Notes

After Finny's funeral in chapter 12, life continues in chapter 13 of A Separate Peace. Gene's class is graduating from Devon and preparing to enter the war effort. Meanwhile, in June, military units move onto the campus to set up sewing machines for the purpose of sewing parachutes together. Brinker and Gene talk about the war and what they are witnessing with great interest. Brinker turns the talk to Leper's failed enlistment and that he would have done better to be stationed here sewing parachutes. Gene feels uncomfortable talking about Leper and says, "Why talk about something you can't do anything about?" (197). This must be Gene's philosophy at this point in his life. He feels powerless to change anything, especially with people over whom he has no control; therefore, why discuss it? Gene's philosophy seems to carry over to what happened to his best friend, Phineas. He doesn't see any reason to talk about Finny after he's gone because ther...

In general, Rikki-tikki is a threat because he is in the same habitat as Nag and Nagaina. A mongoose is a predatory animal, so Rikki-tikki is capable of efficiently killing another animal. Additionally, snakes are a typical prey species for mongooses to hunt. Rikki-tikki is a threat to the snakes because of a basic food chain hierarchy.   Nag and Nagaina definitely feel the potential threat that Rikki-tikki represents once Rikki-tikki proves he is more than capable of dealing with a snake. First, Rikki-tikki proves his quickness by dodging Nagaina's sneaky attack from behind. Second, Rikki-proves his ability to kill when he kills Karait.   The final way that Rikki-tikki is a threat to Nag and Nagaina is that a mongoose is an opportunistic predator. A mongoose survives by hunting many different prey, which doesn't bother the snakes. What does threaten the snakes is that a mongoose will often raid nests and eat the eggs. Nag and Nagaina have chosen this particular yard to lay the...

When Detective Karyl is on the witness stand, Petrocelli asks him if he looked for any clues at the crime scene that would potentially lead to the perpetrator. Karyl says that they looked for clues but didn't find any, then they began questioning suspects. Karyl admits that they questioned a number of people that may have had possible information about the crime and came across Mr. Zinzi, who told them about Mr. Bolden. Mr. Bolden then told them about Bobo Evans and James King. Detective Karyl says, " We often use information from informants, especially in murder cases " (Myers 74). When Asa Briggs, King's lawyer, cross-examines Detective Karyl, he asks Karyl if they typically skip the investigation and run to their "stoolies" for information. Karyl maintains that they treat each case carefully, even though they were unable to find any fingerprints at the scene. Briggs finds it suspicious that Detective Karyl appears to hurry through the crime-scene investi...

Two months after Pearl Harbor was bombed on December 7th, 1941, President Theodore Roosevelt signed Executive Order 9066 on February 19, 1942. It led to the internment of more than 100,000 West Coast Japanese-Americans for the duration of the war. Fearing that these Issei (first-generation Japanese-Americans) and Nisei (second-generation Japanese-Americans) would pose security risks, the United States government took measures to sequester them in ten remote camps in the Midwest. Prior to leaving, many Issei and Nisei had to sell their belongings and homes off at outrageously low prices; this was the only way they could recoup some of the financial losses they incurred from adhering to Roosevelt's special order. Meanwhile, Japanese-Americans in Hawaii were spared internment because wealthy landowners needed their Japanese employees to work the sugar and pineapple plantations. The people who profited the most from the internment of Japanese-Americans were white business owners. The f...

The most obvious way in which Quebec has influenced Canadian culture is through its contribution to linguistic diversity in Canada. Because Quebec (like New Brunswick) is Francophone, Canada has two national languages, and every student in Canada must learn both languages. This means that Canadians are familiar with both English and French traditions, something that may perhaps underlie Canada's traditions of multiculturalism and pluralism. In religion, Quebec had the effect of bringing religious diversity to Canada, in that many of the French settlers were Roman Catholic, as opposed to the Scottish and English settlers of anglophone Canada who were predominantly Protestant. Paradoxically, though, Quebec also has been a bastion of secularism as modeled on post-revolutionary France, with a strong commitment to  laïcité . Politically, Quebec has embraced many progressive values and in some ways moved Canada to the left, especially on social issues. It has also contributed to Canadian...

There were many consequences as cities grew rapidly in the 1800s. Cities grew for several reasons. Immigrants were coming to the United States, and they settled in the cities. Also, people were moving to the cities from the rural areas in search of jobs and in search of an opportunity to do more things that weren’t available in the rural areas. As the population of the cities increased, problems arose. There was an increase in both crime and pollution. Many factories were located in the cities. This contributed to the pollution. Cities struggled with the disposal of trash because of the increased population. With low paying jobs, there was a lot of poverty. This led to an increase in crime. Other issues existed. Housing was in short supply. Many people lived in tenements, which were overcrowded apartments. Kids weren’t attending school. As a result, they often got into trouble. Political machines formed to help the poor people. The political machines were corrupt, yet they eventually c...

We are asked to test the claim that the average wing span is greater than or equal to 64 inches. We have a sample of size 54 with a mean of 62 inches. The population standard deviation is 8 inches. We are asked to test at the 95% confidence level. ` H_0: mu=64 ` This is the null hypothesis and the claim. `H_1: mu < 64 ` This is the alternative hypothesis. Since the alternative hypothesis is one-tailed, we find the critical value z such that the area to the left is .05. From a standard normal table or technology we find the critical value to be -1.645 and the critical region to be z<-1.645. (Some texts will use 1.64 or 1.65 here.) We compute the test value: `z= (62-64)/(8/sqrt(54))~~-1.837 ` Using a standard normal table or technology we get `p~~0.033 ` (My calculator gives `p~~0.0330962301 ` ) Since p=.033<.05 we reject the null hypothesis. There is sufficient evidence to reject the claim that the average wing span is 64 or more inches.

Louisa May Alcott and Henry Wadsworth Longfellow both write about moral heroines who are notable for their sacrifices to others. In Alcott's Little Women , Jo sells her beautiful hair to pay for her mother to visit her father during the Civil War, and her sister, Beth, dies after contracting scarlet fever while tending to a poor family's baby. Longfellow's heroine Evangeline in the poem "Evangeline" follows her beloved, Gabriel, after the British force the Acadians to leave Acadie. She then nurses the poor until she is reunited with her dying lover. The heroines in both writers' works are self-sacrificing people who are committed to altruistic values such as helping the poor, helping their loved ones and family, and disdaining beauty and wealth. These were important values in the time before and after the Civil War, as "Evangeline" was published in 1847, and Little Women was published in 1868. In addition, their heroines are strong and independent i...

