Notes

In Chapter 1, the master is portrayed as a kind man. He provides the horses with good food and quarters, and he speaks to them kindly--as kindly as he speaks to his own children. Black Beauty's mother is his particular favorite, and he refers to her as "Pet" and provides her with carrots. He treats her so kindly that she neighs happily when she sees him and trots up to him. The master calls Black Beauty "Darkie" and gives him pieces of bread. When the master sees a plowboy named Dick throwing stones at the colts for sport, the master immediately jumps over the hedges and hits Dick in the ear. Then, the master fires Dick and tells him never to return to the farm. Old Daniel, the man who is charged with looking after the horses, is also very kind to them. 

Santiago despises the Portuguese man o' war. The turtles eat these jellyfish, "filaments and all," and this is one of the main reasons he likes the turtles. As an older man who still prides himself on his strength and endurance, he feels a kinship with and has respect for these turtles because they can eat the very poisonous Portuguese man o' war without being injured or poisoned. Santiago respects the marlin he battles with. It is a graceful and powerful animal and he recognizes this. Likewise, he admires the green turtles and hawk-bills for their "elegance and speed and their great value." It seems that Santiago also admires the turtles because they can live to a ripe old age. As an old man himself, they probably give him comfort that a fellow creature can live a long life and still be effective. Just as Santiago respects and relates to the marlin, he has a similar kinship with the turtles. He notes how their hearts still beat after they're killed and ...

In Chapter III of The Great Gatsby (Fitzgerald), we are introduced to the "love nest" of Tom Buchanan and Myrtle Wilson.  And a nest it is, being a very small apartment overcrowded with large furniture that is ill-suited for the space. The apartment consists of a living room, dining room, bedroom, and bathroom, all small. The furniture is upholstered in a tapestried material, with a print of "ladies swinging in the gardens of Versailles" (33).  A photo on the wall that appears from afar to be a hen sitting on a rock turns out to be a photo of an old woman in a bonnet.  Some magazines are on the table, scandal rags and a book called Simon Called Peter , which was a bestseller in the twenties, a kind of commentary on Myrtle's reading level and tastes. The apartment is at 158th Street, on the top floor of an elevator building, an area which seems to be on the verge of gentrification today, but which did not exactly qualify as prime New York real estate at that tim...

Just as Mr. Hyde represents the dark underbelly of Dr. Jekyll, the setting of Victorian London possesses such a duality as well.  On the surface, London is the civilized, cosmopolitan capital of one of the most powerful countries in the world. Society is polite, and high moral standards are firmly in place. This is one reason that Dr. Jekyll feels the need to experiment with his fundamental humanness in the first place.  He has found himself drawn to things -- what those things are we never learn -- that are less than seemly for a morally upright, well-respected doctor. Rather than deal with his own demons or accept himself as humanly flawed, Jekyll decides to try to eliminate his own darkness by separating it from his goodness. The problem?  Once separated, the darker part of his nature actually becomes more powerful than the good. Just like Dr. Jekyll possesses a fundamental human propensity for breaking rules or doing things that would not be socially acceptable, so too does London ...

To ascertain the difference between "good" and "bad" knights in Le Morte D'Arthur, we must look at the standard knights were measured by during Arthur's time. This standard is referred to as the medieval code of chivalry. Today, we think of chivalry as courteous behavior, but in Sir Thomas Malory's time (and in Arthur's as well), chivalry constituted specific behaviors that substantiated a knight's loyalty to his king. For example, you may have noticed that Sir Thomas Malory includes considerable examples of martial prowess in his story. This, by itself, is no accident. A chivalrous knight is a battle-ready warrior at all times, especially in service for his lord. Thus, characters such as Sir Launcelot, Sir Lamorak, and Sir Tristam exemplify the qualities of "good" knights when they engage in violent conflict against the king's enemies. Valor in service of the king constitutes service to God, an honorable work for a chivalrous knig...

If we mean the American, or Trans-Appalachian West, then the reasons were fairly simple. American colonists desired more cheap land so that they could become independent landowners. This was the driving force behind westward expansion ever since the establishment of colonies along the North American coasts, and was a source of constant tension between British colonists and Native Americans. In the mid-eighteenth century, the main destination for settlers was the Piedmont of Virginia and the Carolinas and even as far south as Georgia. Settlers, mostly Scots-Irish, made their way down the so-called "Great Wagon Trail" from Pennsylvania into the region, where cheap land was to be had. In a little over a decade, settlers were already moving into the Ohio River Valley and Kentucky, defying a proclamation from King George III that lands west of the Appalachians were not to be settled. So expansion into the West was more the result of the desires of ordinary colonists (and wealthy l...

In both cases, the British Empire shipped thousands of people across the ocean by force and without their consent, where they ended up establishing a new population on a new continent. In both cases, the process was violent, oppressive, and dangerous to the people being transported. But there are some vital differences between the two. Perhaps the most important is how the people were selected. Africans who were sold into slavery were chosen first of all for their race and skin color, and only secondarily as convicted criminals or prisoners of war (as these were the Africans that were most likely to be sold into slavery by the existing African societies). Prisoners sent to Australia were all convicted criminals, most of them as far as we can tell given legally-valid trials in the British courts of law. (Whether these trials were fair or the laws they were based on were just is a more difficult question.) The Africans who were sold as slaves could have otherwise been free individuals; t...

