Notes

Jewel and Cash see themselves in very different ways; Cash is a responsible son who sacrifices himself for his mother, while Jewel is the prized son who always receives his mother's attention. Jewel resents Cash for working to build Addie's casket before she is dead. Jewel says that he resents Cash building the casket: "Where she’s got to see him. Where every breath she draws is full of his knocking and sawing where she can see him saying See. See what a good one I am making for you. I told him to go somewhere else." While Cash is working hard to construct the casket for Addie, Jewel begrudges anyone who takes attention away from his mother's devotion to him. Jewel also feels that Cash is showing off and that "everybody that passes in the road will have to stop and see it and say what a fine carpenter he is." Jewel feels that Cash constructs the casket only for his own glory. Cash, however, is in reality a self-sacrificing person who is concentrated on t...

Nnaemeka is the main character in Chinua Achebe's short story "Marriage is a Private Affair." The story revolves around his father's objections to Nnaemeka's marriage to a girl outside of their ethnic group. In the beginning of the story, Nnaemeka is hesitant to tell his father about Nene, the Ibibio girl he has already proposed to. Because Nnaemeka is Ibo, he believes his father may not approve of the marriage. For the Ibo, it was common for the parents to pick out a suitable mate. In this case, Nnaemeka's father has written him a letter extolling the attributes of Ugoye Nweke, the daughter of the father's neighbor. The father brags that she is perfect for Nnaemeka. She is, above all, a good Christian, which was quite important to the father. Beside the fact he is already engaged to someone else, Nnameka has three objections to Ugoye. He remembers that she was "an Amazon of a girl," meaning she was much bigger than the other girls. Because of he...

Brian means that his mind and body are working in perfect unison.  There is no longer a disconnect between thoughts and actions.  His mind registers a stimulus of some kind, and his body instantly responds without being told to do so by his conscious mind.   The full quote is as follows: None of that used to be in Brian and now it was a part of him, a changed part of him, a grown part of him, and the two things, his mind and his body, had come together as well, had made a connection with each other that he didn't quite understand. When his ears heard a sound or his eyes saw a sight his mind took control of his body. Without his thinking, he moved to face the sound or sight, moved to make ready for it, to deal with it. The quote appears in chapter 11 of Gary Paulsen's  Hatchet.   The chapter mainly focuses on how Brian's mind and body are changing.  Physically, he is becoming much more lean and tan.  That makes sense.  He's surviving outside with a minimal calorie intake...

The rise of totalitarian governments, particularly that of Nazi Germany, was a major cause of World War II. The reason for this is that Adolf Hitler, the German dictator, based his power upon promises of restoring German greatness, and for him, this always entailed, as he made clear in his speeches, German conquest of Europe. Hitler's aggressions, then, which began by his flouting the rules of the Treaty of Versailles by sending German troops into the Rhineland in 1936, were fundamental to Nazi totalitarianism, and they eventually led to the outbreak of war in the fall of 1939. Beyond that, the fact that totalitarian leaders were able to almost totally mobilize their peoples for war, along with the use of new technologies, resulted in unimaginable casualties. Stalin's Soviet Union, for example, suffered nearly 27 million people killed, both victims of Hitler's invading armies and the utter and total sacrifice that Stalin required of his armies and his people. Indeed, these ...

Not at all.  Although Hamlet does pretend to be insane, he does so only with some characters; to others, he is as he always was: thoughtful, articulate, loyal.  Therefore, it is almost the reverse -- Hamlet  seems to contain even more acting because the actor playing Hamlet must play him in two different ways depending on the scene.  Hamlet is not actually insane, something that we can tell, in part, from the fact that he is able to turn the madness on and off at will.  Hamlet tells Horatio that he plans to act as though he were mad so as to throw off any suspicions Claudius might have.  Further, whenever he speaks to Horatio, he is himself; it is only when he speaks to characters like Claudius, Polonius, Ophelia, or Rosencrantz and Guildenstern (people from whom he needs to hide his investigations into his father's murder, for various reasons) that he seems mad.  Therefore, Hamlet's apparent madness actually requires a great deal more acting on the part of both the character a...

John Steinbeck's choice of a title is an allusion to a well-known poem by Robert Burns, the full title of which is "To a Mouse, on Turning Her Up in Her Nest with the Plough." The speaker in Robert Burns' touching poem expresses regret for inadvertently destroying a mouse's nest while plowing. In the next to-last stanza he says: But Mousie, thou art no thy lane, In proving foresight may be vain: The best-laid schemes o' Mice an' Men                        Gang aft agley, An' lea'e us nought but grief an' pain,                        For promis'd joy! The title derived from Robert Burns' poem alludes to the dream of George and Lennie to own their own little farm and to be free of the backbreaking toil and wage-slavery in which they are presently trapped. This dream is the back story. It is repeated to Lennie by George in the first chapter. Lennie never gets tired of hearing it. Later in the story it seems that the dream may actually come...

Tom Robinson is moved to the jailhouse prior to the trial and Sheriff Heck Tate warns Atticus that there is a group of men who are unhappy about it, who have been drinking, and who might plan on making trouble. What he really means is that these men might well end up going to the jail and hurting Tom Robinson. At first, Atticus does not believe this is a possibility. "Don't be foolish, Heck," Atticus said, "this is Maycomb." But Tate argues that it is not the men of Maycomb, but a group from "Old Sarum," who are getting upset. So, in order to be a visible show of protection for Tom Robinson, Atticus goes to the jail and sits outside. It turns out Sheriff Tate is correct and the mob ends up confronting Atticus. Fortunately, his kids and Dill show up and Scout diffuses the whole situation by striking up a conversation with Mr. Cunningham. After the mob leaves, without doing any harm, it's revealed that Mr. Underwood was watching them, with his shotgu...

