Notes

The typical Gothic setting is exotic. Many of the Gothic novels were set in either the remote past—especially the medieval or Gothic period—or in locales remote from the ordinary lives of their readers, such as European castles, monasteries, the Scottish highlands, or remote windswept moors. Often the settings combine extraordinary architectural or natural beauty with signs of decay or some sort of ominous foreboding. By contrast, "The Tell-Tale Heart" is set in an ordinary rooming house. The suspense is generated by the close attention to the narrator's unbalanced state of mind. Unlike in a traditional Gothic novel, which includes extensive descriptions of the setting, this story contains little description of the setting. Instead, it narrowly focuses on the thoughts and feelings of the narrator. Although the atmosphere of tension, suspense, and horror resembles the Gothic in other respects, including setting, the story is not entirely typical of the Gothic genre. 

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'(c))/(2!) (x-c)^2+ (f'(c))/(3!) (x-c)^3+ (f'(c))/(4!) (x-c)^4+...`  To evaluate the given function `f(x) =sqrt(x)` , we may express it in terms of fractional exponent. The function becomes: `f(x) = (x)^(1/2)` . Apply the definition of the Taylor series by listing the `f^n(x) ` up to `n=3.`  We determine each derivative using Power Rule for differentiation: `d/(dx) x^n = n*x^(n-1)` . `f(x) = (x)^(1/2)` `f'(x) = 1/2 * x^(1/2-1)`           `= 1/2x^(-1/2) or1/(2x^(1/2) )` `f^2(x) = d/(dx) (1/2x^(-1/2))`          `= 1/2 * d/(dx) (x^(-1/2))`          `= 1/2*(-1/2x^(-1/2-1))`          `= -1/4 x^(-3/2) or -1/(4x^(3/2))` `f^3(x) = d/(dx) (-1/4x^(-3/2))`           `= -1/4 *d/(dx) (x^(-...

Most encryption software available today use military grade encryption. The term military grade is used for marketing purposes to infer that the software has strong encryption capabilities. Any encryption software worth using today should be based on the Advanced Encryption Standard (AES). The algorithm working under AES uses the same key to encrypt and decrypt data. The algorithm was approved by the National Security Agency (NSA) for top secret data, earning its military grade status. Some of the popular encryption software running the military grade algorithm include the following: BitLocker , which comes prepackaged with the modern Windows operating system. The encryption system has the ability to encrypt entire drives on a PC. Folder Lock is also another popular encryption system running on the Advanced Encryption Standard. The software also comes with file shredding capabilities. 7ZIP is a popular encryption software that runs on the AES protocol and encrypts files and folders t...

A good question. Actually, for all that the chorus calls Romeo and Juliet a "pair of star-cross'd lovers" in the prologue, just about all of the action in this play is due to human choice and action, including the ending. True, neither Romeo nor Juliet chose which families to be born into. That aspect of the play (and their situation) could be considered fate. However, once they start acting, they are choosing their consequences, including the ending of the play. Take, for example, Romeo's actions in Act I, Scene 1. When Balthasar tells him Juliet is dead, he decides to kill himself. That's not fate. It might be passion, but it isn't fate. It also means he chooses not to do other things. Romeo does not check to see if Juliet is dead, doesn't decide to live in her memory, etc. Likewise, when he finds the apothecary to sell him the poison, the man chooses to break the law and sell him that poison. That's not fate. That's choice. When Romeo and Paris ...

In planning your transformation narrative, I would recommend beginning with the main character. Question lists can help flesh out aspects of the character, such as his or her physical characteristics, background, family, interests, and desires. I recommend the character questionnaires from Gotham Writers Workshop ( https://www.writingclasses.com/toolbox/character-questionnaire ). Make sure to give your character flaws because a perfect character is a boring character, but be careful not to make your character so flawed that he or she is unlikable. A successful story almost always depends on a likable protagonist. Otherwise, the reader will not care or be invested in what happens to the character. Once you have a strong idea of who your character is, you can plan what object you want your character to become. Alternately, if you already have an idea of the object, you may want to start your planning there. Your character’s traits may develop around the object you choose. Either way, you...