`3^(3x-7)=81^(12-3x)` To solve, factor 81. `3^(3x-7)=(3^4)^(12-3x)` To simplify the right side, apply the exponent rule `(a^m)^n=a^(m*n)` . `3^(3x-7)=3^(4*(12-3x))` `3^(3x-7)= 3^(48-12x)` Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right. `3x-7=48-12x` `3x+12x=48+7` `15x=55` `x=55/15` `x=11/3` Therefore, the solution is `x=11/3` .

During Romanticism, a literary movement in Europe from about 1800-1850, the idea of the hero or saint changed to emphasize the qualities of introspection and insight over bravery and action. The Romantic hero, who appeared in works by Goethe, Byron, and others, is largely alienated and isolated from society, and the hero is often engaged in a melancholic reflection on his or her flaws or failings. As a result, the Romantic hero often leads a solitary existence and feels more comfortable in nature than in society. The Romantic hero is quite different than the earlier epic hero, including figures such as Odysseus or Beowulf, as the Romantic hero does not find a place within society but is alienated and apart from it. Goethe's Werther in The Sorrows of Young Werther is the quintessential Romantic hero, as he is forever sad about not winning the love of Charlotte, who is engaged to marry another man. Realizing that he will be forever bereft, he decides to kill himself with Charlotte...

Distillation is a process by which a solution is heated, thereby utilizing evaporation to separate a liquid solvent and solid solute. A common type of solution is an aqueous solution, wherein a solute is dissolved in a water solvent. Saline sea water is an example of an aqueous solution that is processed through distillation to obtain the solute of NaCl, or salt.  What if you were a commercial producer of sea salt who wanted to determine if a petroleum oil spill has contaminated your supply? It would be impractical to drain a large amount of a body of water for large-scale distillation and analysis. The resources to perform the process may be expensive, and you would want to protect your crew from this potential hazard. In this case, selecting small samples of water and performing chromatography to determine the elemental composition would be more effective. A gas chromatographic machine will evaporate the liquid sample, allowing the machine to analyze the chemical characteristics and ...

To evaluate the given equation `log_2(x-4)=6` , we may apply the logarithm property:  `a^(log_a(x))=x` . Raised both sides by base of `2` . `2^(log_2(x-4))=2^6` `x-4=64` Add `4` on both sides to isolate x. `x-4+4=64+4` `x= 68` Checking: Plug-in `x=68` on `log_2(x-4)=6` . `log_2(68-4)=?6` `log_2(64)=?6` `log_2(2^6)=?6` `6log_2(2)=?6` `6*1=?6` `6=6`   TRUE There is no extraneous solution. The `x=68` is a real solution for the given equation `log_2(x-4)=6` .

In A Gathering of Old Men, although slapping Janey is rather cruel, Miss Merle realizes that the servant is hysterical and she needs answers from Janey immediately. In the beginning of Gaines's novel, the conflict is established early on as the Cajun farmer Beau Boutan lies dead, having been shot by Mathau. This situation is dire because the Boutan family has a history of violence and Beau is white and Mathau is black. Candy Marshall is white and from the family that once owned the former plantation; nevertheless, she claims she has shot Beau in order to protect Mathau, who has been like a father to her. In Chapter Three, Myrtle Bouchard (also called Miss Merle) has a pie made so she can take it to the Marshall's house where the Major resides. After she arrives at the Marshall home, she observes that the servant Janey has been crying. When Janey tells her about the murder, Miss Merle tries to awaken the drunken Major on the porch, but he is passed out. As a result, she drives a...

The Parson and the Plowman both seem too good to be true, but Chaucer does not seem to be painting their characters with a satirical brush. Chaucer included several misbehaving ecclesiastical characters (the Monk, the Friar, the Pardoner) to point out that the Church in medieval England was not perfect by any stretch of the imagination.  However, the Parson seems to be exactly what he is supposed to be:  a humble servant of Christ.  He is poor, but when he has a small amount of money, he gives it to those in greater need.  He is very concerned about being a good role model and is concerned that "if gold rust, what shall iron do?"  He is compared to a shepherd, thus tying him to the Biblical description of Jesus as "the good shepherd."  There seems to be no satire when Chaucer says, "I think there never was a better priest." The Plowman is also an admirable character, especially when considering that his job is to haul manure.  He is the Parson's brothe...

There are some common misconceptions regarding evolution that I think may have prompted your question. The first misconception is that humans evolved "from" apes or monkeys. The truth is that humans are a kind of ape, although a relatively hairless variety, and we are essentially evolutionary "cousins" to other apes rather than the evolutionary "grandchildren." All existing species of apes descended from a common ancestor, and before that there was a common ancestor which gave way to monkeys  and apes.  The second misconception I believe to be at work here is the common opinion that humans are the ideal form. Some people feel that humans are the best species to ever have existed, and that some day, all existing species will give way to human-like forms. I will explain more in just a moment about how this is not even possible, but for now I would like to mention that it is  teleological.  Teleology assumes that all changes are in a certain direction, with ...

At the beginning of the story, Nadine Gordimer gives the frame story. She tells the reader that she has been asked to write a children's story for an anthology. Initially, she does not accept the offer, replying that she does not write children's stories. She doesn't like the idea that she "ought" to write something. However, her creaking house and worries about crime in the area prevent her from going back to sleep. So, she begins to tell herself a bedtime story. This is to be the so-called children's story that she mentioned earlier. This is her children's story within the frame story.  Sticking with the traditional fairy tale form, she uses phrases like "once upon a time" and "happily ever after." She describes a family in a crime-ridden town, similar to her own. In order for them to "live happily ever after," they continue to improve the security of their home. Eventually, a once simplistic home becomes more like a prison ...

First, we should say that the nineteenth century represents a very long time, and women's rights changed a lot during that period. Second, since your question does not say what country, if any, you are specifically referring to, I will address women's rights in the United States. In that country, women's rights underwent significant changes throughout the nineteenth century, though women never really received what could be called equal treatment. Early in the nineteenth century, women effectively surrendered their legal identity to their husbands when they married. They gave up their property, could not sue for divorce in most states, and were essentially regarded as "covered" legally by their husbands. Except for an early nineteenth century constitutional anomaly in New Jersey that was was closed after women sought to exploit it, women were not allowed to vote anywhere in the United States until a handful of new western states extended the franchise to women near...