From the Power Series table for trigonometric function, we have: `arctan(x) =sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1)`                      `= x -x^3/3 +x^5/5 - x^7/7 + x^9/9-...` Applying it on the integral `int_0^(1/2) arctan(x)/x dx ` where the integrand is `f(x)=arctan(x)/x` , we get: `int_0^(1/2) arctan(x)/x dx =int_0^1 arctan(x) *1/x dx`                          `=int_0^(1/2)sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1) *1/xdx`                          `=int_0^(1/2) sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1) *x^(-1)dx`                          `=int_0^(1/2) sum_(n=0)^oo (-1)^n x^(2n+1-1)/(2n+1) dx`                          `=int_0^(1/2) sum_(n=0)^oo (-1)^n x^(2n)/(2n+1) dx`                          `=int_0^(1/2) [1 -x^2/3 +x^4/5 - x^6/7 +x^8/9-...] dx`  Or  `int_0^(1/2) arctan(x)/x dx =int_0^1 arctan(x) *1/x dx`                          `=int_0^(1/2) 1/x* [x -x^3/3 +x^5/5 - x^7/7 +x^9/9-...] dx`                          ` = int_0^(1/2) [x/x -x^3/(3x) +x^5/(5x) - x^7/(7x) +x^9/(9x)-...] dx`            ...

The Integral test says that this sum will converge if and only if this integral also converges:`int_{1}^{infty} x^k e^{-x} dx ` When integrating this, we would use integration by parts, and we would need to use it k times. The first set of parts is `u = x^k, dv = e^{-x} dx, du = k x^{k-1} dx, v = -e^{-x}` `int u dv = u v - int v du = - x^k e^{-x}|_1^infty + int_{1}^{infty} k x^{k-1} e^{-x} dx ` Then we repeat for `u_1 = x^{k-1}` , and so on until we have only the `e^{-x}` term left. But the important thing is that the last term would only be in terms of a constant times `int e^-x dx` , which clearly converges; and then all the other terms would look like this, for some integer `1 leq p leq k` and some constant C: `C x^p e^{-x} |_{1}^{infty}` The value of this term at `x = 1 ` we can simply calculate; no problem there, it will be some finite number. The limit as x goes to infinity we can also determine by the fact that `e^x` always increases faster than any polynomial as x gets very lar...

One could make the argument that Boo Radley is the loneliest character in the novel for several reasons. After Boo saves the children from Bob Ewell, Sheriff Tate says that he refuses to let the community know about Boo's heroism because the extra attention would seem harmful to Boo. Scout then walks Boo home, and after he enters his house, she mentions that she never saw Boo again. Boo remains inside his house and stays reclusive for the remainder of his life. The fact that Boo never leaves his house, and none of the Maycomb citizens visit him, supports the conclusion that he is the loneliest character in the novel. In Chapter 19, Scout mentions that Mayella might be lonelier than Boo because Mayella has no friends. However, unlike Mayella, Boo does not venture outdoors, nor does he speak to individuals who pass by his home. Boo lives with his brother Nathan, and Mayella has several brothers and sisters to keep her company, which is more evidence to suggest that Boo is the lone...

This is an excellent question to ask, and it happens to be one of those questions where the answer is actually very clear. Statistics wins. Whether you see yourself in a career based in the humanities, law, or business, statistics will give you essential tools for getting along in our modern society. It's like learning civics. It's something that everybody needs. I say this as someone who has great respect for the power and importance of calculus. Calculus is the intellectual gateway for understanding how, in quantitative terms, systems change. It's essential in physics and engineering, and important for natural scientists in many other fields. It's also -- like music theory, logic, geometry, and other abstract studies -- great stuff to know about. If it's a question of either/ or, though, the answer is statistics. Statistics is crucial for becoming an intelligent consumer of information in the modern world.  When you lack training in statistics, you're an easie...

Gordimer begins the story, narrating as herself. This first section is the "frame story." She explains that she's been asked to write a children's story. She is reluctant to do so. She puts the thought aside. Then, she awakens at night to a strange sound in her home. She notes that she has the same fears as people who reinforce their homes with lots of security. She eventually decides that the noise is her house settling because it sits atop of an underground mine. But this event has made it difficult for her to sleep. So, she tells herself a bedtime story. (This seems to be the "children's story" that she was initially commissioned to write.)  This next section is the "story within a story" - the children's story within the frame story. This second story begins like a fairy tale. There is a mother, a father, a little boy, a cat, and a dog. They love each other and seem to have a very good life. They endeavor to "live happily ever afte...

The Rio Grande- Spanish for "big river-" has its source in the mountains of Colorado, runs through New Mexico, Texas, and the country of Mexico, and empties into the Gulf of Mexico. Along the way, this river marks part of the border between the United States and Mexico. In the past, Mexico territory included much of what is today the southwest United States. For much of history, the Rio Grande did not represent a national border, rather a geographic border between the northerly and central parts of Mexico. In 1848, the United States acquired much of the American Southwest through the Treat of Guadelupe, which meant reorganizing national borders. The Rio Grande was a natural choice for demarcating the border because of its geographic significance.

A socially-just solution to the problem in "The Ones Who Walk Away from Omelas" would address the suffering of the child. A socially-just solution represents a desire for equity.  It strives to provide fairness for all people in a social setting. This would mean that the inherent unfairness in Omelas would have to be addressed. For example, freeing the child from being imprisoned would be one socially-just solution. Le Guin's story is predicated upon the idea that the people in Omelas can only be happy because the child suffers.  A solution predicated upon social justice might involve freeing the child, would remedy this predicament.   It would be rooted in fairness for all people and would seek to reverse institutional unfairness.  The child would experience the same freedom that the people of Omelas experience. This mindset is socially-just because it challenges how the townspeople see the child. The townspeople know that they can only be happy because the child is mise...

In Bob Ewell's testimony, he claims that he had seen Tom Robinson "ruttin" (having sex or sexually assaulting) on Mayella. He claims that he saw Tom but was too worried about Mayella to run after him. But in Mayella's testimony, she claims that when her father found her, he was asking who had done it (who had assaulted her). So, in his testimony, he claims to have seen Tom and Mayella together. He is clear about this. But Mayella says that Bob immediately started asking who had "done it." This is perhaps the biggest difference in their stories about what had happened. This is a red flag indicating that one of them (or both) is lying.  Mayella's testimony tells us (the readers) and the jury more about her home life.We also learn more about her relationship with Tom. When Atticus questions her, she first says that she's never asked Tom for help before. Then she says she might have asked him for help before. Mayella gets flustered and continues to contr...