During the Middle Ages (476 AD-1350 AD), the focus on Christianity changed the way in which the human body was depicted. In contrast with the Greco-Roman period, which had many nudes, this period of art produced very few nudes. Religious figures (except for Adam and Eve) during the Middle Ages were rarely shown nude, and other exhibitions of nudity that were common during the period of paganism (such as nude bathing or nude athletics), were not in favor. A piece of art that shows this transition is the Sarcophagus of Junius Bassius, completed in Late Antiquity in 359 AD. This sarcophagus shows nudity as something about which to be embarrassed, as Adam and Eve are depicted as trying to shield or cover up their naked bodies. Art in the Middle Ages often featured religious figures; an example is the stained glass windows of Chartres Cathedral constructed around 1200, which feature religious figures in stories from the Bible. The human body in this era is simplified and even a little grote...

In Chapter 4, Scout mentions that Jem believes in Hot Steams in front of Dill which upsets him. After the children agree to roll the tire, Jem gets revenge on Scout by pushing her as hard as he can. Scout ends up crashing into the Radley porch. Scout is dizzy when she exits the tire and suddenly realizes that she is inside the Radley yard. Scout then runs out of the yard without grabbing the tire. Jem works up enough bravery to finally run into the Radley yard and retrieves the tire. When Jem returns with the tire, he comments that there was nothing to it and says that Scout acts so much like a girl that it's "mortifyin'." A little while later, the children are drinking lemonade and Jem tells them that they are going to play a new game called "Boo Radley." Scout says, "Jem's head at times was transparent: he had thought that up to make me understand he wasn't afraid of Radleys in any shape or form, to contrast his own fearless heroism with my co...

As people moved westward, there were economic effects on our country. As we expanded to the Mississippi River, our economy began to grow. Roads were built, river transportation improved, and railroads expanded. This allowed our businesses to grow and expand also. After we received land in the Louisiana Purchase that was west of the Mississippi River, we sent explorers to this region. Many Americans believed the Great Plains was not a great place to settle. The government was encouraging westward expansion for many reasons. One of these reasons was that it was good for our economy. To encourage movement to the West, the Homestead Act was passed. This law gave people 160 acres of land for free if they lived on it for five years. Most of the people who moved here were farmers. This also helped our economy grow. As people moved westward, they needed and demanded products. As transportation to the West improved, businesses began to expand to the West. Thus, the economic benefits of expansio...

I believe that this question is asking about character motivation and what motivates that particular character to act. Mary Maloney is a good character to use regarding motivation. When readers are first introduced to Mary, she exists to serve her husband. She is patiently waiting for him to get home, and once Patrick gets home, Mary flutters around the house getting him food and drink so that he can relax after his day of work. She wasn’t really watching him, but she knew what he had done because she heard the ice cubes falling back against the bottom of the empty glass when he lowered his arm. He paused a moment, leaning forward in the chair, then he got up and went slowly over to fetch himself another. “I’ll get it!” she cried, jumping up. I assume that her motivation at this point is true love. Maybe complete infatuation, but the end result is the same. She is motivated to do whatever it takes to keep Patrick happy. When he announces that he is leaving her, that motivation ends. So...

Carbon dioxide and other greenhouse gases including methane, nitrous oxide, tropospheric ozone and CFC's are all accumulating in the atmosphere due to human activities. They are the causes of global climate change.  In an actual greenhouse, its glass panels allow sunlight in, but trap heat energy, preventing it from escaping. This causes the temperature inside a greenhouse to be quite warm. Greenhouse gases absorb infrared radiation, the electromagnetic radiation that is radiated heat from the sun. As sunlight strikes Earth, some of it is converted to heat which should radiate back into space. However, the greenhouses gases in the atmosphere slow this process down and warm the temperature of the lower atmosphere. This leads to global warming. Infrared radiation has longer wavelengths than visible light, but shorter wavelengths than microwaves along the electromagnetic spectrum. The shortest wavelengths on the electromagnetic spectrum are gamma rays, followed by X-rays, ultraviole...

George and Lennie share the dream of owning a farm one day. They both dislike the constant traveling that comes with being a ranch worker. Ideally, if they could raise enough money, they would buy a farm and settle down in one place. They differentiate themselves from other workers, who George and Lennie believe tend to be solitary wanderers with no aspirations of making a better future. George and Lennie, on the other hand, try to save their money, and they are always thinking about the future. In these respects, their motivations are quite similar. George is torn between wanting to go off on his own and staying with Lennie. He knows he would have an easier time on his own, but he has grown fond of Lennie and feels like it is his duty to protect him. Lennie is aware of this, and that's why he tries his best to keep George happy. In this way, they differ. The dream of owning the farm is their shared motivation. Additionally, George is motivated by a need to protect Lennie. He feels...

Really, there is not much difference at all between the role of upper-class women in the early nineteenth century and the way Austen writes them.  Austen has represented upper-class women as essentially having to make the choice between marrying whichever man happens to propose to them, no matter how stupid or inappropriate a match he might be, and running the risk that no one will ever ask her again and that she could end up alone, a burden on her family.  Charlotte Lucas, for example, feels that she has few options, and she is anxious -- at twenty-seven years old -- to secure "an establishment" for herself.  She doesn't want to be a burden on her family, and she's rapidly approaching old-maid status.  Therefore, when she gets a proposal from Elizabeth's cousin, the ridiculous Mr. Collins, who literally proposed to Elizabeth fewer than forty eight hours before, she accepts.  She figures she has as much a chance of being happy with him as she does if she remains u...

While this is a story about an outdoor sport, two of the brief indoor scenes are very pivotal. There are basically four indoor scenes: The farmhouse The bar The truckstop diner The truck cab, though, with the snow blowing through the broken window, this could also be considered outdoor. The first pivotal scene occurs when Frank and Tub ask the farmer for a phone and directions to a hospital. Here they learn that Kenny killed the dog not out of meanness or spite, but as a favor to the heartbroken couple. We realize that Kenny, more than likely, was not going to shoot Tub, but was rather pulling another poorly thought-out prank. The next pivotal scene occurs when Frank and Tub stop their journey to the hospital in order to warm up. At the diner, Tub admits to his problem with binge-eating. Frank decides to feed him pancakes as a show of friendship and solidarity. Not only is this gesture damaging to Tub's health, it is also damaging to Kenny's health as he is freezing and bleedin...