Throughout the novel, Chinua Achebe characterizes silence as being ominous and negative. In Chapter 7, Okonkwo and the boys work in "complete silence" until the locusts descend onto the village. Shortly after, Ezeudu tells Okonkwo that Umuofia has decided to kill Ikemefuna. When Okonkwo receives the news, he tells Ikemefuna that he will be taking him home but does not say a word to Nwoye. The next day, the men of the village begin their journey with Ikemefuna. Achebe writes, "A deathly silence descended on Okonkwo's compound" (58). As the group of men travel nearer to the outskirts of Umuofia, they become "silent." As they continue their journey, Achebe describes their surroundings and writes, "All else was silent" (58). The silence provides an ominous mood before Okonkwo kills Ikemefuna. Later in the novel, Obierika travels to visit Okonkwo and tells him that the village of Abame has been wiped out by white men. Obierika tells him that the ...

Entrepreneurship is now such a popular buzzword that its actual meaning can get lost in the conversation. An entrepreneur is someone who starts a new business. While contractors and freelancers get paid for their own work, an entrepreneur invests money (either their own money or investors' money) in building a business that scales up and uses labor other than their own. The difference isn't simply size of the business. A solo freelance graphic designer with a few assistants might have a larger revenue than an entrepreneurial firm that uses artificial intelligence to create company logos, but they are still structurally different. The development of an entrepreneurial firm is usually described as "scaling". Often it begins with the work of a few employees for a limited client pool, but will depend for its success on having a business plan that can grow rapidly to become a significant player in a particular niche. As such businesses grow, they will often change structur...

When an individual consumes food or beverages, they must pass into the esophagus from the throat, in order to enter the digestive system. However, the windpipe (trachea) is in the same area and if food should enter there, it could block the pathway of air to the lungs. The epiglottis is a cartilaginous flap of tissue that covers the larynx and prevents food from entering the windpipe when swallowing.  It is located behind the tongue and in front of the larynx. When swallowing, it covers the entrance to the larynx. When a person is breathing, it is upright so that air can easily pass into the respiratory system.  If the epiglottis becomes inflamed due to infection or injury, it can be very harmful to the individual. They may have difficulty with breathing or swallowing. This condition is known as epiglottitis. I have included a link showing a diagram of the location of the epiglottis. 

Given to solve , `int 1/sqrt(16-x^2) dx` using the Trig substitutions for `sqrt(a-bx^2)` `x= sqrt(a/b) sin(u)` so for , `int 1/sqrt(16-x^2) dx` --------(1) so , `x` can be `x= sqrt(16/1) sin(u)`  = `4sin(u)` => `dx = 4cos(u) du` so,for (1) we get `int 1/sqrt(16-(4sin(u))^2) (4cos(u) du)` =`int (4cos(u))/sqrt(16-16(sin(u))^2) du` =` int (4cos(u))/(4sqrt(1-sin^2(u))) du` = `int (4cos(u))/(4sqrt(cos^2(u))) du` =  `int (4cos(u))/(4cos(u)) du` =` int (1) du` =` u+c` but `x= 4sin(u)` => `x/4 = sin(u)` => `u = arcsin(x/4)` so , => `u+c` = `arcsin(x/4)+c` so , `int 1/sqrt(16-x^2) dx = arcsin(x/4)+c`

Research shows that there are differences in breathing capabilities between men and women ( PubMed ). The rate of breathing is mostly determined by the heart and the lungs. The lungs are responsible for taking in oxygen, which is then bound to the red blood cells and pumped by the heart to the rest of the body through an intricate network of capillaries, veins, and arteries. The reverse occurs when carbon dioxide is expelled from the body. Men are capable of achieving a higher heart rate than women. This affects the amount of oxygen the lungs and heart can deliver to the body. In addition, men have a larger heart and lung capacity compared to women. Under strain, for instance, during physical exercises, the breathing capacity in women is limited compared to that of men. Thus, the input and output with regards to breathing are different between the sexes largely due to structural and functional distinctions.

"By the Waters of Babylon" is set sometime in the future. The date is never specified, but it has to be a  long time in the future. During the story, readers will learn about a "Great Burning" that happened. We also learn that at some point before the story begins, simply touching metal meant certain death. A cataclysmic nuclear disaster or war would explain a great burning. Metal that is full of harmful radiation would have the power to kill as well. The story takes place far enough into the future where that harmful radiation is gone. Additionally, nobody remembers exactly what the Great Burning was. Nobody remembers huge cities of people. A lot of time has passed.   As for a physical location, the story begins just west of present day New York City. Readers are told John travels east for eight days before finally seeing the Place of the Gods (New York). John explores the former New York City for a bit and then returns to his village.

Given to solve, `lim_(x->5^(+)) sqrt(25-x^2)/(x-5)` Removing the negative form the denominator we get = `- lim_(x->5^(+)) sqrt(25-x^2)/(5-x)` = `- lim_(x->5^(+)) sqrt(5^2-x^2)/(5-x)` = `- lim_(x->5^(+)) sqrt((5-x)(5+x))/(5-x)` = `- lim_(x->5^(+)) sqrt((5+x)/(5-x))` =`- [(lim_(x->5^(+)) sqrt((5+x))]/ [lim_(x->5^(+)) sqrt(5-x))]` = `- sqrt(5+lim_(x->5^(+)) x) /sqrt(5-lim_(x->5^(+)) x)` as `x->  5^(+)` ,then the denominator tends from 0 to `-1` . so, `lim_(x->5^(+)) sqrt(25-x^2)/(x-5)=oo`

Social media allow us to create, share, and exchange information with others through electronic networks. In order to describe this activity and its influence as a conversation among four people, it may help you to think of three friends or relatives you are close to. What subject or event would the four of you talk about over social media? It could be about the U.S. presidential campaign, about weather-related issues or disasters, or about something good or bad that happened at school. Think first of the subject, then think how each of the four of you would react to it. Even if you don’t participate in social media in real life, imagine the kinds of messages you would exchange with your friends about the subject if you were in different places and couldn’t talk in person. Write the messages as separate lines for each person’s response after their first names. (For example: "John: I can’t believe this just happened!") The challenge with social media is to figure out what is t...