Before we examine the miscommunication that leads to the deaths of Romeo and Juliet, let's first consider the context that had made it possible. Romeo and Juliet are two lovers from rivaling families (the Montagues and Capulets, respectively) who have met and married in secret to preserve their forbidden love. After Romeo kills Juliet's cousin, Tybalt, in a duel that had also claimed the life of his dear friend, Mercutio, Romeo is banished from Verona by the Prince. To make matters worse, Juliet is ordered by her father, Lord Capulet, to marry another man: Paris, a kinsman of the Prince. In order to escape these unfortunate punishments, Juliet (with the help of Friar Laurence) creates a plan: Juliet will fake her death and be "laid to rest" in the Capulet crypt, where she will there await the return of Romeo. Romeo is to be informed of this plan through a letter sent by Friar Laurence. Unfortunately, a terrible miscommunication occurs which is two-fold: 1) Lord Capule...

The development of megacities, which are cities over 10 million people, means that cities will need to develop efficient, low-emission mass transportation systems in the next decade. The population explosion of many of the world's largest cities has created traffic jams that are mammoth in size. For example, Sao Paulo can have traffic snarls that are 110 miles in length, and people in the U.S. now spend an average of 9 years in their cars (see the BBC link below). Increased car ownership in China now means that Chinese cities are clogged with traffic. Some new forms of transportation are also planning to use stilts to carry commuters on buses well above the gridlock on the ground. This level of congestion is not tenable, so people will have to use efficient mass-transit systems that produce low emissions. The high cost of gas and the laws in many cities that require new forms of transportation to produce less pollution will necessitate the use of new forms of technology to power ve...

The Crayola company makes art materials for children. Because of this, most of their products are not permanent, though some pigments  may be more likely to stain skin, clothing, or surfaces. To address this issue, the company offers a number of art supplies like markers, crayons, and paints which are formulated to be easier to wash off.  Unfortunately, Crayola does not share the specific formulations of their products. However, they do share on their website's Frequently Asked Questions that the main ingredients in Crayola markers are water and dye. They also state in their FAQ that products manufactured by Crayola (but not necessarily all Crayola products) are free from potential allergens like peanuts, eggs, milk, whey, shellfish and D&C Red Dye #40. Crayons contain paraffin wax and pigments, but Crayola is far less specific about the ingredients of colored pencils.  Perhaps if you are concerned about specific ingredients possibly being in the washable Crayola products, you ...

This article is about which rights are protected under the Due Process Clauses of the 5th and 14th Amendments to the Constitution. The essential question related to this debate is whether these amendments only protect "procedural rights," which refers to the process that states and the federal government follow in judicial proceedings, or whether these clauses also protect what are called "substantive rights," which are the actual rights given to individuals. The author of this article, Williams, looks at the historical context in which each of these amendments was written. He argues that when the 5th Amendment was ratified in 1791, there was no recognition of substantive due process rights. He writes:  "The preceding review of the historical evidence regarding the early understandings of 'due process of law' is largely supportive of the traditional view that the Due Process Clause of the Fifth Amendment was originally understood either not to constrain...

The primary way Della and Jim show love for one another is through sacrifice. Della sacrifices her long, beautiful hair to get enough money to buy a special gift for Jim. Meanwhile, Jim sacrifices his family heirloom pocket watch to get enough money to buy a special gift for Della. Each one "sacrificed for each other the greatest treasures of their house." Before Della has the idea to sell her hair to get money for Jim's gift, she was filled with disappointment. She cries because she only had $1.87 to spend on her husband's present. She wants to buy Jim a special Christmas gift and is sad and disappointed when she does not have enough money to do so. Other evidence of their love is in the story. At the beginning, O. Henry wrote that, despite their financial difficulties, Jim was "greatly hugged" by Della each day when he returns home from work. After Della gets home from buying the gift for Jim, she looks in the mirror and begins to regret her decision to cu...

Most of what we learn about Ralph and Piggy's history is found in Chapter one when they converse with each other after their meeting. It is clear from their conversation that the two boys are from different socio-economic backgrounds. Piggy's grammar is an indication that he most probably attended public school and lived in a working-class suburb, as illustrated in the following examples: “I can’t hardly move with all these creeper things.” “All them other kids,” “When we was coming down I looked through one of them windows .." We further learn that he had been raised by his aunt (and probably her husband) since his father died. He is quite embarrassed about speaking of his parents and falls short of saying anything about his mother, when Ralph asks about them. Piggy flushed suddenly. “My dad’s dead,” he said quickly, “and my mum—” He took off his glasses and looked vainly for something with which to clean them. It is clear that his aunt spoiled him since she probably want...