Benedict’s test is used to detect the presence of reducing sugars. All monosaccharides and some disaccharides such as lactose and maltose are called reducing sugars. When Benedict’s test is positive, an orange-red precipitate forms when the Benedict’s reagent is added to a solution contain reducing sugar. The iodine test is a chemical test for starch. When iodine solution which is red is added to starch it turns blue/black in colour. If according to your question, the Benedict’s test is positive, it implies that the solution contains a reducing sugar, in which case an orange-red precipitate forms when the Benedict’s reagent is added. Iodine does not react with reducing sugars and so when iodine (which is red) is added to such a solution, no colour change will be observed unless starch is present, in which case a blue/black colour change gives away the presence of starch. See the table at the end of this article .

The self might be the product of cognitive biases and subjective, erroneous memories. Nonetheless, we are more than emotional and subjective. We also have the capacity for a limited degree of rationality and objectivity. Research by Daniel Kahneman and other psychologists has shown that much of our thinking is automatic and intuitive. We don't consciously deliberate, analyze, and calculate answers. Instead, unconscious processes do the work for us by noticing trends and making use of quick-and-dirty "rules of thumb." Feelings and associations simply pop into our minds. This helps explain why people are prone to making errors based on cognitive biases. The intuitive system (which Kahnmen calls "System 1") makes us jump to conclusions. Sometimes it even makes us blind to evidence that would refute our perceptions and beliefs. This also suggests that our personal memories -- what we believe has happened to us and what we believe about our past behavior -- are based...

The above quote is taken from Chapter 17 of Charlotte Bronte’s Jane Eyre , and the pronoun of “she” refers to Blanche Ingram, a beautiful socialite from the old Victorian aristocracy who wants to marry Mr. Rochester. In the novel, Blanche serves as a foil to Jane because Blanche is arrogant and self-entitled, using her physical beauty to draw the attention of Mr. Rochester.  Conversely, Jane is described as a kind, compassionate soul who attracts Mr. Rochester through her humility and inner beauty. The two women are perceived as foils because they illuminate the contrasting sides of their individual personalities. Thus, on a surface level, this quote elucidates the foil because it sets up the contrast between Jane and Blanche by naming Blanche’s talents.  On a deeper level, there are other literary devices present.  First and foremost, the quote demonstrates an anaphora, which is the deliberate repetition of words or word order at the beginning of each phrase or sentence. In the quote,...

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For a research paper, you can try discussing certain themes from The Odyssey. I will discuss two below. 1) Hospitality This is one of the major themes of the story. Some questions to explore: a) Should hospitality be regarded as a reciprocal arrangement? b) If guests abuse their privilege, what recourse does the host have? c) If the host in question is powerless to prevent her quests from taking further unwanted liberties with her person and property, should she resort to violence? If she cannot do so, should another party resort to violence on her behalf? In the story, Odysseus' wife, Penelope, is powerless against the machinations of her suitors. They shamelessly consume food and drink at Odysseus and Penelope's expense, and they also appropriate every luxury in the couple's palace for their own. Here, you can refer to the text to help you provide examples for the suitors' despicable conduct. With Odysseus missing and Telemachus weakened by his fear, Penelope is force...

Those Pilgrims who wrote about their experiences at Plymouth described the area in different ways. In his History of Plymouth Plantation , the most famous account of the settlement, William Bradford, the governor of Plymouth, described the region alternately as a "hideous and desolate wilderness, full of wild beasts and wild men." Bradford's purpose in writing the History was to illustrate the workings of God in providing for his band of Separatists in such a hostile environment. In an often-cited passage, Bradford describes, for example, a Patuxent village, deserted due to a smallpox epidemic that preceded the Pilgrims, as being cleared out by God for their benefit. Another famous Pilgrim leader, Edward Winslow, described the area as teeming with natural resources, including fish, shellfish, berries, and good land for growing Indian corn. Winslow concluded that "men might live as contented here as in any part of the world." Winslow, who developed a friendship ...

Certainly by the end of the play, Macbeth could be said to be a purely evil character, remorseless and cruel. But he is not that way throughout the play. At the beginning, Macbeth is portrayed as an honorable Scottish thane, loyal to his kinsman Duncan, who rewards his loyalty with titles. But he is ambitious, as we see when the witches tell him he will be King of Scotland. Macbeth realizes he has "black desires" which he must hide from the world. And he believes that he must commit murder to fulfill these desires, which he does. But it is his wife that serves as a driving force behind the murder of Duncan, planning it, goading Macbeth into carrying it out, and smearing the King's guards with blood to attempt to implicate them in the killing. Macbeth clearly feels guilty about the murder, but it marks a crucial turning point in his development. He plans the murder of Banquo on his own (though he feels remorse for it as well, as his vision of the murdered man's ghost i...

The term "white elephant" is commonly used to describe a useless or burdensome possession. In Asian folklore it is said that white elephants were sacred, but because of their sanctity could not be used to perform any manual labor. Thus, the elephant became useless to its possessor and quite expensive to maintain. The term white elephant is still in use today as friends or office workers gather and give and receive white elephant gifts, mainly just for the fun of it. Most people have these useless gifts around the house somewhere. In Hemingway's short story, Jig refers to the hills in the distance as looking like white elephants in her conversation with the man. In this case, the term is a veiled reference to the unborn child she is carrying. It becomes a way for the idea of abortion to be introduced into the story. That the girl believes the hills look "lovely" seems to indicate she wants to keep the child. A little later she even says they don't resemble wh...

    John Proctor, protagonist of Arthur Miller’s The Crucible , is a dynamic character struggling with the denigration of the world around him and his own personal demons. He recognizes the hypocrisy of the courts, seen most notably at the end of Act III when he cries out, “God is dead!” and voices both his and Danforth’s moral shortcomings. Giving a false confession to a “false” or, at least, immoral judge seems justified. But internally, Proctor struggles with his own heart and the judgment he makes about himself. An admitted lecher, Proctor battles with finding any goodness in himself. As he tells Elizabeth, he cannot “mount the gibbet like a saint” because he is not that man. He struggles with what a false confession will mean for his children, his legacy.  Proctor struggles with how he sees himself, a man not worthy of a dignified, honest death because he is not a dignified, honest man. He knows, because of his sins, he should not mount the scaffold with the saint-like Rebecca Nur...