"A Horse and Two Goats" is a story by Indian author R. K. Narayan. Its main focus is cultural insularity and miscommunication. Although some of the effect of this is comic, it also raises some serious points about the harm that such insularity does to both India and the colonial powers attempting to govern India and help India's development.  Both Muni and the American do not know each others' languages and thus have difficulty understanding one another. Muni therefore thinks that the American is trying to buy his goats, while the American thinks that Muni is selling him the statue. If we look at the story more analytically, though, we find that it addresses more complex issues. First, as Muni is a poor villager, as readers, we feel that he is justified in having little knowledge of American culture, but we also think that the American, who traveled to India, and is intent on bringing back souvenirs to show off his sophistication, should be more sensitive to Indian cu...

One of the themes of the story is the possibility of redemption, especially for sinners. The baby in the story, christened Thomas Luck, is born from Cherokee Sal, a prostitute. After Sal dies in childbirth, the men at the camp are redeemed by taking care of the baby. They give him a christening, and, as Harte writes, "Soon after the ceremony, Roaring Camp began to change." The proprietor of the store where the men play cards decides to install rugs and mirrors, and the rowdy and disheveled men, seeing themselves in the mirrors, decide to care for their hair, beards, and clothes. They keep their voices down in the camp so that the baby can sleep, and the camp becomes a place of serenity. When a flood courses through the town, the baby is sadly killed, and Kentuck, who cared for the baby, is mortally injured. He goes out to sea, taking the baby with him--a symbol that he brings the luck and redemption he has achieved with him to his demise. Another major theme of the story is t...

One of the symbolic meanings to Pirandello's short story is how war is the source of endless pain. Pirandello's short story shows how there is nothing restorative in war. The small train carriage is filled with people who will never experience the battlefield. However, they all experience the hurt intrinsic to the war experience.  The justifications behind war do not alleviate any of their pain.  The mother who sends her son to the front can find no solace in his departure.  The other passengers on the train are more interested in displaying how their pain is worse than anyone else's.  The passenger who enters and speaks with authority might be the only one who shows a conviction about the necessity of war.  When he talks about "good boys" who leave to "serve their country," it galvanizes the other passengers. When he speaks of the message in his son's final letter, it provides a temporary relief from war's pain.  This is undercut with the mother...

In  Paper Towns,  John Green is arguing that we often misinterpret other people and that identity (particularly in adolescence) is a fluid, ever-changing phenomenon in a person's life.  This is quite apparent in the book with Quentin's changing ideas about Margo. In Quentin's mind, Margo continues to exist, much unchanged, as she did when they were children. The "love" that he feels for her is really love towards a perception he has of her that isn't real. Quentin realizes this at the end of the novel and gives up his relentless pursuit of her.  This idea about the divide between reality and perception is further encapsulated in the title and one of the motifs throughout the book: paper towns. Paper towns are fake towns printed on maps to prevent plagiarism; they seem to exist when you are looking at the map but are, in fact, not real. However, that part of the map still exists; it's just that you won't find what you expected when you get there.  Quent...

The narrator adopts an ironic attitude towards this mighty king for having been knocked off his pedestal--and through Ozymandias, sends a warning all tyrants. He feels a certain contempt for the bragging and egomania in Ozymandias. The poem goes as follows: the narrator meets a traveller who has seen the statue of a once mighty ruler in the desert. Now it is just two legs standing up. The face, called the "visage," lies shattered on the ground, where the traveler see its "sneer of cold command." "Sneer" is an especially derogatory term.  On the base of the statue, the following words appear:  'My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair!' But none of these works remain. The desert is completely empty, except for sand. The narrator is calling on "the mighty" to despair, because their delusions of grandeur will also be reduced to this. Like Ozymandias, none of them are as great as they think they are. In t...

One of the main themes in this novel is the absurd way in which the Partition of India was carried out in 1947 to create India and Pakistan. The main character, Lenny, lives a privileged life in Lahore, so she finds herself suddenly becoming Pakistani as India is divided into India and Pakistan. The Partition process is accompanied by ethnic violence, and ethnic and religious strife is also one of the themes of the book. Another main theme is the treatment of women and the intersection of gender and class. Ayah, Lenny's beloved nanny with whom Lenny spends most of her days, is a seductive lower-class woman who exercises a great deal of sexual power in a society that often demeans women. In fact, Ayah's suitors are Muslim, Hindu, and Sikh, showing the power of her seduction to smooth over ethnic divides. It is through Ayah that Lenny, from a wealthy family, learns about the ways in which women in other classes live. Ayah is abducted and raped, and she is forced to marry a man sh...

Although women sometimes appeared in morality plays of the middle ages or in court masques, they were forbidden by law to perform on stage in commercial plays such as those staged by William Shakespeare at the Globe Theatre. The theater at the time was sometimes considered immoral and for women to perform would have been scandalous. Therefore, the women's parts in Shakespeare's plays were portrayed by boys and men. From 1642 to 1660 the theaters in London were closed during the Puritan reign of Oliver Cromwell. It wasn't until the restoration of King Charles II that theaters reopened and women were finally given permission to perform on stage. The first known female performance came at Thomas Killigrew's Vere Street Theatre in 1660 as a woman, possibly an actress named Anne Marshall, played Desdemona in Othello . One of the most popular actresses of the time was Nell Gwynn, also a mistress of the king. Maybe the most famous Shakespearean actress was Sarah Siddons who wa...

The South called the election of Lincoln a farce.  Lincoln got so little support in the South that he was not even on many Southern ballots.  Southerners saw the election of Lincoln as proof that the North was growing more powerful and at some point in the future would vote to do away with slavery.  Even Southerners who did not personally own slaves had bad feelings about this because there was the question of what to do with all of the freed slaves.  Tensions were quite high in 1860, and part of the campaign to elect Lincoln was quite militant in nature--the Wide-Awakes held military-style torchlight parades at night.  While this was meant to excite the electorate, some radical Southerners feared that the North would seek to create a tyranny over the South and change its longstanding institutions if Lincoln were elected.  It should also be remembered that Lincoln was elected with a minority of the popular vote.  While this has happened before in American history, Southerners pointed o...

In Act 1, Scene 4 of Macbeth, King Duncan meets Macbeth for the first time since the great battle. Duncan expresses his boundless gratitude for Macbeth's indispensable help against the enemy and concludes by saying, rather ironically: Only I have left to say, More is they due than more than all can pay. This is ironic because the audience knows full well that Macbeth is thinking of taking everything away from Duncan. It is almost as if Duncan knows Macbeth's intentions and is unconsciously giving him permission to do it. Macbeth's reply is loaded with irony. He tells the King: The service and the loyalty I owe, In doing it pays itself. Macbeth is saying just the opposite of what the audience knows he is thinking. 