Harold Krebs is the main character of Ernest Hemingway's short story "Soldier's Home." He has recently returned from Europe where he participated in some of the most important battles of World War I. Judging by the narrator's description of Krebs, he most likely suffers from what was then called "shell shock" and is now more commonly referred to as Post-Traumatic Stress Disorder. As a result of this he is portrayed as basically anti-social. He complains that no one cares to listen to his true stories about the horrors of war and so he sinks to lying in his description of his experience. He doesn't seem to have any close friends, just acquaintances at the local pool room, and it is suggested that his relationship with his mother deteriorates after his return from the war. He even tells her that he doesn't love her and that he cannot pray with her. The only other person he speaks to is his sister Helen, who obviously looks up to Harold and demands ...

From the table of power series, we have: `(1+x)^k = 1 +kx+ (k(k-1))/2! x^2 +(k(k-1)(k-2))/3!x^3 +` ...  To apply this on the given integral `int_0^0.2 sqrt(1+x^2)dx` , we let: `sqrt(1+x^2) =(1+x^2)^(1/2)`  Using the aforementioned power series, we may replace the "`x` " with "`x^2` " and "`k` " with "`1/2 or 0.5` ". `(1+x^2)^(1/2) =1 +0.5x^2+ (0.5(0.5-1))/2! (x^2)^2 +...`              ` = 1 +0.5x^2 -0.25/2! x^4 +...`              `= 1 +x^2/2-x^4/8 +...` The integral becomes: `int_0^0.2 sqrt(1+x^2)dx = int_0^0.2[1 +x^2/2-x^4/8 +...]dx` To determine the indefinite integral, we integrate each term using Power Rule for integration: `int x^ndx =x^(n+1)/(n+1)` . `int_0^0.2[1 +x^2/2-x^4/8 +...]dx = [x +x^3/(2*3) -x^5/(8*5) +...]|_0^0.2`                 `= [x +x^3/6 -x^5/40+...]|_0^0.2` Apply definite integral formula: `F(x)|_a^b = F(b) - F(a)` . `F(0.2)=0.2 +0.2^3/6 -0.2^5/40+` ...              `=0.2+1.3333x10^(-3)-8x10^(-6)+` ... `F(0) =0+0^3/6-0^5/40+...

In The Story of My Life , Helen Keller describes herself as an avid learner. As soon as she got the language connection at the pump, she began learning words as quickly as possible. She sought out these words so she could communicate about people and things in her environment.  Aside from language, Helen also had a curiosity about the world. The book describes her many adventures in learning, facilitated by a teacher who wanted her to learn.  Helen did not shy away from a learning challenge. It is difficult for a sighted deaf person to learn to speak and more so for a blind and deaf person. But Helen set a goal of learning to speak, and she did.  It was very unusual for women to go to college, but Harvard had established a college for women, Radcliffe, and Helen went there. Going to college was difficult because none of the textbooks were in Braille. Someone had to read each text and finger spell each word in Helen's hand.  There are two factors that contribute to the fascination w...

The present value of a payment P, made after n years with the annual rate of interest r is equal to P/(1+r)^n. The annuity in the problem consists of payments of $1000 at the end of 10 consecutive years, in addition to one payment of $5000 at the end of year 6. The present value of this annuity is: 1000/(1.04) + 1000/(1.04)^2 +...(1000/(1+1.04)^10 + 5000/(1.04)^6 = 1000*(1/1.04+1/1.04^2 +...1/1.04^10) + 5000/(1.04)^6 = 1000*(1.04^10-1)/(1.04 - 1) + 5000/(1.04)^6 = 1000*(1.04^10-1)/(1.04 - 1) + 5000/(1.04)^6 = 15957.68 The present value of the annuity is $14534.37

In Harper Lee’s novel To Kill a Mockingbird , Bob Ewell threatens Atticus for humiliating him during the trial.  We learn that “Mr. Bob Ewell stopped Atticus on the post office corner, spat in his face, and told him he’d get him if it took the rest of his life” (Lee).  Atticus said “We don’t have anything to fear from Bob Ewell, he got it all out of his system that morning” (Lee).  The other characters do not seem to understand his viewpoint, so he explains: “Jem, see if you can stand in Bob Ewell’s shoes a minute. I destroyed his last shred of credibility at that trial, if he had any to begin with. The man had to have some kind of comeback, his kind always does. So if spitting in my face and threatening me saved Mayella Ewell one extra beating, that’s something I’ll gladly take. He had to take it out on somebody and I’d rather it be me than that houseful of children out there.” (Lee) Atticus seems to be under the impression that Bob Ewell only needed to save face and uphold his public...