In John Steinbeck's  Of Mice and Men, animals provide rich symbolism throughout the novel. While the setting of the novel, rural California, provides an appropriate landscape for many animals, the most significant include mice, rabbits, and dogs. Steinbeck repeats these images throughout the novel, allowing the reader to examine the hierarchy of strength among both animal and man, and the idealized American dream.  Early in the character's development, Steinbeck introduces the relationship Lennie has with animals, particularly small, soft, innocent animals. George catches Lennie with a dead mouse in his pocket and throws it into the brush.  Lennie explains that his Aunt Clara used to give him mice to play with, but that she isn't around anymore. After the death of Aunt Clara, George promised to take care of Lennie, which likens Lennie's relationship to George to that of an animal. Although he is large in size and possesses physical strength, Lennie does not have the sk...

Alcott's short story "Transcendental Wild Oats" is based on the time she spent with her family in a Transcendental community called Fruitlands in Harvard, Massachusetts. She described her experiences as a fable, or a story that has a moral, because it conveyed the impracticality and gender inequality of the utopian living that the Transcendental movement envisioned.  Rather than using her family's real names, she refers to them in the story (written many years after her experiences in the 1840s) with pseudonyms. For example, her father, Bronson Alcott, is referred to as "Abel Lamb," and the other characters have allegorical names such as "Sister Hope." The male heads of the farm, Abel Lamb and Timon Lion (Lion represented the real-life Charles Lamb), start the Transcendental community with idealistic hopes that they describe in the following way: The inner nature of each member of the Family is at no time neglected. Our plan contemplates all such d...

The very first details in the story foreshadow the end.  In the first line, we learn that Mrs. Chestny suffers from high blood pressure and has been going to a class at the local YMCA to lose some weight.  Her face gets redder and redder throughout the story, as Julian does things to purposely upset her, and this serves as more foreshadowing.  At one point, her face is an "angry red," and soon after, it becomes "unnaturally red, as if her blood pressure had risen."  All of this detail prepares us for her eventual stroke at the story's end. Further, Mrs. Chestny first says that at least she "'won't meet [herself] coming and going,'" and then a short while later, she quotes the saleslady as having said precisely the same thing in the store.  The repetition of the idea that Mrs. Chestny expects to be the only person she meets who has the financial resources to purchase this unique and costly hat seems to foreshadow the fact that she's abou...

Certain characters like Mr. Collins, Caroline Bingley, and Mrs. Bennet help to make the novel comical.  Mr. Collins is a prize idiot, something that everyone but Mrs. Bennet and Mary seem to realize.  He has stupid opinions about marriage and women's reading and propriety and how to treat women, and he fails to realize just how ridiculous he is.  Then, Miss Bingley tries again and again to lower Elizabeth in the eyes of Mr. Darcy, failing repeatedly.  Her machinations to tempt him into love with her are so transparent and obvious that they end up being funny.  Mrs. Bennet is another such character: her constant complaining about her "nerves," her desperation to marry her daughters off to whomever she can, and her husband's complete inability to be in the same room with her for more than five minutes together make her comical too. Further, scenes like the one at the Netherfield ball, when Elizabeth is almost convinced that her family has conspired to make themselves ri...

In Stephen Crane’s short story “The Bride Comes to Yellow Sky,” Scratchy Wilson runs into a situation he is ill equipped to deal with. It was a well-known fact in Yellow Sky that when Scratchy Wilson was drinking, trouble was sure to follow. Usually, Jack Potter, the town marshal, was the person responsible for keeping the peace. Unbeknownst to the citizens of Yellow Sky, Potter got married in San Antonio that morning, and was currently traveling home with his wife on the train that stopped in their outpost town. The couple attempts to sneak into town, and back to Jack’s house before any town’s people see him. But Scratchy, having left the center of town, is already on his way. Scratchy confronts Jack Potter as he arrives home with his new wife. Although Scratchy wants a gun fight with Jack, he is informed about Jack’s new circumstances, and told Jack is not carrying a gun. It is the perfect time for Wilson to take his shot, but he is in foreign territory. Jack is married, he has a wif...

The character of Bill Benty is developed fully so that his sister Molly Wells can act as a dramatic foil to him. Bill Benty, the paternal grandfather, orchestrates the plan to manage the differences among the relatives and friends who will attend the baptism of his son's daughter so that there will be no unpleasantness before or after the ceremony at their home where a reception is to be held. Benty is the consummate manager, who advises his wife that the biggest concern when the two sides of families get together is the "blood-letting issues." This "unbeatable, humane, wise, experienced administrator" feels that the issues that concern each side need to be aired prior to the big occasion. Therefore, he invites his son and his son's wife, along with their baby, to dinner the week before in order to discuss the baptismal ceremony and what will happen afterwards at the reception in their home. He tells his wife, "If the issues can be solved to anyone'...

Both Dee from Walker's "Everyday Use" and Beneatha from Hansberry's  A Raisin in the Sun  learn from their education that their cultural heritage is rooted in African traditions.  Dee is the only member of her family to go away to college, and when she returns home to visit her mother and her sister Maggie, Dee has changed her name to Wangero because she wishes to erase any ties with slave masters.  Dee is also quite interested in preserving the family's cultural artifacts because she believes that they are relics that represent the family's African cultural heritage.  Similarly, Beneatha learns African history in college, which causes her to dismiss what she believes are materialistic American practices, and this dynamic is most evident in her ending her relationship with George in order to date Joseph Asagai.  So education teaches both Dee and Beneatha to honor their African cultural heritage.

When protein is ingested, it is metabolised by the body into amino acids. The amino acids are further broken down into ammonium ions which the body utilises in the biosynthesis of nitrogenous compounds required for body building.   The body is unable to store excess amino acids not so utilised. In a process called deamination, the excess amino acids are then converted into ammonia in the liver by a series of chemical reactions. The ammonia produced exists in dynamic equilibrium with ammonium ions in aqueous solution. The body prevents the ammonia from accumulating in the body because it is very toxic to body tissues. Through a series of reactions referred to as the ornithine cycle, the liver detoxifies the ammonia into water and a less toxic nitrogenous compound called urea. Being very soluble, urea easily dissolves in blood and gets transported to the kidneys where it is filtered off and passed out of the body in solution with water as urine.