`lim_(x->1) (x^11-1)/(x^4-1)` To solve, plug-in x = 1. `lim_(x->1) (x^11-1)/(x^4-1) = (1^11-1)/(1^4-1) =0/0` Since the result is indeterminate, to determine the limit of the function as x approaches 1, apply L'Hopital's Rule. To do so, take the derivative of the numerator and denominator. `lim_(x->1) (x^11-1)/(x^4-1) = lim_(x->1) ((x^11-1)')/((x^4-1)') = lim_(x->1) (11x^10)/(4x^3) = lim_(x->1) (11x^7)/4` And, plug-in x=1. `= (11*1^7)/4 = 11/4` Therefore,  `lim_(x->1) (x^11-1)/(x^4-1)=11/4` .

There seems to be a discrepancy in your question: if `x >=1` , then the limits of the integral should be 1 and infinity. This means it would be an improper integral and it would not converge (as you will see after we take the integral). I am going to take the indefinite integral - without the limits - and the appropriate limits can be plugged in later. Before taking the integral, let's simplify the radical expression under the radical: `sqrt(1 +1/x^2) = sqrt((x^2+1)/x^2) = sqrt(1+x^2)/x` . The integral then becomes (omitting the coefficient of `2pi` for now): `int sqrt(1+x^2)/x^2 dx` . Notice that it contains the radical expression `sqrt(1 + x^2)` . The traditional way to take such integrals is by using trigonometric substitution `x = tant` . Then, `dx = sec^2tdt` and `t = arctanx` . The advantage of this substitution is that it allows to simplify the radical expression using the trigonometric identity `tan^2t + 1 = sec^2t` . `sqrt(1+x^2) = sqrt(1+tan^2t) = sqrt(sec^2t) = sect` ...

In the discipline of rhetoric, repetition and restatement are staples, and Jonathan Edwards makes great use of both in this iconic sermon from 1741. Accomplished orators and students of rhetoric understand that the first and last things a speaker says are usually what stay with an audience; this phenomenon is known to educators as "primacy" and "recency." Edwards's thesis was, of course, that sinners who did not act quickly to reform themselves faced an agonizing afterlife in the fires of hell, where God's wrath would hurl them for their impiousness.  In the last paragraph of the sermon, Edwards use the word "fly" twice to describe what sinners must do: escape God's wrath and (metaphorically) leave Sodom.  He uses the words "every one" twice to emphasize that no one in the congregation should feel complacent about their salvation.  And lastly, Edwards uses the word "wrath" twice to hammer his point home: God is angry with al...

John Donne is a clever poet who uses what is called a metaphysical conceit to woo his mistress. He tells her that as a flea has bitten both of them, their blood has already been mingled, making her protestations against sleeping with him void and useless. While this type of approach from a man to a woman could be seen as objectionable in today's world, Donne is worthy of studying and reading today in part because of the cleverness of his conceit and of his argument. In addition, people today still seek arguments to convince other people to date them and pursue romantic relationships with them. Many of these arguments are far feebler than that of John Donne, so it is worthwhile looking at how he pleads his case. Reading John Donne's poem also reminds us that the relationships of his time were not that different from the relationships of today and that there are continuities in the way that people approach each other romantically. 

The electric resistance of a material is a property that represents the opposition to the passage of the electric current. From the microscopic point of view the resistance depends on the atomic structure of the material. From the macroscopic point of view, the resistance depends on the linear dimensions of the material. The value of the resistance of a wire can be calculated using the following expression: R = ρL/s Where: ρ, is the specific resistance which is related to the material; also has a temperature dependence. L, is the length of the wire. S, is the area of cross section of the wire. For a circular cross section wire, we have: R1 = ρL/πr1^2 = (4ρL)/(πd1^2) If the diameter is halved, we have for the resistance: R2 = (4ρL)/[π(d1/2)^2] = (16ρL)/(πd1^2) By comparing the values of resistance: R2/R1 = (16ρL/πd1^2)/(4ρL/πd1^2) R2/R1 = 16/4 = 4 R2 = 4R1 So, the resistance increases four times.

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 ...

Because the field of artwork is broad, I will focus on painting. There are many ways in which medieval painting differed from that of the Renaissance, which is what makes the latter period so important as an era of innovation. First, nearly all medieval painting is religious in its subject matter. A great deal of Renaissance painting is, too, but more liberties are taken in the portrayal of the icons. Renaissance painters individualized the figures, allowed them to emote, showed the natural movement of the body, and often depicted subjects according to classical standards of beauty. Medieval iconography is less inspired and quite redundant.  Moreover—and this leads to the second major difference—there is no depiction of perspective in medieval painting. The figures appear flat and two-dimensional. Vanishing point perspective developed during the Renaissance. With this technique, a set of parallel lines are perpendicular to a picture plane, drawing one's eye to a single point in spa...

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Sociological approaches to literature can be divided into two types with two different purposes: 1. Some sociologists mine literature and other arts to discover the ways people think about society. For example, by reading novels or watching films, one can observe what sort of consumer or other habits are considered markers for prestige within various societies. Such sociologists as Pierre Bourdieu (and earlier, Thorstein Veblen) investigate cultural consumption as a way of understanding various societies. 2. Some literary critics focus on how social factors affect the production and consumption of literature. In other words, unlike the sociologists described in (1) who read literature to understand society, literary critics study society to understand literature better. Thus Marxist and feminist critics will often investigate how class and gender affect writers' lives and reputations as well as the ways that characters in literary works behave and think. 

Rolf and Azucena share a dynamic relationship in “And of Clay Are We Created” by Isabel Allende. Originally, when Rolf arrives at the site of the mudslide he is working as a reporter for a major news outlet, but he leaves a changed man. He locates Azucena, the little girl partially buried in the clay. While observing her situation, he realizes her situation is not just a story to be covered as a job. He knows he must stay with her and facilitate her rescue. At first he frantically tries to get aid for her, but as time passes he realizes he has become an emotional support system for the girl. As night falls, she pleads with him to stay with her. “Don’t leave me alone,” she begged. “No, of course I won’t leave you.” During the hours the two spend together, they connected. The little girl demonstrated her bravery as she faced increasingly dire circumstances. As Rolf observes Azucena’s strength, he changes from her support system to a man who bravely faces his difficult past. This is somet...