Holling's backpack tore at the seams and dumped out all of its contents.  His pack was loaded with four cans of chili and all of the utensils for the entire class.   During the month of June, Holling, his class, and his teachers go on an end of the school year camping trip into the mountains.  The vehicles can't make it all the way to the camping spot, so the students must carry all of the supplies to the final spot.  Mrs. Sidman and Mrs. Baker select a few of the boys to carry the heavy packs with food and cooking gear for the entire group.  Holling gets the pack with all of the eating utensils and four big cans of chili.  Holling tells his readers that his pack was an older pack.  During his long, arduous hike up the mountain, the seams on the pack began to tear loose.  As Holling and the pack jostled along the trail, utensils began falling out.  Nobody noticed this because Holling was the last person up the trail.  

The storm is a metaphor for the rising passion between Calixta and Alcée. In literary terms, this is also called the "pathetic fallacy." The "pathetic" term refers to "pathos" which means to evoke emotion or sympathy. Note the "path" in the words sympathy and empathy as well. The pathetic fallacy, in this case, suggests that nature (the storm) is mirroring or showing empathy for the characters, Calixta and Alcée. As the energy of the storm rises, so does the sexual tension between these two characters. Being in the house, with doors and windows closed, the temperature in the house increases. This parallels the rising "heat" and tension between Calixta and Alcée. A bolt of lightning strikes a tree and this dramatic moment signals the moment when Alcée moves to embrace Calixta: Calixta put her hands to her eyes, and with a cry, staggered backward. Alcée's arm encircled her, and for an instant he drew her close and spasmodically to him...

Catharsis  refers to a purging, or evacuation, of emotions which often evokes a change or restoration of the one experiencing catharsis. Aristotle, a Greek philosopher and one of the most influential thinkers in human history, stated in his own work Poetics: "Tragedy, then, is an imitation of an action that is serious, complete, and of a certain magnitude; in language embellished with each kind of artistic ornament, the several kinds being found in separate parts of the play; in the form of action, not of narrative; through pity and fear effecting the proper purgation [ catharsis ] of these emotions."  Aristotle is conveying here the power that a high quality Tragedy can have in evoking this catharsis in its audience. Oedipus Rex in particular, which Aristotle praised as an example of a perfect Tragedy, effects catharsis by promoting the feelings of pity and fear in the audience centering around the guilt that Oedipus feels after he becomes blind. When his sight, physically, ...

Recall the  Root test  determines 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. We may apply the Root Test to determine the convergence or divergence of the series `sum_(n=1)^oo(n/500)^n` . For the given series `sum_(n=1)^oo(n/500)^n` , we have `a_n = (n/500)^n.` Applying the Root test, we set-up the limit as:  `lim_(n-gtoo) |(n/500)^n|^(1/n)=lim_(n-gtoo) ((n/500)^n)^(1/n)`  Apply Law of Exponent: `(x^n)^m = x^(n*m)` . `lim_(n-gtoo) ((n/500)^n)^(1/n) =lim_(n-gtoo) (n/500)^(n*(1/n))`                                `=lim_(n-gtoo) (n/500)^(n/n)`                                `=lim_(n-gtoo) (n/500)^1`                                `=lim_(n-gtoo) (n/500)` Evaluate the limit as `n` approaches `o...

`(x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3)` Factorize the denominator of the first term by using the identity: `a^2-b^2=(a+b)(a-b)` `=(x+3)/((x+5)(x-5))-(x-1)/(x-5)+3/(x+3)` LCD of the above expression is`(x+5)(x-5)(x+3)` `=((x+3)(x+3)-(x+5)(x+3)(x-1)+3(x+5)(x-5))/((x+5)(x-5)(x+3))` expand the terms in the numerator and combine the like terms to simplify, `=((x^2+6x+9)-(x^2+3x+5x+15)(x-1)+3(x^2-25))/((x+5)(x-5)(x+3))` `=((x^2+6x+9)-(x^2+8x+15)(x-1)+3(x^2-25))/((x+5)(x-5)(x+3))` `=((x^2+6x+9)-(x^3+8x^2+15x-x^2-8x-15)+3(x^2-25))/((x+5)(x-5)(x+3))` `=((x^2+6x+9)-(x^3+7x^2+7x-15)+(3x^2-75))/((x+5)(x-5)(x+3))` `=(x^2+6x+9-x^3-7x^2-7x+15+3x^2-75)/((x+5)(x-5)(x+3))` `=(-x^3+x^2-7x^2+3x^2+6x-7x+9+15-75)/((x+5)(x-5)(x+3))` `=(-x^3-3x^2-x-51)/((x+5)(x-5)(x+3))` `=(-(x^3+3x^2+x+51))/((x+5)(x-5)(x+3))`