The suffering child in LeGuin's story "The Ones Who Walk Away from Omelas" is the scapegoat for the misery of others, so that the others are able to live in comfort and happiness. The concept which LeGuin explores in this work of philosophical fiction is that of the greater good, a concept explored in William James's The Moral Philosopher and the Moral Life.  In this work James writes on a supposition that one person might be able to absorb the pain, illness, and misery for all others: Or if the hypothesis were offered us of a world in which...millions [could be] kept permanently happy on the one simple condition that a certain lost soul on the far-off edge of things should lead a life of lonely torture.... This miserable creature that is confined is essential to the comfort of all the others in the community. In Omelas, then, all the "goodness and grace of every life...." depends upon the condition of this child imprisoned in a basement of one of the attrac...

Limit comparison test is applicable when `suma_n` and `sumb_n` are series with positive terms . If `lim_(n->oo)a_n/b_n=L` where L is a finite number and `L>0` , then either both series converge or both diverge. Given series is `sum_(n=1)^oon/((n+1)2^(n-1))` Let the comparison series be `sum_(n=1)^oo1/2^n=sum_(n=1)^oo(1/2)^n` The comparison series is a geometric series with ratio `r=1/2<1` A geometric series with ratio r converges, if `0<|r|<1` So, the comparison series `sum_(n=1)^oo(1/2)^n` converges. Now ,let's apply the limit comparison test with `a_n=n/((n+1)2^(n-1))` and `b_n=1/2^n` `a_n/b_n=(n/((n+1)2^(n-1)))/(1/2^n)` `a_n/b_n=((2n)/((n+1)2^n))/(1/2^n)` `a_n/b_n=(2n*2^n)/((n+1)2^n)` `a_n/b_n=(2n)/(n+1)` `lim_(n->oo)a_n/b_n=lim_(n->oo)(2n)/(n+1)` `=lim_(n->oo)(2n)/(n(1+1/n))` `=lim_(n->oo)2/(1+1/n)` `=2>0` Since the comparison series `sum_(n=1)^oo1/2^n` converges, so the series `sum_(n=1)^oon/((n+1)2^(n-1))` as well ,converges by the limit comparis...

Scout makes several mistakes which get her into trouble on her first day of school. The first mistake Scout makes comes after she reads aloud in class. Miss Caroline then criticizes Scout's father for teaching her how to read, and Scout responds by telling her teacher that nobody taught her to read. Scout comments that Jem told her that she had the ability to read at birth because she was a "Bullfinch" who was swapped at birth. Scout says Miss Caroline thought she was lying and told her not to let her imagination get away from her. Scout naively believed her brother and realizes her explanation "annoyed" Miss Caroline. The second mistake Scout makes comes after recess. While Miss Caroline is holding up flashcards with beginner words on them, Scout gets bored and writes a letter to Dill. Miss Caroline catches Scout writing the letter and tells Scout that her father needs to stop teaching her how to write. Miss Caroline is clearly offended that Scout is not payin...

King George III is not mentioned in the Constitution. The Constitution of the United States was written in 1787, more than a decade after the colonies had declared their independence from Great Britain, and four years after independence was formally established by the Treaty of Paris. So King George was not relevant to the Constitution, though its prohibitions against religious tests, noble titles, writs of assistance, and other clauses certainly were a tacit reaction to the actions of the King and Parliament.  It is likely, however, that this question is referring to the Declaration of Independence, which levies many accusations against King George. These accusations ranged from claims that he refused to approve laws that were good for the colonies, to his approval of unjust taxes, to allegations that he urged enslaved people and Native Americans to rise up against the Americans during the early days of the Revolution. Of course, most of these actions, to the extent they actually occu...

Given` xdx + (y+e^y)(x^2+1)dy = 0` =>` x + (y+e^y)(x^2+1)dy/dx = 0` =>` x/(x^2+1) + (y+e^y)dy/dx = 0` => `(y+e^y)dy/dx = -(x/(x^2+1))` =>` (y+e^y)dy = -(x/(x^2+1))dx` by integrating on both sides we get , `int (y+e^y)dy = int -(x/(x^2+1))dx` =>` y^2/2 +e^y +c = - (1/2)ln(x^2+1)` => `y^2+2e^y = -ln(x^2+1)+C`  where C is an arbitrary constant

`int (x^2+x+1)/(x^2+1)^2 dx` To solve, apply partial fraction decomposition. To express the integrand as sum of proper rational functions, set the equation as follows: `(x^2+x+1)/(x^2+1)^2=(Ax+B)/(x^2+1)+(Cx+D)/(x^2+1)^2` Multiply both sides by the LCD. `x^2+x+1=(Ax+B)(x^2+1) + Cx + D` `x^2+x+1=Ax^3+Bx^2+Ax+B+Cx+D` `x^2+x+1=Ax^3+Bx^2+(A+C)x+B+D` Express the left side as a polynomial with degree 3. `0x^3+x^2+x+1=Ax^3+Bx^2+(A+C)x+B+D` For the two sides to be equal, the two polynomials should be the same. So set the coefficients of the polynomials equal to each other. x^3: `0=A`     (Let this be EQ1.) x^2: `1=B `     (Let this be EQ2.) x: `1=A+C`     (Let this be EQ3.) Constant: `1=B+D`     (Let this be EQ4.) In the equations, the values of A and B are already known. So only the values of C and D have to be solved. To do so, plug-in the value of A to EQ3.  `1=A+C` `1=0+C` `1=C` Also, plug-in the value of B to EQ4. `1=B+D` `1=1+D` `0=D` So the partial fraction decomposition of the integran...