Absolutely, the imagery enhances the meaning of the story and, therefore, a reader's understanding of it.  The imagery concerning the seven rooms of the abbey where Prince Prospero and his friends hide from the Red Death is particularly rich.  In order from east to west, the rooms are draped in blue, then purple, then green, orange, white, violent, and, finally, black and "blood" red.  Because these rooms are ordered from east to west, the direction from which the sun rises and the direction in which it set, they could be understood to symbolize the span of a human life (just as the space of a day does: sunrise = birth, sunset = death).   Further, the idea that death is represented by the final room of black and red is supported by the symbolism of the ebony clock.  Black is often used to represent death (as is red in this story, since the plague's "Avatar and its seal [is] the redness and the horror of blood), and clocks are also often symbols of mortality.  The...

The first question is extremely broad. On that very general level, one can say that some civilizations subsist by hunting and gathering. These migratory groups tend to stay in small bands rather than forming large groups because hunting and gathering can only support low population densities. Due to their migratory nature, they develop little in the way of technology. Other peoples undergo the "neolithic transition", learning how to domesticate plants and animals. This more efficient food production is the precondition for urbanization. Agriculture produces a food surplus, meaning that classes of artisans develop who improve technology. Large urbanized cultures require laws and complex political organization. The Code of Hammurabi strove towards justice as it would have been understood in ancient Mesopotamia. It emphasized the duty of the king to protect the weak, the poor, and widows and orphans, and to act fairly. It created fixed punishments for various sorts of crimes. As...

The bad behavior of Laurie in the exposition of the story "Charles" foreshadows the way in which he will conduct himself at school. For, it is apparent that he is undisciplined. Laurie's willfulness and disrespect is suggested in the verbs  renounced and swaggered  when the mother narrates that the boy decides on his own to dress in blue jeans and a belt rather than his usual overalls with bibs. Then, too, he walks with an older girl to school without even waving good-by to his mother. After the school day is finished, Laurie returns home in "the same way" that he has departed. He lets the door slam behind him and in a "raucous" voice Laurie shouts, "Isn't anybody here ?" While the family has lunch, Laurie speaks "insolently to his father" and he knocks over his baby sister's milk. He tells his parents "not to take the name of the Lord in vain." This statement, of course, indicates that Laurie must have cursed and...

Antigone shows her strong-willed nature throughout the play, never wavering in her resolve to do the right thing. She is willing to die for what she believes in and won't give in or allow anyone to sway her with illogical arguments. In the beginning of the play, she approaches her sister Ismene to ask for Ismene's help burying their brother Polyneices. Ismene refuses due to her fear of disobeying authority, especially when that authority is male. Antigone replies: ANTIGONE: If that is what you think, I should not want you, even if you asked to come...  But I will bury him; and if I must die, I say that this crime is holy: I shall lie down With him in death, and I shall be as dear To him as he to me.  She expresses her belief in the innate sanctity of her decision to bury Polyneices. Antigone believes she is following the laws of the gods and allowing her brother's spirit to journey into the next world, and she will not allow the king's law to stop her, even if it means ...

Hitler was able to conquer much of Europe very quickly as he expanded Germany’s territory. There were reasons why he was able to accomplish this. Germany was able to move through Europe very fast. Austria, Czechoslovakia, and Poland all fell into Germany’s hands before the war began. Part of the reason why this happened was that the Allies were so busy dealing with the effects of the Great Depression, they ignored Germany’s initial aggressive actions. When Germany began to build up their military and move it into the Rhineland, no action was taken. The same thing occurred when Germany annexed Austria. When the Allies gave part of Czechoslovakia to Germany with the Munich Pact, and when Hitler broke that agreement by taking the rest of Czechoslovakia, people knew that war was likely. That occurred when Germany invaded Poland. Hitler had built a strong German military. Most of the countries in Western Europe weren’t prepared to deal with this lightning-fast moving military. German airpla...

Our Earth has two distinct motions: rotation and revolution. Earth rotates on its own axis and this motion is known as its rotation. Earth also moves around the Sun and this motion is known as its revolution. Earth undergoes both motions simultaneously. It is the Earth's rotation that is responsible for day and night on the planet. We experience day time when our geographical region is facing the Sun and when it is not (due to Earth's rotation), we experience night time. Earth takes about 24 hours to complete one rotation and hence our days are 24 hours long.  The revolution of Earth around the Sun, along with Earth's axial tilt, is the reason we have seasons. Earth takes about 365 days to complete one revolution, which is also the length of our year. Hope this helps. 

In general, spiders produce webs to catch prey because it is an efficient method for them to gather food. They may also serve to protect the spider from predators. They make the webs by producing silk, a sticky substance which is produced from their spinneret glands located at the tip of their abdomen. Spiders have a variable number of spinneret glands depending on their functions, but most spiders have three pairs. There are spiders with only one pair while others have up to four pairs of spinneret glands. Each of the spinneret glands generates silk for different purposes. The silk produced to catch prey tends to be sticky, while that used to wrap the prey tends to be finer in texture. Some spiders may produce as many as seven or eight different types of silk in their lifetime. The silk produced from the spinneret glands is made out of protein and it is used in spinning the spider’s web. This is an energy-consuming process which requires large amounts of protein to achieve. The spider...

To find a tangent line to a polar curve,`r=f(theta)` we regard `theta` as parameter and write it's parametric equations as, `x=rcos(theta)=f(theta)cos(theta)` `y=rsin(theta)=f(theta)sin(theta)` We are given the polar curve `r=asin(theta)` Now let's convert polar equation into parametric equation, `x=asin(theta)cos(theta)` `y=asin(theta)sin(theta)=asin^2(theta)` Slope of the line tangent to the parametric curve is given by the derivative `dy/dx` `dy/dx=((dy)/(d theta))/((dx)/(d theta))` Let's take the derivative of x and y with respect to `theta` `dx/(d theta)=a[sin(theta)d/(d theta)cos(theta)+cos(theta)d/(d theta)sin(theta)]` `dx/(d theta)=a[sin(theta)(-sin(theta))+cos(theta)cos(theta)]` `dx/(d theta)=a[-sin^2(theta)+cos^2(theta)]` `dx/(d theta)=a(cos^2(theta)-sin^2(theta))` use the trigonometric identity:`cos(2theta)=cos^2(theta)-sin^2(theta)` `dx/(d theta)=acos(2theta)` `dy/(d theta)=a(2sin(theta)d/(d theta)sin(theta))` `dy/(d theta)=a(2sin(theta)cos(theta))` Use the trig...