Odysseus has a reputation as a clever man and orchestrates the Greek's winning pass in The Iliad . However, The Odyssey , which follows Odysseus on his journey home, shows a different side to him.  I'm going to assume we're talking about The Odyssey . It takes ten years for Odysseus to return to Ithaca, and some of it is his fault and some of it isn't. Gods play a huge role in Greek epics, with personal initiative only going so far. Odysseus's journey is extended partly by his own hubris, and partly by the wrath of the gods. Odysseus never wanted to go to war at all. He left when his son Telemachus was an infant, and the Trojan war lasted ten years. It's safe to assume that he wants to get home as quickly as possible. Two things work in his favor towards this goal; he's clever and he has a protector in the goddess Athena. However, his journey takes ten years because of both his choices and the whims of Poseidon.  Odysseus's fatal flaw is hubris or pride....

Standpoint theory argues that how we experience and talk about the world is rooted in the totality of our own experiences. This moves away from the simplistic notion that all Latina women, for example, must think alike, because as well as being Latina, a woman might also be upper or lower class, a recent illegal immigrant or someone whose family has lived in the United States for many generations, a resident of a big city or a rural area, trans- or cis-gendered, young or old, etc. Standpoints are always intersectional. When we talk about everyday lives, they don't exist in a vacuum and cannot be understood through some singular perspective. Instead, the objective conditions of our lives are refracted through multiple simultaneous subjectivities. The historical grounding of standpoint theory is Hegel's understanding of the nature of the master-slave relationship, something that Marx expanded into an analysis of class. The dominant group in a relationship does not just have objec...

Your thesis statement, sometimes also called a topic sentence or "big idea" of your paper, should convey to your audience what your paper or presentation will be about. Though the thesis statement is introduced in the introduction of your paper--or during the introduction portion of a spoken presentation--it is sometimes the most difficult part of an essay to write! Consider this: what is the main idea of your presentation? In one or two sentences, what information are you hoping to present and support? If you had just one minute to tell someone very quickly the subject of your paper, what might you say? Your thesis statement should be related to the body of your essay or presentation. The thesis statement may contain or summarize important points about tropical ecology and the Blue Footed Booby--use the body of your paper to expand upon and support these ideas. For example, if the main food source for the Booby was at risk, you might tell us in your introduction that this is...

When Odysseus is disguised as an old beggar, brought to his home in Ithaca by Eumaeus, his loyal swineherd, the suitors force him into a fight with another local beggar, Irus. One way in which Odysseus shows hospitality to Irus, his opponent in the match, is that he doesn't kill him. This might sound like an odd way to define hospitality to a present-day reader; however, Odysseus and Irus have been pitted against each other by the suitors, and the suitors have said that whichever of them wins the fight gets to eat.  Odysseus is still the master of this house, even if no one is aware that he is home, and he shows Irus hospitality by merely knocking him out instead of killing him. Athena has filled out Odysseus's muscles, making him even more powerful, and yet he restrains himself and allows the old man to live.

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 determine the Taylor polynomial of degree `n=4 ` from the given function `f(x)=1/x^2` centered at `c=2` , we may apply the definition of Taylor series. For the list of `f^n(x)` up to `n=4` , we may apply Law of Exponent: `1/x^n = x^-n`  and  Power rule for derivative: `d/(dx) x^n= n *x^(n-1)` . `f(x) = 1/x^2 or x^(-2)` `f'(x) = d/(dx)x^(-2)`            `=-2 *x^(-2-1)`            `=-2x^(-3) or -2/x^3` `f^2(x)= d/(dx) -2x^(-3)`            `=-2 *d/(dx) x^(-3)`            `=-2 *(-3x^(-3-1))`            `=6x^(-4) or 6/x^4` `f^3(x)= d/(dx) 6x^(-4)`            `=6 *d/(dx) x^(-4)`            `=6 *(-4x^(-4-1))`            ` =-24x^(-...