The Convention on the Prevention of Marine Pollution by Dumping of Wastes and Other Matter (London Convention) was held in 1972 and sought to establish laws and protocols to address the issue of ocean pollution. The Convention led to the establishment of the London Protocol in 1996, which prohibits the dumping of wastes from sea vessels, aircraft, and other man-made structures into the sea. The London Protocol also prohibits the dumping of the vessels at sea. Participating countries are expected to issue permits for disposing wastes at sea. Additionally, dumping of some wastes considered hazardous is completely banned by the protocol. The International Maritime Organization has also established treaties to address the issue of ocean and sea pollution. The International Convention for the Prevention of Pollution from Ships of 1973 sought to prevent and address accidental and operational pollution by ships at sea. The Protocol following the convention was adopted in 1978. The instruments...

Toward the end of the story, after the narrator has killed, dismembered, and hidden the body of the old man in order to rid himself of the "vulture eye," he hears a knocking at his door. Though it is only four o'clock in the morning, the narrator says, "I went down to open it with a light heart, -- for what had I now to fear?" The implication, then, is that the narrator has a light heart because he has no fear of being caught. He has already taken "wise precautions" to be sure that the body will not be discovered and that no blood was left to stain the floors (he'd thought to use a tub to catch it all when he took the old man's body apart). He feels that he has no reason to fear anyone who might be knocking at his door at this hour because he has been so careful, so meticulous, and that he has committed the perfect crime.

The first myth that Baldwin explodes is that America's greatest threat is from Russia.  He declares that America's greatest threats are domestic, and that specifically, any attempts to right the wrongs of the denial of civil rights will be forcefully resisted by the status quo in the country.   A paradox that Baldwin confronts is that America likes to think of itself as a country that values independent thought and free speech; but when people become a little too free in their thinking and speech, they become inconvenient to have around. Baldwin observes, in this speech to a group of teachers, that American schools exist to "perpetuate the aims of society." Baldwin criticizes a society that claims to value "liberty and justice for all" but perpetuates a myth about black people: their value to society is proven only by their devotion to white people. Baldwin goes on to say that it is a myth that the "Negro revolution" is upsetting the country; in hi...

The unnamed narrator is in many ways the opposite of Bartleby: an optimistic and stable man, the lawyer seems to be a completely devoted contributor to both society and the economy in general. Thus, it's possible Melville chose the lawyer as his narrator to more dramatically emphasize Bartleby's stagnation and listlessness. Unlike his employer, Bartleby seems completely apathetic about his work, and seems to have no faith in the occupation that he has chosen for himself. Indeed, Bartleby seems to be simply going through the motions in life and is uninterested in his work. As such, the lawyer's optimistic work ethic and contribution to the work force is, in some sense, deconstructed. Therefore, we can hypothesize that Melville chose a stable and normal lawyer as his narrator in order to call into question, through Bartleby's apathy, the robust American work ethic represented by this lawyer.  

Set, or Seth, is an Egyptian god.  He is the god of storms, deserts, chaos, and war.  According to Egyptian mythology, Set killed and mutilated his own brother, Osiris.  Despite that horrible deed, Set is not always an evil god.  Often he is portrayed as the protector of Ra.  In all cases, Set has a human body and some kind of animal head, but the type of animal head has changed throughout the mythology.   In the book  The Egypt Game , the children use Set as an evil god.    “Ummm,” April said. “Or else we could be evil high priestesses who are going to offer him as a human sacrifice on the crocodile altar to—what was that evil god’s name?” “Set?” “Yeah, that’s the one.” April jumped to her feet. Throwing up her arms, she chanted, “Almighty Set has promised his servants, the crocodile gods of the Nile, the bloody heart of the young Pharaoh, Marsh—uh, Marshamosis!” She dropped to her knees. “O mighty Set, god of evil, we hear and obey.” The Egypt Game that the children play is make bel...

At the beginning of Chapter 15, Sheriff Tate and a group of Maycomb citizens visit the Finch residence to discuss with Atticus the possibility of changing the venue of the trial. Sheriff Tate voices his concerns about the Old Sarum bunch causing trouble, but Atticus dismisses them. The community members comment that it is a special occasion, but Atticus remains unconcerned. Later on that night, Atticus decides to sit outside of Tom Robinson's jail cell as a precaution. Jem, Scout, and Dill decide to look for Atticus and find him reading the newspaper outside of Maycomb's jailhouse. Out of nowhere, a group of cars arrive from the Meridian highway, and the Old Sarum bunch gets out and surrounds Atticus. Their leader, Walter Cunningham, tells Atticus to move out of the way, but Atticus refuses. Then, Scout runs out from her hiding place, and Jem and Dill follow her. Atticus tells Jem to take the children home, but Jem refuses to leave. Jem knows that his father is in a dangerous...

Maclaurin series is a special case of Taylor series that is centered at `c=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))/(1!)x+(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^(-2x)` , we may apply the formula for Maclaurin series.. To list derivative functions `f^n(x)` , we may apply derivative formula for exponential function: `d/(dx) e^u = e^u * (du)/(dx)` . `f(x)=e^(-2x)` Let `u =-2x` then `(du)/(dx)= -2 .` `d/(dx) e^(-2x) = e^(-2x) *(-2)`                  `= -2e^(-2x)` Applying `d/(dx) e^(-2x)= -2e^(-2x)`   for each derivative function, we get: `f'(x) = d/(dx) e^(-2x)`         `=-2e^(-2x)` `f^2(x) = d/(dx) (- 2e^(-2x))`             `=-2 d/(dx) (e^(-2x)) `             `=(-2)*(-2e^(-2x))`             `=4e^(-2x)` `f^3(x) = d/(dx) (4e^(-2x))`             `=4d/(dx) (e^(-2x)) `             `=4*(-2e^(-2x))`    ...

The headlines of major papers announced that the U.S. suffered an aerial attack at Pearl Harbor on December 7, 1941. The following day, President Franklin D. Roosevelt asked Congress to declare war. After this happened, on December 11, 1941, Germany and Italy, who were allies to Japan, also declared war upon the United States. Japan's attack upon the American forces in the Pacific were made in order to cripple the naval forces so that Japan could control that area. However, the U.S. recovered from its losses and struck back in a devastating bombing mission over Tokyo, named the Doolittle Raid. This mission was clearly a retaliation against the bombing in Hawaii, and it helped to restore the morale of the Armed Services. Also, in June of that year, the United States Navy defeated Japanese forces in the Battle of the Midway. Furthermore, in 1945, the U.S.captured the islands of Iwo Jima and Okinawa that lie near Japan. These victories, along with the bombing of the cities of Hiroshim...