Operation Wetback was a program implemented in 1954 in the United States, with the help of the Mexican government, to deport undocumented immigrants. Approximately a million immigrants were rounded up and deported within a few months. The history of this actually dates back to the Bracero Program of 1942 which facilitated migrant manual laborers from Mexico finding employment in the United States. Along with documented workers also came undocumented ones who because of their lack of legal status were subject to extremely low wages and bad working conditions. Many of the Mexican immigrants who were in the United States legally and the Mexican government initially supported or at least were partially favorable to Operation Wetback as a way of improving the life of documented workers. The motives behind Operation Wetback were fueled by nativism and racial prejudice. The actual implementation was inhumane, with many of the deported laborers suffering or even dying in transit and families b...

First, the title itself would have evoked to people familiar with World War 2 the image of a B-17 or B-24 bomber. When these bombers went on missions, they needed to protect themselves from enemy fighters. The ball turret was a spherical manned gun mount that was extended from the bottom of the bomber; much of the turret was made of glass so the gunner could have a clear view of targets. Due to the shape of the turret, the gunner was strapped in a fetal position.  In the first lines of the poem, we get the imagery of the gunner curled in a fetal position almost like a newborn animal, covered with "wet fur." We get the image of the plane being six miles from earth, increasing our sense of the gunner's vulnerability and isolation. Next, we have the images of fighter planes and flak attacking the bomber. The final visual image is of the dead gunner with his body so shredded and mangled that it needs to be washed out of the turret with a hose. 

The labor movement impacted our political system. Labor unions have generally supported the Democratic Party since the start of the New Deal in the 1930s. They have supported Democratic candidates in elections at the state and national levels. This gave them some clout with the Democratic Party. This clout still is important today as unions tend to support candidates from the Democratic Party. The Democrats have generally supported pro-worker laws. They have supported raising the minimum wage and allowing for collective bargaining between unions and management. Through collective bargaining, workers were able to increase their pay and improve their benefits. They also were able to improve their working conditions. When labor unions were at their peak levels of membership, there was a decrease in income inequality between the rich and the poor. The standard of living of workers had increased. As unions recently lost some of their power, these trends have been reversed. Unions also helpe...

Gerald Croft is presented as being much the same as the Birling's - self-centred, selfish, conceited, privileged and spoilt. Eva Smith has been as much a victim with him as she has been with the Birlings. He manipulates and uses her and when he has had enough of her, discards her. He believes that his money and privilege entitles him to do as he pleases with her and he tries to whitewash his guilt by providing her with money and a temporary home.   In Act One, we find that Gerald shares the same kind of perspective about things as his future father in law. They especially agree about their position and the accumulation of wealth. When Mr. Birling states the following, he agrees wholeheartedly:  We employers at last are coming together to see that our interests – and the interests of capital – are properly protected. And we're in for a time of steadily increasing prosperity.  He comes across as a sycophant, agreeing with practically everything Mr. Birling says, no matter how i...

There is a lot of emotion in both  Hamlet  and  Macbeth , and this emotion varies widely. There are, however, significant similarities in the ways Shakespeare displays the emotion of despair in famous soliloquies in both plays, and so it's worth analyzing this trend more closely. In Act 3, Scene 1 of  Hamlet , Hamlet utters some of the most famous words in English literature during his "To be, or not to be" speech (56-89). In this speech, Hamlet displays muted despair as he contemplates suicide. This is a classic scene, and in it Hamlet broods on the difficult nature of existence and ponders whether or not there is any meaning to life at all. In Act 5, Scene 5 of  Macbeth , Macbeth speaks his "To-morrow, and to-morrow, and to-morrow" soliloquy (19-28), a much shorter speech that wrestles with the same themes and emotions as Hamlet's "To be, or not to be." Reflecting on his wife's recent death, Macbeth despairs and regards life as a meaningless ...

In the chapter "Picky Eater" in Something to Declare , Alvarez writes, "Mostly, if I was eating out, I didn't expect food to taste all that good" (page 76). She writes that in the Dominican Republic, women prided themselves on being very good cooks, so people only went out to restaurants for social reasons. If they wanted a meal that was prepared well and sanitarily, they ate at home or at a relative's house. When she was growing up in the 1950s, the Dominican Republic did not have a developed tourism industry yet, so the island only had simple restaurants catering to workers and food stands in the street. Her family was not allowed to eat in "la calle," or the street, because they thought that they might get sick from unclean food or water. They worried constantly about whether the food was spoiled, as refrigeration wasn't good.  Before Alvarez came to the United States, she had never eaten in a restaurant, except in an ice cream shop. She and...

It is said that, when asked, Henrik Ibsen denied that A Doll's House was a feminist play; instead, he asserted it was a humanist play . Humanism , a social movement developed during the Renaissance, thought it necessary to re-introduce ancient Greek and Roman culture and philosophies into civilization. Humanists promoted a return to studying ancient Greek and Roman texts, and from these texts, they developed philosophies that endorsed fully participating in life , appreciating life's luxuries and beauties, and engaging in "rich and varied human relationships" ( "Renaissance Humanism," The History Guide). Humanists especially endorsed individualism  through promoting the pursuit of individual liberties, and rejected any form of oppression, especially the oppression that is a direct result of social class systems ("Renaissance Humanism"). Ibsen saw his play, as well as his works in general, as humanist rather than feminist because his themes did ...