--The Exclusionary Rule The Exclusionary Rule pertains to evidence that is gathered or attained from an illegitimate search and seizure, a method that is in violation of the Fourth Amendment. The Fourth Amendment to the Constitution is meant to protect the individual's privacy in its prohibition of government intrusion. In addition, the Exclusionary Rule applies to the Fifth Amendment because it protects people from self-incrimination by prohibiting the improper attainment of statements that are self-incriminatory. It also applies to the prohibition of evidence attained improperly. That is, if evidence that is gathered in violation of the Fourth Amendment leads police to other evidence that would not be otherwise attained, then the Exclusionary Rule applies to both the initial evidence and the related evidence, as well. [https://www.law.cornell.edu/wex/exclusionary_rule] --Why the Exclusionary Rule is disturbing The prohibition of evidence gathered through great effort and time oft...

There are several significant scenes throughout the novel To Kill a Mockingbird that portray racism. At the beginning of Chapter 11, Mrs. Dubose, Maycomb's most notorious racist, makes several derogatory comments toward Jem and Scout as they walk past her house. She says, " Your father's no better than the niggers and trash he works for! " (Lee 135). Her racist comment upsets Jem so much that he loses his temper and ruins her camellia bushes on his way home from the store. Another scene in the novel that depicts Maycomb's ugly racism takes place in Chapter 25, following Tom Robinson's death. Scout comments on Maycomb's reaction by saying, " To Maycomb, Tom's death was typical. Typical of a nigger to cut and run. Typical of a nigger's mentality to have no plan, no thought for the future, just run blind first chance he saw. Funny thing, Atticus Finch might've got him off scot free, but wait---? Hell no. You know how they are. Easy come, eas...

Recall that an infinite series converges to a single finite value `S`   if the limit of the partial sum `S_n ` as n approaches `oo` converges to `S` . We follow it in a formula: `lim_(n-gtoo) S_n=sum_(n=1)^oo a_n = S ` . The given infinite series `sum_(n=0)^oo 4(-1.05)^n`  resembles the form of geometric series with an index shift:  `sum_(n=0)^oo a*r^n` . By comparing "`4(-1.05)^n`  " with  "`a*r^n` ", we determine the corresponding values: `a = 4` and `r =-1.05` .  The convergence test for the geometric series follows the conditions:  a) If `|r|lt1`  or `-1 ltrlt1 ` then the geometric series converges to `sum_(n=0)^oo a*r^n = a/(1-r)` .  b) If `|r|gt=1` then the geometric series diverges. The `r=-1.05` from the given infinite series falls within the condition `|r|gt=1` since `|-1.05|gt=1` . Therefore, we may conclude that infinite series `sum_(n=0)^oo 4(-1.05)^n`   is a  divergent series .

It is very difficult to say what the impact of Lincoln's death was, because he left few clues as to how he planned to conduct the aftermath of the war. We can be fairly certain that he did not plan to pursue a program of retribution against Southern leaders, a position which alienated him from some Republicans, but whether he would have pursued a vigorous program to achieve civil rights for African-American freedmen in the South is another question. The issue was not mentioned in his early "Ten Percent" plan for Reconstruction, issued rather early in the war, but he did indicate at the war's end that he would favor voting rights for some black men that served during the war. He gave a speech to that effect, in fact, shortly before he died. It is also impossible to know how Lincoln would have managed the growing faction of Republicans who demanded federal action to ensure equality for African-Americans. So many of the problems that occurred under Reconstruction were ex...

This story functions as a satire because it makes the argument that most people -- "98.4 percent of all those who die in a given month," in fact -- live such uneventful lives, are so "satisfied" with their lives, that they do nothing special at all, nothing that would warrant either reward or punishment.  A satire is a text that uses humor, irony, and wit to expose human weakness or folly in order to, hopefully, spur some kind of change in the person or people it targets.  The human weakness exposed by this text is that we have, evidently, become too complacent.  As the Man from Hell tells the Hippie Boy, "I'm sure you haven't any particular aim in mind" in regard to the stick, to which the Boy responds, "I'm not interested in aims," and the Hippie Girl confirms, "Aims are out-of-date."  It's as though they (and we) have no goals, at least not any extraordinary ones: that the vast majority of people, in reality, lack go...

