliber and range." It could then be argued that Zaroff does indeed give them somewhat of a fair chance. Of course, a really fair chance would involve also giving them the same type of pistol which he carries and a map of the island. The general, however, is quite uncanny in his abilities and even Rainsford, a seasoned hunter himself, has difficulty eluding Zaroff. The general also has the aid of trained tracking dogs if his prey is particularly skilled, as Rainsford proves to be. Ultimately, it takes a daring leap into the sea for Rainsford to avoid death at the general's hands. With this in mind, it is evident that Zaroff has too many advantages for the game to be considered fair.

`sum_(n=2)^oo ln(n)/n^3` Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence...

The integral test is applicable if `f` is positive and decreasing function on infinite interval `[k, oo) ` where` kgt= 1` and `a_n=f(x)` . Then the series `sum_(n=k)^oo a_n ` converges if and only if the improper integral `int_k^oo f(x) dx ` converges. If the integral diverges then the series also diverges.

For the given series `sum_(n=2)^oo ln(n)/n^3` ,  `a_n =ln(n)/n^3` .

Then applying `a_n=f(x)` , we consider:

`f(x) =ln(x)/x^3`

The graph of f(x) is:

As shown on the graph, f is positive on the infinite interval `[1,oo)` . To verify of the function will eventually decreases on the given interval, we may consider the derivative of the function.

Apply Quotient rule for the derivative:` d/dx(u/v) = (u'* v- v'*u)/v^2` .

Let `u = ln(x)` then `u' = 1/x`

      `v = x^3` then `v' = 3x^2`

Applying the formula,we get:

`f'(x) = (1/x*x^3- 3x^2*ln(x))/(x^3)^2`

           `= (x^2-3x^2ln(x))/x^6`

           `=(1-3ln(x))/x^4`

Note that `1-3ln(x) lt0` for larger values of x which means `f'(x) lt0` .Based on the first derivative test, if ` f'(x) lt0` then `f(x)` is decreasing for a given interval I. This confirms that the function is ultimately decreasing as `x-> oo`. Therefore, we may apply the Integral test to confirm the convergence or divergence of the given series.

We may determine the convergence or divergence of the improper integral as:

`int_2^ooln(x)/x^3dx= lim_(t-gtoo)int_2^tln(x)/x^3dx`

To determine the indefinite integral of `int_2^tln(x)/x^3dx` , we may apply integration by parts:` int u dv = uv - int v du`

`u = ln(x) then du = 1/x dx.`

`dv = 1/x^3dx ` then `v= int 1/x^3dx = -1/(2x^2)`

Note: To determine` v` , apply Power rule for integration `int x^n dx = x^(n+1)/(n+1)`

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

                ` =x^(-3+1)/(-3+1)`

                 ` = x^(-2)/(-2)`

                ` = -1/(2x^2)`

The integral becomes: 

`int ln(x)/x^3dx=ln(x) (-1/(2x^2)) - int -1/(2x^2)*1/xdx`

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

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

                    ` =-ln(x)/(2x^2) + 1/2*(-1/(2x^2))`

                    ` = -ln(x)/(2x^2) -1/(4x^2)`

Apply definite integral formula: `F(x)|_a^b = F(b) - F(a)` .

`-ln(x)/(2x^2) -1/(4x^2)|_2^t=[-ln(t)/(2t^2) -1/(4t^2)] -[-ln(2)/(2*2^2) -1/(4*2^2)]`

                           `= [-ln(t)/(2t^2) -1/(4t^2)]-[-ln(2)/8 -1/16]`

                           `=-ln(t)/(2t^2) -1/(4t^2) + ln(2)/8 + 1/16`

                          `=-ln(t)/(2t^2) -1/(4t^2) +1/16 (ln(4) +1)`

Note:`ln(2)/8 + 1/16 = 1/16 (2ln(2) +1)`

                          ` =1/16 (ln(2^2) +1)`

                         ` =1/16 (ln(4) +1)`

 Apply  `int_2^tln(x)/x^3dx=-ln(t)/(2t^2) -1/(4t^2) +1/16 (ln(4) +1)` , we get:

`lim_(t-gtoo)int_2^tln(x)/x^3dx=lim_(t-gtoo) [ -ln(t)/(2t^2) -1/(4t^2) + 1/16(ln(4)+1)]`

                                 ` = -0 -0+1/16(ln(4)+1)`

                                 ` =1/16(ln(4)+1)`

  Note: `lim_(t-gtoo) 1/16(ln(4)+1)=1/16(ln(4)+1)`

           `lim_(t-gtoo) 1/(4t^2)= 1/oo or 0`

            li`m_(t-gtoo) ln(t)/(2t^2)=[lim_(t-gtoo) -ln(t)]/[lim_(t-gtoo) 2t^2]=-oo/oo`

Apply L' Hospitals rule:

`lim_(t-gtoo) ln(t)/(2t^2) =lim_(t-gtoo) (1/t)/(4t)`

                     `=lim_(t-gtoo) 1/(4t^2)`

                     `= 1/oo or 0`

The  `lim_(t-gtoo)int_2^tln(x)/x^3dx=1/16 (ln(4) +1)` implies that the integral converges.