The trial is perhaps the most crucial scene in the play. In Act IV, Scene I, Shylock demands the right to cut a pound of flesh from Antonio’s body. The court’s decision determines Antonio’s fate. The duke appeals to Shylock’s sense of compassion, to no avail. Shylock says he will stick to his promise: “And by our holy Sabbath have I sworn / To have the due and forfeit of my bond.” Antonio has willingly signed an agreement to allow Shylock a pound of his flesh if he did not repay Shylock on time. The duke believes there is nothing to be done. Bassanio attempts to offer money, which Shylock refuses. Antonio’s friends hurl insults at Shylock and cry for their friend, but Shylock does not yield. Portia, disguised as a lawyer, arrives and describes to Shylock the wonders of mercy: “it is twice blest; / It blesseth him that gives and him that takes.” She declines to simply pardon Antonio because that will set a flawed precedent. Portia eventually manages to find a loophole in Shylock’s argum...

Othello' tragic flaw has been the subject of much debate. Some scholars argue it is jealousy, and other scholars believe it is Othello's lack of self-esteem. I would argue that Othello's tragic flaw is his jealousy because Iago's deceitful mechanisms trigger perilous jealousy which consumes Othello, causing him to experience feelings of insecurity, doubt and rage. Iago, who is manipulative and willing to destroy Othello because Othello promoted Cassio instead of him, devises a plan by which he will manage to cause Othello's downfall. His main victims are Cassio and Othello's wife, Desdemona. Iago wants Othello to believe that Cassio and Desdemona are having an affair, and he plants seeds of doubt in Othello's mind. For example, when Othello sees Cassio and Desdemona together, Iago says: Cassio, my lord! No, sure, I cannot think it, That he would steal away so guilty-like, Seeing you coming. Although Iago does his best to make Othello descend into irrationali...

At the end of the story, Charlie is different from the person he was at the beginning. He does not want people to pity him, and he decides to leave town. After the operation, he started to develop his cognitive abilities and became a genius. He also realized how people treated him before he changed, and their true intentions.  He also got an opportunity to participate in the advancement of scientific knowledge. Anyway I bet Im the first dumb person in the world who ever found out somthing importent for sience. Although the effects of the operation started to wear off, Charlie remembered some of the things he learned. His ability to read and write was fading, but he learned about friendship, respect, and self-worth among other aspects of life. Charlie did not give up on his wish to become smart again, but he understood his situation better than he did in the beginning.

At the beginning of this chapter, which is the concluding chapter in this book, is a shocking fact about the war's consequences that has since been backed up by historians (and is not usually taught in schools).  The shocking fact is that Britain (and not Germany) was thrown into economic disarray by the end of World War I.  "The paradox was--and still is--that Germany, the loser, was worse off."  Ferguson backs up this paradox with many facts supporting his idea before leading into the thought that, without this irony, Germany may not have been able to gain the momentum for World War II.   Germany lost more due to a "blow to their prestige" (such as in the loss of their colonies) than due to actual "economic worth."  The reparations Germany was asked to pay, says Ferguson, was unreasonable; therefore, loans were in order.  This put Germany in a better position than the reader might expect.  In fact, "tax reform was deliberately botched out of the...

One thing that links the events, plot, setting, and characters together is the life story of Mrs. Luella Bates Washington Jones. Events that Roger experiences now are similar to events Mrs. Jones experienced earlier in her life: they both experienced events sprung from limited life situations that led them to do things they should not have done. The plot—a boy does wrong and gets a second chance at living rightly—reflects what Mrs. Jones says of her own life: "I were young once and I wanted things I could not get." The setting   is initially on the street, but is primarily in Mrs. Jones's home, which, as Roger sees, is a reflection of her life, a life in which needs are simply met, but modest gifts are given nonetheless. The characters are linked by the "contact" Roger makes with Mrs. Jones's life: "But you put yourself in contact with me," said the woman. "If you think that that contact is not going to last awhile, you got another thought com...

Chaucer shares specific physical characteristics about the Pardoner that actually provide a great deal of insight into his character.  In the medieval period, many people were believers in the concept of physiognomy, which was supposed to allow people to judge human nature based on physical features--in other words, you could judge a book by its cover. Almost all of the qualities that are mentioned by Chaucer paint a picture of the Pardoner as an emasculated character.  His "hair as yellow as wax, hanging down smoothly like a hank of flax," sounds more like a description of a female's hair style.  The description of his small, goat-like voice is also emphasizing his lack of male characteristics because it suggests that the Pardoner's voice has not/will not change to a lower register. Chaucer the narrator labels him as a "gelding, or a mare," suggesting that the Pardoner either was born with defective sexual organs or had undergone castration. Considering th...

At the beginning of the play, Macbeth is presented as a courageous general who fears nothing and is so loyal to his king and country that he would face any enemy to protect them. He is deemed honorable and seen as worthy of the king's admiration and reward. It is Macbeth's overriding ambition that makes him evil. He is obsessed with the idea of being king of Scotland. Macbeth realizes he will not become liege by normal succession because King Duncan has two male heirs, Malcolm and Donalbain, who precede him in their claims to the throne. Furthermore, Duncan had already named Malcolm next in succession by bestowing him the title 'Prince of Cumberland.' Therefore, the only manner in which Macbeth can achieve "the golden round" is to assassinate the king and his sons and then claim the title. What most profoundly symbolizes the beginning of Macbeth's descent into evil is his response to Ross's announcement that King Duncan bestowed the title 'Thane of...

In Chapter 17 of The Omnivore's Dilemma , Pollan cites the book  Animal Liberation by Singer. The argument Singer makes is that if one human being cannot use another simply because that human is more intelligent, then humans can not exploit animals simply because humans possess more intelligence. This is the premise of equality, and it requires us to treat animals so that we help them avoid pain, even if their interests are not the same as ours. This is what philosophers call "arguments from marginal cases." If we include infants or people with disabilities as people who deserve consideration, we should also include animals, the reasoning goes. Pollan says that we exclude animals from our consideration, we are guilty of what he calls "speciesism," which one day could be considered akin to racism. Pollan also believes that the reason we can so brutally kill animals is that we are so removed from them. He believes that if we saw the industrial ways in which anim...