The Second Wave of feminism in the United States began in the 1960s and persisted throughout the next two decades. At this time, women championed the right to work outside the home for equitable pay, reproductive rights, and raised awareness about the prevalence of sexual assault and domestic abuse. I think that in some small ways, the feminist movement of today is stronger, but it is not quite the same as the atmosphere and activism of the mid-century. Technology has had a huge impact on women's movements around the world as social media, email, and the ability to create public webpages enables people to spread awareness much more easily and quickly. Not only is it possible to share information relating to women's issues, the internet and social media can offer a private safe space for personal expression for those who are unable to be open about their gender, sexuality, or social concerns in other realms of life. Though technology makes it  easier  to facilitate this kind of ...

Evaluate `sum_(n=1)^(oo)nsin(1/n) ` This series diverges. We use the limit test: if the series converges the limit of the nth term must be 0 as n grows without bound. `lim_(n->oo)nsin(1/n)=1 ` We use L'Hopital's rule as we have the indeterminant form `oo * 0 ` `lim_(n->oo)n*sin(1/n)= ` `lim_(n->oo) sin(1/n)/(1/n) = 0/0` Use L'Hopital's rule to get: `lim_(n->oo) = (-cos(1/n)/(1/n^2))/(-1/n^2) = cos(1/n)` `lim_(n->oo)cos(1/n)=1`

When writers use metaphors, they use non-literal language to make connections between two things that aren't otherwise connected. For example, imagine you said, "He's a dog." You're referring to a man with no standards. He's not literally a dog. He's human. In "Mirror," Plath definitely uses metaphors. There are a number in the poem. Take the first few lines as examples: "I am silver and exact. I have no preconceptions. Whatever I see I swallow immediately Just as it is, unmisted by love or dislike." If the speaker is the mirror, then it is not literally true that it swallows things. Images of things pass into mirrors like they are being swallowed, though, and that's the connection. Likewise, mirrors do mist, but the literal mist is water condensing on them. Here, "unmisted by love or dislike" is a metaphor for being emotionally unmoved, or objective. That's how mirrors see things.

There are several different ways that  The Arabian Nights , or  The Thousand and One Nights , explores, plays off of, and subverts women's roles and stereotypes. One of the main ways that this collection of stories explores power is through the book's frame narrative. The king is angry at women because he discovers his wife having an affair. He has his first wife executed and decides that he will now marry virgins, have sex with them, and then kill them the following morning before they have the chance to be unfaithful to him or hurt him in other ways. This storyline is already one example of a stereotype of masculinity — that of a violent, power-hungry king who uses his power to hurt women. When he marries Shahrazad, however, she tells him stories each night to keep him interested, prevent him from killing her, and thus save other women in the kingdom from his wrath. This frame narrative suggests the ways in which, in a violent patriarchal world where men seemingly have all th...

Parametric curve (x(t),y(t)) has a horizontal tangent if its slope `dy/dx` is zero i.e when `dy/dt=0` and `dx/dt!=0` It has a vertical tangent if its slope approaches infinity i.e it is undefined, which implies that `dx/dt=0` and `dy/dt!=0`   Given parametric equations are: `x=4cos^2(theta) ,y=2sin(theta)` Here the parameter is `theta` Let's take the derivative of x and y with respect to `theta` `dx/(d theta)=4(2cos(theta)d/(d theta)cos(theta))` `dx/(d theta)=4(2cos(theta)(-sin(theta)))` `dx/(d theta)=-4(2sin(theta)cos(theta))` Use trigonometric identity: `sin(2theta)=2sin(theta)cos(theta)` `dx/(d theta)=-4sin(2theta)` `dy/(d theta)=2cos(theta)` For Horizontal tangents, set the derivative of y equal to zero `dy/(d theta)=2cos(theta)=0` `=>cos(theta)=0` `=>theta=pi/2,(3pi)/2` Let's check `dx/(d theta)` for the above angles, For `theta=pi/2` `dx/(d theta)=-4sin(2*pi/2)=-4sin(pi)=0` For `theta=(3pi)/2` `dx/(d theta)=-4sin(2*(3pi)/2)=-4sin(3pi)=0` So, there are no horizontal ...

Morphs and allomorphs are both ways to describe the phonetic expressions (that is, the actual sounds produced) of the smallest meaningful parts of language in the study of morphology: morphemes. A word like "unhappy" has two meaningful pieces: "un" and "happy," which together convey the meaning "not happy." Each of the meaningful parts is a morpheme, the phonetic expression of which is called a morph. Morphs can be further classified into "lexical" or "grammatical": lexical morphs are the meaningful roots, like "happy" or "man," and these are often free-standing words. Grammatical morphs modify the root in a meaningful way, but may not stand as a free word; in English, suffixes like [-able] or prefixes like [un-] are grammatical morphs.  Allomorphs are phonetic variants of a morph. A good example of allomorphy is the plural suffix in English, which can have the allomorphs [-s], [-z], or [-ez] depending on t...

The Green New Deal follows from initiatives put into place after the Great Depression and during President Franklin D. Roosevelt’s administration. The initiatives were targeted at improving the nation’s economy by creating jobs, reforming the financial sector and restoring the economy to acceptable secure and stable levels. The Green New Deal by the Green Party of the United States is based on four key pillars that are aimed at economic and social reforms. The Green New Deal seeks to establish an Economic Bill of Rights to ensure that all citizens have access to employment and to protect their rights as workers and as property owners. The deal also seeks to support locally based green businesses through accessible financing and research into sustainable sources of energy. The deal’s financial initiative seeks to reform the sector by imposing more stringent regulation and controls on Wall Street. Socially, the Green New Deal aimed at instituting democratic reforms by protecting the peop...