Conclusion: The integral `int_2^ooln(x)/x^3dx`   is convergent therefore the series `sum_(n=2)^ooln(n)/n^3` must also be convergent. 

In what way does Kathrine Mansfield use language, structure, and imagery to generate effect and significance in "Prelude" (specifically with regard...

Katherine Mansfield's short story "Prelude" was published in one of the writer's short story collections in 1920. But that wasn't the story's first publication: in 1918, it was released under a different title with Virginia and Leonard Woolf's Hogarth Press. The title was "The Aloe."

The original title hints at the significance of the aloe plant in this narrative. The aloe, covered with thorns, is a central symbol. 

First, let's establish a bit of context for this plant. "Prelude' is about a family moving from one house to another, and the experience that four central female characters (Linda, the lady of the house; Beryl, her unmarried sister; Mrs. Fairfield, the sisters' elderly mother; and Kezia, Linda's young daughter) have during this transition. The house is spacious and beautiful, as are the gardens outside. There's an aloe plant there that's particularly interesting to some of the characters. Let's look at Kezia's initial interaction with the plant:

Nothing grew on the top except one huge plant with thick, grey-green, thorny leaves, and out of the middle there sprang up a tall stout stem. Some of the leaves of the plant were so old that they curled up in the air no longer; they turned back, they were split and broken; some of them lay flat and withered on the ground.

Whatever could it be? She had never seen anything like it before. She stood and stared. And then she saw her mother coming down the path.

"Mother, what is it?" asked Kezia.

Linda looked up at the fat swelling plant with its cruel leaves and fleshy stem. High above them, as though becalmed in the air, and yet holding so fast to the earth it grew from, it might have had claws instead of roots. The curving leaves seemed to be hiding something; the blind stem cut into the air as if no wind could ever shake it.

"That is an aloe, Kezia," said her mother.

"Does it ever have any flowers?"

"Yes, Kezia," and Linda smiled down at her, and half shut her eyes. "Once every hundred years."

Mansfield's language here, in the initial description of the aloe, is clipped and foreboding. Words and phrases like "thick," "thorny," "split and broken," and "flat and withered" seem ominous: what kind of foreshadowing might she be experimenting with here? (One of the themes of the story is the cycle of life, the passage of time, and the experience of several generations of women in the same family.) That the tree, to Linda, seems to have "claws instead of roots" only reinforces the idea that this tree is a symbol of danger or death.

Linda's language in the last sentence of this passage indicates both hope (yes, the aloe will flower) and melancholy (but only once every century.) It's worth noting that many literary critics and academics interpret that Linda is pregnant in this short story; that idea is only suggested, not explicitly stated.

Despite the dark initial encounter with the aloe, the same plant continues to fascinate Linda. Later, she's in the garden with her mother:

"I have been looking at the aloe," said Mrs. Fairfield. "I believe it is going to flower this year. Look at the top there. Are those buds, or is it only an effect of light?"

As they stood on the steps, the high grassy bank on which the aloe rested rose up like a wave, and the aloe seemed to ride upon it like a ship with the oars lifted. Bright moonlight hung upon the lifted oars like water, and on the green wave glittered the dew.

"Do you feel it, too," said Linda, and she spoke to her mother with the special voice that women use at night to each other as though they spoke in their sleep or from some hollow cave–"Don't you feel that it is coming towards us?"

She dreamed that she was caught up out of the cold water into the ship with the lifted oars and the budding mast. Now the oars fell striking quickly, quickly. They rowed far away over the top of the garden trees, the paddocks and the dark bush beyond. Ah, she heard herself cry: "Faster! Faster!" to those who were rowing.

How much more real this dream was than that they should go back to the house where the sleeping children lay and where Stanley and Beryl played cribbage.

"I believe those are buds," said she. "Let us go down into the garden, mother. I like that aloe. I like it more than anything here. And I am sure I shall remember it long after I've forgotten all the other things."