The speaker in this poem uses plural pronouns ("we," "us," and "our") instead of singular pronouns ("I," "me," or "my") because he is speaking not just for himself but for the entire group of soldiers experiencing the frigid cold as they remain trapped on the battlefield. For example, when the speaker says "Our brains ache, in the merciless iced east winds that knive us," he means that it's not just his own brain that hurts: it's the brains of his comrades, too; and it's not just to him that the wind that feels like a knife: it feels that way to the others as well.  By presenting the group of soldiers as a unified whole instead of speaking as an individual, the speaker of the poem emphasizes their communal sense of loyalty to one another as they endure the painful and horrifying exposure to the cold weather. That sense of community, or comradeship, is important in this otherwise extremely bleak poem. The ...

To apply  Root test  on a series sum a_n, we determine the limit as: `lim_(n-gtoo) root(n)(|a_n|)= L ` or                          `lim_(n-gtoo) |a_n|^(1/n)= L ` Then, we follow the conditions: a) `Llt1` then the series is  absolutely convergent . b) `Lgt1` then the series is  divergent . c) ` L=1` or  does not exist   then the  test is inconclusive . The series may be divergent, conditionally convergent, or absolutely convergent. In order to apply  Root Test  in determining the convergence or divergence of the  series  =`sum_(n0)^oo (-1)^n*e^(-n^2)` , we let: `a_n=(-1)^n*e^(-n^2)` We set-up the limit as:  `lim_(n-gtoo) |(-1)^n*e^(-n^2)|^(1/n) =lim_(n-gtoo) |(-1)^n|^(1/n)*|e^(-n^2)|^(1/n)`                                          ` =lim_(n-gtoo) 1 *(e^(-n^2))^(1/n) `                                          ` =lim_(n-gtoo) (e^(-n^2))^(1/n)` Apply the Law of Exponents:  `(x^n)^m= x^(n*m)` and `x^(-n)= 1/x^n` . `lim_(n-gtoo) (e^(-n^2))^(1/n) =lim_(n-gtoo)e^(-n^2*1/n)`                    ...

On Friday, July 10th, Dr. James Moody, the Medical Examiner, speaks to the prosecuting attorney, Sandra Petrocelli, on the witness stand alongside Detective Williams, and they explain their involvement in the case. Dr. Moody tells Petrocelli that the bullet entered the left side of Nesbitt's body and traversed upward through his lung. He says that the bullet tore through the lung and esophagus which caused heavy internal bleeding, before finally stopping in Nesbitt's upper trapezius area. When Petrocelli asks if he could tell with reasonable certainty the time and cause of death, Moody says that Nesbitt's death was a combination of trauma to his internal organs, as well as his lungs filling up with blood. Dr. Moody then states that Nesbitt would not have been able to breathe because of the blood in his lungs. Petrocelli then says, " You mean he literally drowned in his own blood " (Myers 137). Steve gasps at Petrocelli's comment, while James King tilts his h...

The theme of friendship is indeed strong in this play; specifically, the friendship between Bassanio and Antonio is significant because their relationship is the catalyst for many of the play's major plot points. It is Antonio's love for Bassanio that prompts him to offer Bassanio a loan to help him woo Portia. Antonio procures the money from Shylock, who in turn levies a strict penalty for late repayment. Portia sees Antonio's stress resulting from his friend's predicament, and vows to help him. It is Bassanio's capacity for friendship and loyalty that insures even greater love from Portia. Antonio is also quite possibly in love with Bassanio, perhaps in a platonic way, but the text suggests deeper romantic feelings, as we see in this quote: Commend me to your honourable wife: Tell her the process of Antonio's end; Say how I lov'd you; speak me fair in death; And, when the tale is told, bid her be judge Whether Bassanio had not once a love. There is every i...

We can argue that appeasement caused World War II because it allowed Hitler and the Nazis to build Germany’s military power until it was strong enough to fight a major war. Additionally, appeasement emboldened Germany, making it think the Allies would never have the will to fight. This made Germany much more aggressive and encouraged it to take the steps that eventually led to war. If the French and British had not appeased Hitler, he would not have been able to build the German war machine. The Treaty of Versailles prohibited Germany from having a strong military. In 1935, Hitler renounced the treaty and started to rearm Germany with no regard for what the treaty said. If the French and British had stood up to Hitler at that time, he would not have been able to continue to rearm. The Treaty of Versailles said Germany could not have military troops or installations in a region of Germany called the Rhineland. In 1936, Hitler put troops in that area. Again, if the French and British had...

In the novel, there are five prominent Greaser characters: Ponyboy Curtis, his brothers Darry and Sodapop, Johnny Cade, and Dallas Winston. Ponyboy is the narrator and at the beginning of the story, is only fourteen years old, the youngest of the gang. His oldest brother is Darry, who takes care of Ponyboy and Sodapop because the three of them are orphans. Darry is stern and responsible. Sodapop is the middle brother, who is good looking and happy-go-lucky. Everyone likes Soda. He isn't the smartest of the gang, but he gets along with everyone and always lightens the mood. Johnny Cade is the second youngest of the group and is described as "the gang's pet, everyone's kid brother" (12). Johnny's father beats him and as a result, he is a quiet but very loyal friend. He is not the toughest of the gang, but Ponyboy is close to him and everyone watches out for him. Dallas Winston (Dally) is the toughest member of the Greasers. Originally from New York, he is the cl...

Based on Theodore Taylor's dedication in The Cay , which states, "To Dr. King's dream, which can only come true if the very young know and understand," we can tell that Taylor's most dominant theme in the book concerns the need to overcome racism . Therefore, it can be said that the greatest effect Timothy has on Phillip is helping him overcome his racism by developing color blindness . We first learn of the racism Phillip has been taught to believe when he wakes up on a raft with Timothy after having been unconscious for four hours. Phillip's first thoughts upon seeing Timothy is that Timothy was "black and ugly" (p. 33). When Phillip begins crying because he doesn't feel Timothy has given him enough water and doesn't understand their need to conserve, Phillip reflects on his mother's racist views .  Though Phillip never previously agreed with his mother, he is now beginning to think she is right in saying of blacks, "They are ...