One of the themes which connects "Rapaccini's Daughter" and "The Birthmark" is that of the intellectual pride of the scientist. In Hawthorne's time, science was not what chemistry and physics are today; rather, it was closer to alchemy, which has spiritual ties. Scientists of this time sought to not only solve the mysteries of nature, but also to master and perfect them. Both Rapaccini and Alymer seek to master nature by perfecting their beloved women, and in so doing, they allow their pride to dominate them. "Rapaccini's Daughter" Dr. Rapaccini seeks to protect his daughter from the world by wrapping her in poison to which she develops an immunity because of her father's potions. However, in doing so, he has denied her any human companionship but his own, and, selfishly, he has loved science more than his own flesh and blood. Thus, her life becomes a counterfeit, leaving her bereft of the love that drives the world: the love between woman ...

A power series centered at `c=0` is follows the formula: `sum_(n=0)^oo a_nx^n = a_0+a_1x+a_2x^2+a_3x^3+...` The given function `f(x)= 3/(3x+4)` resembles the power series: `(1+x)^k = sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!) x ^n` or ` (1+x)^k = 1+kx +(k(k-1))/(2!)x^2+(k(k-1)(k-2))/(3!)x^3+(k(k-1)(k-2)(k-3))/(4!)x^4+...` For better comparison, we let `3x+4 = 4 ((3x)/4 + 1)` . The function becomes: `f(x)= 3/4 ((3x)/4 + 1)` Apply Law of exponents: `1/x^n = x^(-n)` . `f(x)= 3/4((3x)/4 + 1)^(-1)` Apply the aforementioned formula for power series on  `((3x)/4 + 1)^(-1)` , we may replace "x" with "`(3x)/4` " and "`k` " with "`-1` ". We let:  `(1+(3x)/4)^(-1) = sum_(n=0)^oo (-1(-1-1)(-1-2)...(-1-n+1))/(n!) ((3x)/4) ^n`  `=sum_(n=0)^oo (-1(-2)(-3)...(-1-n+1))/(n!)((3x)/4) ^n`  `=1+(-1)((3x)/4) +(-1(-2))/(2!)((3x)/4)^2+(-1(-2)(-3))/(3!)((3x)/4)^3+(-1(-2)(-3)(-4)/(4!)((3x)/4)^4+...` `=1-(3x)/4 +(2)/2((3x)/4)^2- 6/6((3x)/4)^3+24/24((3x)/4)^4+...` `=1-(3x)/4...

This question is referencing a passage late in T.S. Eliot's "The Love Song of J. Alfred Prufrock." To put it in context, I've listed the passage in full: I shall wear flannel trousers, and walk upon the beach. I have heard the mermaids singing, each to each. I do not think that they will sing to me (123-5). To understand this passage, which is one of the most important parts of the poem, you also have to understand the underlying themes of the piece. Like much of Eliot's most famous work, "Prufrock" depicts the emptiness and hollow isolation of modern life. The narrator appears to be a middle-aged man struggling to find meaning and purpose in the crushing context of the modern world. Moreover, if one reads between the lines, it seems the speaker is particularly lonely and longs for a romantic relationship (or at least female companionship). He lacks the courage or assertiveness to actively connect to another person, however, so he seems doomed to a life ...

`intx^2/(x-1)dx` Rewrite the integral as , `intx^2/(x-1)dx=int(x^2-1+1)/(x-1)dx` `=int((x^2-1)/(x-1)+1/(x-1))dx` `=int(((x+1)(x-1))/(x-1)+1/(x-1))dx` `=int(x+1+1/(x-1))dx` apply the sum rule, `=intxdx+int1dx+int1/(x-1)dx` Apply the power rule and standard integral `intdx/x=ln|x|` `=(x^(1+1)/(1+1))+x+int1/(x-1)dx` Apply integral substitution `u=(x-1)` for `int1/(x-1)dx` `du=dx` `int1/(x-1)dx=int(du)/u` `=ln(u)` substitute back`u=(x-1)`, `=ln|x-1|` So the final integration and adding a constant C to the solution yields, `=x^2/2+x+ln|x-1|+C`

An introduction to an essay about climate change should give an overview of our current state of knowledge, the difference between anthropogenic (human-caused) and non-anthropogenic climate change, and the impacts of climate change on living organisms. A good start to an essay on climate change will start with a hook. What do we know? We know that humans are impacting Earth's climate system and that a changing climate has negative effects for the planet as a whole. A strong first sentence will help to call attention to the issue and will communicate the subject, attitude, and direction of your paper. Secondly, the introduction should make very clear for a reader that the kind of climate change we talk about most often (in politics, media, daily life) is the anthropogenic kind. Throughout Earth's climate history, fluctuations have propelled the Earth in a back-and-forth pattern from high to low temperatures. Evidence for this fluctuation exists in climate records like ice caps,...