Throughout the novel, Golding suggests that absolute power is corrupting and dangerous by depicting Jack's tyrannical leadership over his group of savages. After Jack usurps power from Ralph, he immediately begins to use fear as a means of controlling his tribe. He perpetuates the belief in the "beast" by sacrificing the severed pig's head and mentions that the "beast" has the ability to shape shift. The more Jack's power increases, the more ruthless he becomes. Jack begins to punish boys who disagree with him or do not follow his orders, and encourages violence. Once Jack realizes that he is in complete control over his tribe, he orders his savages to capture Samneric and commands them to hunt Ralph. Golding suggests that absolute power is dangerous and the individuals who are under the control of a tyrant are subjected to violence and oppression.

When Jem and Scout find the two soap dolls in the Radley's tree, Scout's first reaction is fear. She believes they are "hoo-doo" (voodoo) dolls, screams, and throws them. Jem retrieves the dolls and begins looking between the female soap doll and Scout's hair, noticing that both have bangs. Jem realizes before Scout does that the dolls are miniature representations of the two of them, and his reaction causes Scout to realize the same. Boo Radley left the soap dolls in the tree as a gift to the children, and it serves as evidence that he had been closely observing them, enough to perfectly reproduce their haircuts and clothing. Jem is the first to realize that the soap dolls represent him and his sister, and this realization proves to the two that the gifts in the tree are actually intended for them.

The idea of the "best" college is a little difficult to determine. Websites like U.S. News and World Report provide annual rankings of universities and colleges in the United States (linked below). However, that site's ranking methodology has been critiqued as not fully considering some factors students may care about and over-weighing others to the point that colleges and universities can try to spend money in certain areas of the school to "game the system" and increase their rankings. To determine the best colleges and universities for you, it is important to determine what you care most about in an educational experience and as a person. Do you want small classes? If so, you should look at institutions' faculty-to-student ratios. The size of the college may also be important for you to consider. Some people like the closeness that is often felt by students of smaller schools, while others believe more opportunities are available when there are more stude...

When Montague first arrives in Act V, Scene 3, he laments, Alas, my liege, my wife is dead to-night; Grief of my son's exile hath stopp'd her breath: What further woe conspires against mine age?   Not only has Montague had to endure what no father should—outliving Romeo, his only child—but now in this tragic time he must also bury his wife. She has died of a broken heart over Romeo's death. If that much grief has killed her, imagine what incredible pain Montague must be experiencing.   On top of the pain of losing his whole family, Montague surely must feel a great deal of guilt. After all, his stubborn hatred and feud with Lord Capulet indirectly led to the two lovers’ deaths, as the Prince suggests when he says, Capulet! Montague! See, what a scourge is laid upon your hate, That heaven finds means to kill your joys with love. If Montague is partly responsible for Romeo’s death, that means he is partly to blame for the death of Lady Montague, too. There are layers upon lay...

The reader can certainly sympathize with Buck when he goes from his privileged and easy life with the Judge to the rough and tumble life of the trail. Buck developed the ego to go with his unofficial position as the king of the estate, but when he is stolen and taken away by the gardener, it is easy to feel sorry for him as he learns to deal with physical abuse and the privations of the trip north. It is also easy to sympathize with Buck because he lives with a sense of justice and fairness that is appealing to the reader. He makes mistakes but learns quickly and there is a sense that the brutality and violence of the dogs in the Yukon is a reflection of the harsh reality of life there for humans as well.  Because Buck becomes a ruthless killer, it can also be necessary  not  to sympathize with him, even if the conditions seem to justify his ruthless and brutal actions. Buck also begins to separate himself from the world of men and the loyalty to instinct overcomes his loyalty to manki...

Jing-Mei's mother wants her daughter to retain the customs and traditional female roles particular to Chinese culture. She wants to mold Jing-Mei in this way, but also with just enough American influence to promote and encourage Jing-Mei to become a typical American success story. There is nothing wrong with trying to instill an awareness of her old and new cultural influences in a child, but Jing-Mei's mother is too controlling. This idea of molding Jing-Mei clashes with the American ideals of individuality and self-reliance. Growing up in America, Jing-Mei has more of that cultural influence of individuality than her mother does. She doesn't resent her mother for encouraging her to succeed. She resents her mother for controlling her life and attempting to mold her (Jing-Mei's) personality. Jing-Mei is making the shift from obedient daughter to a more self-motivated young woman. This is the shift from one "kind" to another. When her mother gives her an ultima...

Maclaurin series is a special case of Taylor series that is centered at `a=0` . The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n`  or `f(x)= f(0)+(f'(0)x)/(1!)+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +...` To determine the Maclaurin polynomial of degree `n=5` for the given function `f(x)=e^(-x)` , we may apply the formula for Maclaurin series.. To list `f^n(x)` , we may apply derivative formula for exponential function: `d/(dx) e^u = e^u * (du)/(dx)` . Let `u =-x` then `(du)/(dx)= -1` Applying the values on the derivative formula for exponential function, we get: `d/(dx) e^(-x) = e^(-x) *(-1)`                      `= -e^(-x)` Applying `d/(dx) e^(-x)= -e^(-x)`  for each `f^n(x)` , we get: `f'(x) = d/(dx) e^(-x)`             `=-e^(-x)` `f^2(x) = d/(dx) (- e^(-x))`            `=-1 *d/(dx) e^(-x)`            `=-1 *(-e^(-x))`            `=e^(-x)`  `f^3(x) = d/(dx) e^(-x)`             `=-e^(-x)` `f^4(x) = d/(dx) (- e^(-x))`  ...

In the story, Amir briefly felt distant from Soraya when she told him the truth about her past, while he was unable to share his past. Soraya told Amir about how in the past she ran away with a man. She was rebellious, and the man was into drugs. Members of her community talked about it, and the situation brought shame to her family. Eventually, her father found her, and she went back home. Amir, on the other hand, thought of telling Soraya about his past, but he couldn’t talk about it and decided to keep it a secret. Amir wanted to tell Soraya of how he betrayed Hassan, how he framed him for theft, which led to the end of a forty-year relationship between his father and Ali. According to Amir, Soraya was better than him because she had the courage to tell him the truth.

At the beginning of the story, the Otis family denies the ghost's existence. In Chapter Two, however, the ghost makes his first appearance and Mr Otis reacts to him in a rather humorous way: he offers him some Lubricator to oil his noisy chains. Later, in Chapter Three, the ghost attempts to scare the family by wearing an antique suit of armour. The family reacts with violence, as though the ghost is an unwanted visitor to the house. Mr Otis, for instance, pulls out his revolver: The United States Minister...called upon him, in accordance with Californian etiquette, to hold up his hands! In this scene, the twins also attack him with their pea-shooters. During his escape, he lets out a frightening groan which prompts Mrs Otis to offer him some tincture for his "indigestion." In contrast, the only member of the family who treats the ghost with any kindness and sympathy is Virginia. She has a conversation with the ghost in Chapter Five in which she learns of his past and his...