One of the most dominant themes in Schlink's story is the approach human beings take towards accepting responsibility. Set amidst the backdrop of post-Holocaust Germany, a major theme seen in the actions of Hanna and Michael is how they approach responsibility for their actions. Michael is not able to affirm full responsibility for his relationship with Hanna.  He cannot vouch support for her in court, when he knows that his version of the truth is significant to her defense.  As he tries to sort out his feelings towards her, his inability to accept full emotional responsibility is displayed. Even though he makes books on tape for her, he is unable to fully embrace his obligation to her. At the end of the novel, Michael makes the donation of money in Hanna's name, but struggles in acknowledging the emotional connection between them. In much the same way, Hanna struggles to take responsibility for her role in the Holocaust.  Even though she accepts blame in order to conceal her ...

Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at` x=c` . The general formula for Taylor series is: `f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n` or `f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...` To apply the definition of Taylor series for the given function `f(x) = sin(3x)` , we list `f^n(x)` using  the derivative formula for trigonometric function: `d/(dx) sin(u) = cos(u) *(du)/(dx)` and `d/(dx) cos(u)= -sin(u)*(du)/(dx)` . Let `u = 3x` then` (du)/(dx) =3` . `f(x) =sin(3x)` `f'(x) = d/(dx) sin(3x)`            `= cos(3x)*3`            `=3cos(3x)` `f^2(x) = d/(dx) 3cos(3x)`             `=3 d/(dx) cos(3x)`             `=3*( -sin(3x)*3)`             `=-9sin(3x)` `f^3(x) = d/(dx)-9sin(3x)`             `= -9 d/(dx)sin(3x)`              `=-9 * cos(3x)*3`            `= -27cos(3x)` `f^4(x) = d/(dx) -27cos(3x)`             `...

The lady's tower is a grey prison. Outside the tower wall, the poet describes the many signs of life. There are fields of barley and rye. The roads running through the fields are full of people. In other words, the world outside of her tower is teeming with life. She is stuck in a drab, lifeless interior. The small boat (shallop) flows down the river. She waves but they do not see her. The shallop floats freely. In contrast, the lady is not free to move about. She is imprisoned. The other significant aspect is that she is a mystery to the people of the outside world. In the next stanza, the speaker says that only the reapers hear her in the early morning. They conclude that it is the "fairy Lady of Shallot." She is the damsel in distress or the damsel imprisoned. Like Penelope waiting for Ulysses or Rapunzel waiting for a prince, the Lady waits for Sir Lancelot. She waits while everyone outside moves freely. The boat (shallot) moves freely and does not hail her. This emph...

The given two points of the exponential function are (1,2) and (3,50). To determine the exponential function `y=ab^x` plug-in the given x and y values. For the first point (1,2), plug-in x=1 and y=2. `2=ab^1` `2=ab`          (Let this be EQ1.) For the second point (3,50), plug-in x=3 and y=50. `50=ab^3`       (Let this be EQ2.) To solve for the values of a and b, apply substitution method of system of equations. To do so, isolate the a in EQ1. `2=ab` `2/b=a` Plug-in this to EQ2. `50=ab^3` `50=(2/b)b^3` And solve for b. `50=2b^2` `50/2=b^2` `25=b^2` `+-sqrt25=b` `+-5=b` Take note that in the exponential function `y=ab^x` , the b should be greater than zero `(bgt0)` . When `blt=0` , it is no longer an exponential function. So consider only the positive value of b which is 5. Then, plug-in b=5 to EQ1. `2=ab` `2=a(5)` Isolate the a. `2/5=a` Then, plug-in `a=2/5` and `b=5` to `y=ab^x` So this becomes: `y=2/5*5^x` Therefore, the exponential function that passes the given two points is `y=2/5...

What a great question! Honestly, you can answer this question in just about any way that you see fit. The only "objective" requirement is that your choices fit the mood of Bradbury's original piece. Focus on making the mood lonely and cold. I'd really like to say that there are actual humans that work at the mental hospital, but I just don't believe that's how it would be. At the end of the story, Leonard is ordered to get into the police car. The reader and Leonard both learn that the car has no human officer. As he passed the front window of the car he looked in. As he had expected, there was no one in the front seat, no one in the car at all. Bradbury has created a world where people do not leave their homes. I don't believe they leave their homes to go to work or to socialize. Now, on to how the Center is furnished and staffed. Again, it's entirely up to you. In my head, I picture that there are some robots. I believe that the robots are necessary,...

Hannah says this quotation during the rising action of The Devil’s Arithmetic when she finds herself immersed in the life of the concentration camp during the Holocaust in the 1940s.  Within the context of her reverie, Hannah has been forced onto a train into one of the Nazi concentration camps.  Hanna is forced to do backbreaking work and tattooed and shaved against her will.  Hannah realizes that many people are dying within the Nazi gas chambers.  It is an inhuman environment where a person is not really able to “live” but only able to “survive.”  The things that Hannah is experiencing are so horrific that she decides not to think about them because “thinking is dangerous.”  Too much deep thought could cause Hannah to fall into despair about what is happening.  Instead, “in this place she would not think, only do.”  In other words, she would carry on the actions of life: eat, work, and sleep.  Hannah decides to do this in order to survive the Holocaust as the character of Chaya.

Good question! Economists, political scientists, and sociologists are actually still working on this one. If you just do a raw correlation between a country's income and its incidence of terrorism, there is a negative correlation: Poorer countries tend to have more terrorism. That doesn't prove that poverty causes terrorism, however—it could just as well be that terrorism causes poverty (it's not hard to see why it would be difficult to run a business in a place where suicide bombers are blowing people up), or that some third factor (like a weak or corrupt government) causes both poverty and terrorism. Further research has generally failed to find a convincing causal link from poverty to terrorism. Terrorists as individuals are usually fairly well-educated, middle-class people, though they are often unemployed and socially isolated. In addition to the sources at the bottom of my answer, here are some sources to read on the empirical research done on poverty's relationsh...