One of the reasons to recommend this book is that it has been very popular since it was written in 1843.  For a book to be popular consistently for that long must mean there is something to it!  Why do people love A Christmas Carol so much? First of all, the book is an uplifting tale.  Even if it is not Christmastime people like the story, and around Christmas, people are sentimental and enjoy it even more.  It explores the themes that go with the holiday, such as taking care of others and enjoying your family. The characters in this book are also compelling.  Ebenezer Scrooge’s transformation from grouchy and lonely miser to munificent old uncle warms the heart.  Anyone can recite Scrooge’s favorite line from the beginning of the story, or Tiny Tim’s Christmas toast, “God bless us every one! “A merry Christmas, uncle! God save you!” cried a cheerful voice. It was the voice of Scrooge’s nephew, who came upon him so quickly that this was the first intimation he had of his approach. “Bah...

To find the convergence of the series `sum_(n=2)^oo 1/(n(ln(n))^p) ` where `pgt0` (positive values of `p` ), we may apply integral test. Integral test is applicable if f is positive, continuous, and decreasing function on an interval and let `a_n=f(x)` . Then the infinite series` sum_(n=1)^oo a_n` converges if and only if the improper integral `int_1^oo f(x) dx ` converges to a real number. If the integral diverges then the series also diverges. For the infinte series series `sum_(n=2)^oo 1/(n(ln(n))^p)` , we have: `a_n =1/(n(ln(n))^p)` Then,` f(x) =1/(x(ln(x))^p).` The `f(x)` satisfies the conditions for integral test based on the following reasons: -` f(x)` is continuous since` x(ln(x))^p !=0` for any x-value on the interval `[2,oo)` -` f(x)` is positive since `1/(x(ln(x))^p)gt0 ` for any x-value on the interval `[2,oo).` -` f(x)` is decreasing since `f'(x)` is negative  for large value of `x` . It eventually decreases at the tail of the series. To evaluate the convergence of t...

Examples of satire abound in Mark Twain's  The Adventures of Huckleberry Finn , but perhaps none are as excellent as the duke and the king. Two of my personal favorite characters, the duke and the king are conmen whose actions suggest multiple satirical connotations. For our purposes, I'd like to focus on the fact that, by naming two conmen "the duke" and "the king," Twain satirizes political leaders at large. It quickly becomes clear that the duke and the king are liars and criminals. Juxtaposing their lofty, imagined nobility with their repeated get-rich-quick schemes, Twain shows both men to be opportunistic parasites who prey on the innocent. Between the two of them, the duke and the king swindle several river communities by various means, such as staging a fake play and impersonating a dead man's relatives to steal his inheritance. Additionally, the two men eventually rule the raft with iron fists, ordering Jim and Huck around with authoritarian pom...

I just answered a question concerning "Salvation" that might be helpful to this question. With regards to how time passes, the essay begins a few weeks before an important revival meeting at Hughes's aunt's church. The build-up for this revival meeting over the next few weeks happens quickly, over the course of a single paragraph. Then, Hughes spends the rest of this essay describing this single revival meeting, which most likely lasts several hours (at one point Hughes says, "Now it was really getting late. I began to be ashamed of myself, holding everyone up so long.") The fact that most of the essay revolves around a single event in time tells us that this event was an important milestone in Hughes's life. It's important to note that the essay is written from the point-of-view of Hughes as an almost 13-year-old boy, a child on the brink of adulthood. Thus, while the essay mainly covers a single event lasting just a few hours, Hughes's child sp...

In Chapter 10 of Harper Lee's To Kill a Mockingbird , Scout learns for the first time that Atticus is a sharpshooter. Having previously thought that Atticus is feeble because of what Scout thinks is his old age, Scout is very impressed to learn that Atticus can do something worthy of boasting about. Yet, Jem tells her not to boast about it because he understands Atticus is ashamed of his ability to take life so easily. Atticus displays his sharpshooting skills when he is forced to rescue the neighborhood from a rabid dog. By the end of the chapter, Scout comments to Jem that they would "really have something to talk about at school on Monday," but Jem warns her not to say anything about Atticus's shooting skills. Jem understands that Atticus gave up shooting as soon as he comprehended, as Miss Maudie phrases it, that "God had given him an unfair advantage over most living things." Since Jem understands how much Atticus values life , he also understands why ...

The answer to this question can be found in Chapter One, or "The GOP's Rise as 'the White Man's Party'." This chapter describes the ascent of George Wallace, the "redneck poltergeist" who began serving as the governor of Alabama in January of 1963 under the auspice of protecting segregation. After losing the 1958 election because of relatively "soft" stance on race, Wallace ran again in 1962; this time, he veered far right on the issue of race, even going as far as to court the support of the Ku Klux Klan. Wallace quickly became adept at exploiting White hatred of Black individuals using non-racial language. He used the concept of "states' rights" as an abstraction to represent white supremacy; this technique of raising fear and hatred without mentioning race (and, in fact, denying that one is racist) became known as "soft porn racism." Wallace realized that the language of racism was increasingly rejected, and, thus...

Hello! We have to prove that `sum_(k=1)^n a_k=sum_(k=1)^n (3k-2) = (n(3n-1))/2` for all n>=1. First, establish the base of induction for n=1: `sum_(k=1)^n (3k-2)=3*1-2=1` and `(1*(3*1-1))/2=1.` These numbers are equal, so the base is established. Now, assume that for some n the statement is true and consider the statement for n+1: `sum_(k=1)^(n+1) (3k-2) = ((n+1)(3(n+1)-1))/2.` Whether it is true? The sum at the left is eqial to `sum_(k=1)^(n) (3k-2)+a_(n+1), = sum_(k=1)^(n) (3k-2)+(3(n+1)-2)` which is equal to `(n(3n-1))/2+(3(n+1)-2)` by the induction assumption, and this is the same as `(3n^2-n+6n+2)/2=(3n^2+5n+2)/2.` The expression at the right is `((n+1)(3n+2))/2=(3n^2+3n+2n+2)/2,` which is the same. This way, the induction step is also proved and the initial statement is proved also.