She put her hand on her mother's arm and they walked down the steps, round the island and on to the main drive that led to the front gates.

Looking at it from below she could see the long sharp thorns that edged the aloe leaves, and at the sight of them her heart grew hard. . . . She particularly liked the long sharp thorns. . . . Nobody would dare to come near the ship or to follow after.

"Not even my Newfoundland dog," thought she, "that I'm so fond of in the daytime."

Here, Mansfield uses imagery and structure to great effect. For reasons that we, as readers, can't quite understand yet, Linda is greatly intrigued by the aloe. She seems to find the plant both compelling and fear-inducing. There's contradiction in her experience of the plant ("I like that aloe" seems at odds with "her heart grow hard.")

Mansfield also plays with structure here, particularly with repetition. "Long sharp thorns" is a phrase she repeats twice in the same paragraph.

Also note the author's use of the ellipsis: it's as if her thoughts are not complete, as if she is trailing off while thinking about the aloe and what it signifies. There's some abiguity to Linda's complicated feelings about the plant, and we, as readers, are also left with questions about exactly what the aloe (and the story) means.

What is the theme of "To Autumn"?

Ostensibly, Keats's "To Autumn" is a paean of praise to this most inspirational of seasons. But, as is always the case with Keats, there is considerably more to this than meets the eye—a richer, more complex vision lurking beneath the opulent pleasures of nature, bursting to shine forth.

A recurring theme in Keats's odes is the fragility and transience of the natural world. And we encounter it once again here. Keats delights in providing us...

Ostensibly, Keats's "To Autumn" is a paean of praise to this most inspirational of seasons. But, as is always the case with Keats, there is considerably more to this than meets the eye—a richer, more complex vision lurking beneath the opulent pleasures of nature, bursting to shine forth.

A recurring theme in Keats's odes is the fragility and transience of the natural world. And we encounter it once again here. Keats delights in providing us with lush descriptions of this "season of mists and mellow fruitfulness," while at the same time recognizing that the season, like each one of us, must one day pass, no matter how beautiful it is. But this shouldn't cause worry; new life will emerge from the old in a never-ending cycle of death and rebirth:

And full-grown lambs loud bleat from hilly bourn; 

   Hedge-crickets sing; and now with treble soft 

   The red-breast whistles from a garden-croft

      And gathering swallows twitter in the skies.

The season is drawing to a close, but nature is blossoming into full maturity as it points toward the onset of winter. The lambs are now "full grown," and the swallows are starting to gather in the skies.

Nature is so remarkably fruitful in all its variety. At times, it threatens to overwhelm us with the sheer scale of its fecundity. Man is the junior partner here; in his relationship to nature it is the world of the animals, the clouds, and the sweet, luscious fruit that dominates. In the midst of this endless cycle of seasonal change, there is nothing we can do but stand and admire. We must simply sit back and, in our reverie, enjoy the joyous bounties of nature, our sadness at their passing tinged with a realization that they will one day return.

What are Patrick Henry's reasons for wanting to rebel against the British rule?

Patrick Henry's chief argument in the "Speech in the Virginia Convention" is that it would be futile for the Virginia Colony to try to negotiate any further with the British.  He reminds his audience that "we have been trying that for the last ten years."  Although the speech has many strong appeals to various emotions, Henry also very logically recites the strategies the colony has already tried: "We have petitioned; we have remonstrated; we have...

Patrick Henry's chief argument in the "Speech in the Virginia Convention" is that it would be futile for the Virginia Colony to try to negotiate any further with the British.  He reminds his audience that "we have been trying that for the last ten years."  Although the speech has many strong appeals to various emotions, Henry also very logically recites the strategies the colony has already tried: "We have petitioned; we have remonstrated; we have supplicated; we have prostrated ourselves before the throne, and have implored its interposition to arrest the tyrannical hands of the ministry and Parliament."  He then reminds his listeners what Britain's response has been: "Our petitions have been slighted; our remonstrances have produced additional violence and insult; our supplications have been disregarded; and we have been spurned, with contempt, from the foot of the throne."

Henry does not believe that there is any reason to think that the colony's relationship with Britain will improve.  Trade will continue to be restricted, taxes will be crippling, the threat of violence against the colony will be constant, and the colony will not have a voice in Parliament.  In Henry's view, the only way the desired changes will come is if the colony separates from Britain.  Henry is trying to convince his audience that the only way to achieve independence is through a declaration of war.  

In what ways are the Ewell children feral?