Jordan doesn't narrate all of Chapter IV, but she does narrate one section of the chapter. After Nick describes the usual guests at Gatsby's parties, Gatsby and Nick go into town, and Gatsby eventually introduces Nick to one of his associates, Meyer Wolfsheim. Later that afternoon, when Nick meets up with Jordan at the Plaza Hotel, she tells him the story of how Gatsby and Daisy met, years ago, and how Daisy ended up marrying Tom Buchanan when Gatsby went away to fight in World War I. I suspect one of the reasons Jordan narrates this section of the novel is that it's a rather long story she tells, and filtering it through Nick's consciousness would dilute it. Everything in the novel hinges on this story, and allowing Jordan to tell it helps draw attention to it in a way that it would not if Nick narrated. In addition, having Jordan tell it puts the reader in the same position as Nick. He hears the story, unfiltered, from her, and it seems as though he listens in rapt at...

In the novel, disease highlights the fracturing of the Ojibwe identity. Peter Barry describes this process of fragmentation in terms of hybridization or duality. The role of disease is two-fold: Erdrich draws attention to the fragmenting nature of disease on both a macro and micro level. At the macro level, disease threatens the viability of the entire Ojibwe societal structure. At the micro level, disease is a metaphor for the conflicting duality that epitomizes the post-colonial Ojibwe experience. Peter Barry asserts that the post-colonial experience encapsulates the journey to overcome this hybridity. The first stage describes the "Adopt" stage, where the native mind absorbs European norms as universally relevant. The second stage describes the "Adapt" stage, where the native mind adapts European values to native suppositions. The last stage is the "Adept" stage, where the native mind has achieved full independence from colonial philosophical constructs...

The narrator explains Paul's mother's terrible secret in the opening chapter of "The Rocking Horse Winner." She is unable to feel love for her children or for anyone else. Only the children seem to understand this. Only she herself knew that at the centre of her heart was a hard little place that could not feel love, no, not for anybody. Everybody else said of her: "She is such a good mother. She adores her children." Only she herself, and her children themselves, knew it was not so. They read it in each other's eyes. Paul senses intuitively that his mother does not love him, but he thinks it must be possible to win her love somehow. The problem seems to relate to his father. His mother no longer loves his father because his father has not lived up to his mother's expectations. She is socially ambitious, but she needs money to keep up the aristocratic mage which is so important to her. Her husband does not make enough money. She tells Paul that his f...

The series given in the problem is `sum_(n=1)^oo e^(-2n)` . This is a convergent series. `sum_(n=1)^oo e^(-2n)` = `sum_(n=1)^oo 1/e^(2n)` This is a geometric series with first term `a = 1/e^2` and common ratio `r = 1/e^2` . The sum `sum_(n=1)^oo e^(-2n) = (1/e^2)/(1 - 1/e^2)` = `(1/e^2)/(e^2/e^2 - 1/e^2)` = `(1/e^2)/((e^2 - 1)/e^2)` = `1/(e^2 - 1)` The required sum of the series `sum_(n=1)^oo e^(-2n) = 1/(e^2 - 1)`

There are three common states of matter or substances: solid, liquid and gas. In general, when solids are heated, they convert to the liquid phase (melting) and when liquids are heated, they convert to the gaseous phase (boiling). However, there are some solids that directly convert to the gaseous phase when heated. This process is known as sublimation. Some examples of solid substances that undergo sublimation include, camphor, dry ice, iodine crystals, and naphthalene balls, among others. These solids will not convert to the liquid phase when heated, instead they will directly convert to the gaseous phase. In comparison, when we heat solid iron or aluminum, these substances convert to the liquid phase. Similarly, when we heat water, it converts to the gas phase (steam). The substances that undergo sublimation are able to bypass the stage of solid to liquid conversion and they directly convert to the gas phase. Hope this helps. 

The given series `sum_(n=0)^oo (2/3)^n` is in a form of the geometric series.  Recall that the sum of geometric series follows the formula: `sum_(n=1)^oo a*r^(n-1)` . or with an index shift: `sum_(n=0)^oo a*r^n = a+a*r + a*r^2 +...` The convergence test for the geometric series follows the conditions: a) If `|r|lt1`  or `-1 ltrlt 1` then the geometric series converges to `sum_(n=0)^oo a*r^n =sum_(n=1)^oo a*r^(n-1)= a/(1-r)` . b) If `|r|gt=1` then the geometric series diverges. By comparing   `sum_(n=0)^o(2/3)^n` or `sum_(n=0)^oo1*(2/3)^n` with the geometric series form `sum_(n=0)^oo a*r^n` , we determine the corresponding values as: `a=1` and `r= 2/3` . The `r= 2/3` falls within the condition `|r|lt1` since `|2/3|lt1` or `|0.67| lt1` . Note: `2/3 ~~0.67` . By applying the formula: `sum_(n=0)^oo a*r^n= a/(1-r)` , we determine that the given geometric series will converge to a value: `sum_(n=1)^oo(2/3)*(2/3)^(n -1) =1/(1-2/3)`                                   `=1/(3/3-2/3)`             ...

In Children of the Prison Boom , Wakefield and Wildeman document the effects that the vast increase in incarceration rates in the United States since the 1970s has had on children, particularly African-American children. An African-American child born around 1990 whose father dropped out of high school has a 50.5% chance of having his or her father imprisoned, according to Wakefield and Wildeman, as compared to 7.2% of white children whose fathers dropped out of high school. This racial disparity in rates of imprisonment has significant effects on the equality of white and African-American children, as parental imprisonment has been connected to children's mental health and behavioral issues. For example, there is a 46% gap in behavioral problems between white and African-American children because of parental imprisonment. In addition, parental imprisonment is linked to homelessness and infant mortality. The homelessness of children can also affect their access to healthcare and th...