Heptonstall is an ancient village in Yorkshire, England, the birthplace of Ted Hughes. Before the Industrial Revolution, it was home to weavers, who had large windows in their dwellings so that the sunlight would brighten the area where they worked. However, as Hughes's poetry demonstrates, humanity cannot truly dominate nature. Furthermore, there is something savage about nature in Hughes's poems. Hughes himself wrote that his poetry exhibited "The collision of the pathos of the early industrial revolution – that valley was the cradle of it – with the wildness of the place." Heptonstall is also where the writer Sylvia Plath, wife to Ted Hughes, is buried. In the first stanza of his poem "Heptonstall," Hughes describes this village where life has long struggled against death. It is black from age and the Industrial Revolution's pollution and dead dreams. A poet who describes his poems "as a sort of animal" ( Poetry in the Making , London, 1967,...

Walter Mitty leads a life that is probably a lot different than the one he thought he would lead at a young age.  He is a devoted family man who probably has a nice desk job, but he desires more adventure in his life.  In the opening scene, he imagines that he is a captain responsible for getting his crew through a storm.  In reality, his wife jolts him back to reality by asking him about his fast driving and telling him to wear his gloves.  In another scene, he is a world-renowned surgeon who is saving lives with fountain pens, when in reality he is annoying a parking lot attendant with his distracted nature.  Mitty likes his fantasy life because it lets him remember what it is like to have masculine dreams of saving the day and being a hero--he feels that this does not exist for him in real life.  

There are a few similarities between Charlotte Bronte's  Shirley  and her novel  Jane Eyre. For one thing ,  there is no doubt that Shirley is a continuation of the discourse on women by Brontë that began with her previous novel. Victorian novels Both novels are classified as Victorian narratives that critique certain aspects of Victorian society and the historical setting. The two novels both fall under the category of the popular “public” novel, as there are characters of various social classes and the narrative informs the reader about the society of the time. Certainly, industrialization is a part of the focus of Shirley but not a concern in Jane Eyre.  Nevertheless, the narrative of Brontë's next novel also involves its plot with class consciousness and the role of women in society, as does Jane Eyre .   Not unlike Jane, Caroline, who is also an orphan, secretly loves a man who is in a higher socio-economic class than she is. Caroline also has an identity crisis, but aft...

Khaled Hosseini's novel  The Kite Runner revolves around the sins and guilt of its protagonist, Amir. In his childhood, and at the beginning of the text, Amir witnesses the rape of his friend Hassan during a kite running contest. Hassan is raped because he refuses to give up Hassan's kite to the local bully when he is running it in the kite running contest. Amir says and does nothing to prevent the rape. In his confusion and shame, he rejects Hassan. Amir lives with this guilt for the rest of his childhood, and it ends up shaping many of his adulthood decisions.  At the end of  The Kite Runner , Amir has rescued Hassan's son, Sohrab, from sexual slavery. This rescue causes Amir significant physical, mental, and fiscal sacrifices. It's not until the final scene, in which Amir runs the kite for Sohrab, that Amir finally redeems himself. By making the decision to assume Hassan's role, Amir absolves himself of his childhood prejudices and sins. 

As a general rule, private industry seems to be more economically efficient than government. It's not entirely clear why this is so (there are some theoretical reasons to support it, but they aren't as strong as a lot of people think), but it is quite clear that it is so — we have seen vividly in countries such as Russia and China how nationalizing industries has suppressed or even reversed economic growth, while privatizing industries has expanded growth. There are certain tasks for which private industry is not well-suited. National defense is the obvious one, and hardly anyone disputes that defense is a service that should be provided primarily or even entirely by the government. In general, there is a case to be made for government involvement if any of the following conditions hold: Public goods: Goods that, once they are made, can be used freely by all; private industry has little incentive to make such goods despite their high value, because if everyone can use them they...

In the novel Half of a Yellow Sun , one of the main characters is Odenigbo, a mathematics professor at the University of Nskukka in Nigeria. Odenigbo is highly intelligent, forceful, and passionate about the Biafran cause.  At the beginning of the novel, we see Odenigbo speaking to his friends about the need for an independent Igbo (Nigerian ethnic tribe) land. As a member of the Igbo tribe, Odenigbo initially supports the Biafran War.  As the story progresses, Odenigbo demonstrates his dedication to the Biafran cause by serving as a minister in the new Biafran government. However, as the Biafran soldiers begin to lose the conflict and the Biafran nation fails, Odenigbo must give up his dream of an independent nation. 

Given to solve , `lim_(x->oo) cosx/x` by applying the squeeze theorem we can solve the limits and it is as follows, as we know the boundaries of the `cos(x)` as `-1<=cos(x)<=1` now dividing the above expression with `x` , we get `-1/x<=cos(x)/x<=1/x` now applying the limits of x-> oo for the above expression, we get `lim_(x->oo) (-1/x)<=lim_(x->oo) cos(x)/x<=lim_(x->oo) (1/x)` now upon `x-> oo` we get `lim_(x->oo) (-1/x) =(-1/oo) =0` and `lim_(x->oo) (1/x) = (1/oo)=0` so, `lim_(x->oo) (-1/x)<=lim_(x->oo) cos(x)/x<=lim_(x->oo) (1/x)` =>`0<=lim_(x->oo) cos(x)/x<=0` =>`lim_(x->oo) cos(x)/x =0`

Curley and his wife are two of the important characters in John Steinbeck's novella Of Mice and Men . They act as antagonists to the main characters of George and Lennie. George and Lennie come to work on the ranch owned by Curley's father. Through the first few chapters, the reader learns very little about the two, except that Curley is often belligerent and ready to fight, and that his wife is derisively described by the working men on the ranch as a "tramp" or a "tart." It is not until Chapter Five that more is revealed about Curley's wife when she is alone with Lennie in the barn. She confesses to Lennie that she is terribly lonely and that she doesn't even like Curley ("He ain't a nice fella."). She also claims that she could have been in the movies and that a man had approached her at the "Riverside Dance Palace" telling her that he could make her into an actress. He offers to send her a letter with details, but she neve...