The Ewell children in To Kill a Mockingbird are feral because they live in filth and are unruly and uneducated.

The Ewell children are mostly taken care of by the oldest child, Mayella. Her father is a drunk who beats her and the other children. The property they live on is in a constant state of dirty, cluttered disrepair. Scout says that the Ewells go to the dump and bring things home, then leave those...

The Ewell children in To Kill a Mockingbird are feral because they live in filth and are unruly and uneducated.

The Ewell children are mostly taken care of by the oldest child, Mayella. Her father is a drunk who beats her and the other children. The property they live on is in a constant state of dirty, cluttered disrepair. Scout says that the Ewells go to the dump and bring things home, then leave those items—from old shoes to a discarded dentist's chair—on their property.

She says that people in town aren't sure how many Ewell children there are, indicating that some people say six and others nine. Scout says, "There were always several dirty-faced ones at the windows when anyone passed by." At the trial, she says that the children are often sick and some of them have something called ground-itch.

Scout is in class with Burris Ewell. On the first day, Miss Caroline tries to send him home to wash his hair after "a cootie" falls out of it. Scout describes him, thinking, "He was the filthiest human I had ever seen. His neck was dark gray, the backs of his hands were rusty, and his fingernails were black deep into the quick." When he leaves, he says he won't be back. He says he only comes to the first day of school every year, which is apparently what most of the Ewell children do.

What are some of the traditional ways to celebrate Kwanzaa?

Kwanzaa is traditionally celebrated after Christmas; it lasts from December 26 to January 1. Created by Maulana Karenga, a black activist, Kwanzaa is a festival derived from the civil rights movement, and it pays homage to the global African community. Kwanzaa is a composite of several African harvest traditions, and it celebrates seven principles (or Nguzo Saba): Umoja (Unity), Kuji-chagulia (Self-determination), Ujima (Collective Work and Responsibility), Ujamaa (Cooperative Economics), Nia (Purpose), Kuumba (Creativity), and...

Kwanzaa is traditionally celebrated after Christmas; it lasts from December 26 to January 1. Created by Maulana Karenga, a black activist, Kwanzaa is a festival derived from the civil rights movement, and it pays homage to the global African community. Kwanzaa is a composite of several African harvest traditions, and it celebrates seven principles (or Nguzo Saba): Umoja (Unity), Kuji-chagulia (Self-determination), Ujima (Collective Work and Responsibility), Ujamaa (Cooperative Economics), Nia (Purpose), Kuumba (Creativity), and Imani (Faith).

The above principles are celebrated in order during the seven-day festival. On each day, one of seven candles or Mishumaa Saba is lighted. Mishumaa Saba consists of three green candles, three red candles, and one black candle. On the first day of Kwanzaa (December 26), the black candle (symbolizing Umoja or unity) is lighted. As a rule, the Mishumaa Saba (seven candles) are placed in the kinara (candle holder), and the kinara is then placed on a mkeka (mat) that rests on top of an African tablecloth. The black candle is always placed in the center of the kinara.

On the right of the black candle, three green candles representing Ujima, Nia, and Imani are placed. On the left of the black candle, three red candles representing Kujichagulia, Ujamaa, and Kuumba are placed. The three colors are derived from the black nationalist flag that Marcus Garvey created. The kinara symbolizes the deep respect African families have for their ancestors. During Kwanzaa, some people visit nursing homes, elderly family members, or elderly friends to show their appreciation for the aged. Ears of corn or mihindi are also placed on the mkeka to represent fertility and the number of children in the family.

On the sixth day of Kwanzaa, many celebrants enjoy a karamu or feast. Many wear traditional African clothing to attend the karamu. During the feast, a Unity cup or kikombe cha umoja is used to perform a libation ritual. The libation (or tambiko) is usually juice, water, or wine; each person drinks from the cup as a sign of unity. After everyone has drunk, the last portion of the tambiko is poured out in the direction of the four winds to honor the ancestors. The dishes that are shared during the feast varies. Some families choose to enjoy Caribbean, South American, or traditional African diaspora dishes.

Menus can include Jollof rice, collard greens, Yassa chicken, beef and groundnut stew, and sweet potato biscuits. Here's an example of a Kwanzaa karamu menu: Kwanzaa feast.

On the seventh and last day of Kwanzaa, celebrants traditionally give gifts or zawadi to their friends and family members. Some gifts are homemade, in honor of the Kwanzaa principles of creativity, accomplishment, and self-determinism. Children are also given gifts to reward accomplishments and to promote future successes. In all, these are some of the traditional ways to celebrate Kwanzaa.