To determine the power function `y=ax^b` from the given coordinates: `(4,8) ` and `(8,30)` , we set-up system of equations by plug-in the values of `x` and `y` on `y=ax^b` . Using the coordinate `(4,8)` , we let `x=4` and `y =8` . First equation: `8 = a*4^b` Using the coordinate `(8,30)` , we let `x=8` and `y =30` . Second equation: `30 = a*8^b` Isolate "a" from the first equation. `8 = a*4^b` `8/4^b= (a*4^b)/4^b` `a= 8/4^b` Plug-in` a=8/4^b` on `30 = a*8^b` , we get: `30 = 8/4^b*8^b` `30 = 8*8^b/4^b` `30 = 8*(8/4)^b`  `30 = 8*(2)^b` `30/8= (8*(2)^b)/8 ` `15/4=2^b` Take the "ln" on both sides to bring down the exponent by applying the natural logarithm property: `ln(x^n)=n*ln(x)` . `ln(15/4) =ln(2^b)` `ln(15/4) =b*ln(2)` Divide both sides by `ln(2) ` to isolate b. `(ln(15/4))/ln(2) =(b*ln(2))/(ln(2))` `b =(ln(15/4))/ln(2) or 1.91` (approximated value). Plug-in `b= 1.91` on `a=8/4^b` , we get: `a=8/4^1.91` `a~~ 0.566`  (approximated value) Plug-in `a~~0.566` and `b ~...

The poet (or speaker) expresses his emotions and attitudes both directly through narration and indirectly through dialogue and action. The rhetorical question in the first stanza suggests that the speaker is attracted to the little girl and feels sorry for her: "feels its life in every limb / What should it know of death?" In the third stanza, the speaker directly says that the child makes him feel "glad," plus he describes her eyes as "fair," again indicating his favorable view of her. After that, the conversation takes over until the end, when the speaker shows his exasperation and surprise at the girl's stubbornness by saying he was "throwing words away" and that she "would have her will." The way the speaker portrays the girl through her words also expresses his emotions indirectly. Although the speaker challenges the girl's counting abilities and/or her definition of "sisters and brothers," the little girl insists...

That part of the story is suspenseful for sure; however, it is oddly suspenseful. It's odd that part is suspenseful because readers get no details of the underground fight that ensues. Essentially, readers are told Rikki-tikki went in the hole and came out alive. That shouldn't be suspenseful, but it is.   The reason it is suspenseful is because Kipling uses the most suspenseful technique of all: the unknown. The unknown is scary because our imaginations take over. All Kipling does is feed those imaginations with small, hinting details. As Rikki-tikki plunges down the hole, we are told a mongoose should never choose to do that. The underground passage is the snake's home territory. Nagaina knows all the ins and outs. Rikki-tikki is fully aware that he has no idea when the passages will open up and allow her to strike. By this point in the story, readers are accustomed to Rikki-tikki being in control and almost fearless; however, that is not happening at this point. Readers ...

To be "prosaic" is to be concerned with everyday, mundane, practical considerations. It is the opposite of being poetic, romantic, or focused on exalted subjects. So Raina is being self-deprecating, and chiding herself for doubting that Sergius could live up to the romantic ideals from her favorite literary works and operas. She makes reference to cowardice because she had  "…an uneasy fear that [Sergius] might cut a poor figure there beside all those clever Russian officers." In Raina's view -- based on her romantic stories from literature and opera -- there are clearly defined sex roles. Great men do heroic deeds. Women aren't called upon to show as much physical courage as the men do -- they don't have to risk death in battle. But they are supposed to demonstrate their mettle by showing unwavering faith in the heroism of their men folk. They don't question whether the whole thing is a misguided delusion, or fear that their men are going to fail or...

`int (4x - 2/(2x+3)^2)dx` To solve, express it as difference of two integrals. `= int 4x dx - int 2/(2x+3)^2dx` Then, apply negative exponent rule `a^(-m)=1/a^m` . `= int 4xdx - int 2(2x+3)^(-2)dx` For the second integral, apply the u-substitution method.  `u = 2x + 3` `du = 2dx` Expressing the second integral in terms of u variable, it becomes: `=int 4xdx - int (2x+3)^(-2) * 2dx` `=int 4xdx - int u^(-2) du` For both integrals, apply the formula `int x^ndx= x^(n+1)/(n+1)+C` . `= (4x^2)/2 - u^(-1)/(-1) + C` `=2x^2 + u^(-1) + C` `= 2x^2 + 1/u + C` And, substitute back `u = 2x + 3` `=2x^2+1/(2x+3)+C` Therefore, `int (4x - 2/(2x+3)^2)dx=2x^2+1/(2x+3)+C` .

Integrate `int(x^2+2x-1)/(x^3-x)dx` Rewrite the rational function using partial fractions. `(x^2+2x-1)/(x^3-x)=A/x+B/(x+1)+C/(x-1)` `x^2+2x-1=A(x^2-1)+Bx(x-1)+Cx(x+1)` `x^2+2x-1=Ax^2-A+Bx^2-Bx+Cx^2+Cx` `x^2+2x-1=(A+B+C)x^2+(C-B)x-A` Equate coefficients and solve for A, B, and, C. `-A=-1`  `A=1` ` ` `A+B+C=1` `1+B+C=1` `B+C=0` `C-B=2` `C+B=0` `2C=2` `C=1` `B+C=0` `B+1=0` `B=-1` `int(x^2+2x-1)/(x^3-x)dx=int(1/x)dx-int1/(x+1)dx+1/(x-1)dx` `=ln|x|-ln|x+1|+ln|x-1|+C` `=ln|[x(x-1)]/(x+1)|+C` The final answer is: `=ln|[x(x-1)]/(x+1)|+C `