Mitochondrial DNA is passed from mothers to offspring. Fathers don't, as a rule, contribute this kind of genetic information to the next generation. Currently, scientists don't know for certain what the evolutionary advantage is for this arrangement. But they assume there is an advantage, because the pattern is so widespread: It must have evolved for a reason. One speculation is that the genetic information passed through the male line tends to get damaged just prior to fertilization. Therefore -- according to this theory -- organisms are better off jettisoning it. To better under all this, let's review the basics. In the cells of animals and other eukaryotes, DNA is found in the nucleus. But the mitochondria are distinctive among the remaining organelles: They, too, carry DNA -- genetic information that regulates their own functioning. Both egg cells and sperm cells contain nuclear DNA, each bearing half the complement of chromosomes of a normal, non-gamete cell. During fe...

There are several scenes throughout the novel where Ralph utilizes his survival skills. In Chapter 2, Jack suggests that they use Piggy's glasses to light the fire. Ralph then takes Piggy's glasses and focuses the sun's heat onto a small area of dry wood. Golding writes, "Ralph moved the lenses back and forth, this way and that, till a glassy white image of the declining sun lay on a piece of rotten wood. Almost at once a thin trickle of smoke rose up and made him cough" (56). Starting a fire is an important survival skill that Ralph has mastered. Another scene throughout the novel that depicts Ralph utilizing his survival skills takes place in Chapter 3. The ability to build a shelter is an important aspect of survival. Ralph, Simon, and the other boys successfully build one shelter together. During an assembly meeting in Chapter 5, Ralph says, "We all built the first one, four of us the second one, and me 'n Simon build the last one over there" (G...

Where I teach, at the college level, I have noticed an increase in the use of worksheets, something that, in my opinion, is not necessarily a good trend, although they do have utility in some situations.  The advantages and disadvantages of using worksheets depend on the content area and how they are being used, I think, in other words, a question of context.  First, how useful worksheets are is a matter of the course being taught.  In subjects such as math, physics, or chemistry, they offer the student a means of practicing problem-solving, either in the classroom or as homework.  In courses such as these, the students must have the opportunity to grapple with the problems presented, and this is a decided advantage.  However, in subjects such as English, history, or sociology, most of the worksheets I have seen tend to focus on specific details, rather than encouraging students to see the bigger picture or to think critically.  For example, if a worksheet includes questions on what ch...

Merriam-Webster's dictionary defines villain as "a character in a movie, story, etc. who does bad things". Lady Macbeth shames her husband into killing King Duncan, and then she frames the sleeping guards with the murder by planting the bloody daggers on them. That alone is enough to label her as a villain, and so it would be easy to stop there. The wonderful thing about Shakespeare, however, is that you don't have to stop there. His characters are meant to be interpreted and performed by actors, not just read silently by students in a classroom. The actor doing the interpreting has to do more than base a character's actions on a dictionary definition. As she exists on the page, Lady Macbeth is a conspirator in murder and a callous traitor who throws a country into turmoil by upending its monarchy. But Shakespeare wrote very few villains who had no concrete motivation for doing evil. One example of this kind of villain would be Don John in Much Ado About Nothing ...

The  BEST   defense humans have against viral diseases is a healthy and strong immune system. In order to have a healthy immune system it is vital that you sleep well and have a balanced diet with lots of nutrition. You also should exercise daily, maintain a healthy weight, don't smoke and if you drink alcohol, drink in moderation. If you get sick when you immune system is down, then take antibiotics, if you get sick again your body could have no effect from these antibiotics and you could become extremely ill. The best way to ward off a non-deadly virus is to let your immune system deal with it.  A few other good defenses include good personal hygiene (washing your hands, avoid placing fingers near face). Try to sneeze into your elbow to avoid spreading germs that your body may be immune to, but somebody else's body may not be immune to. I will leave you with something to think about... We all have contaminants of Meningitis/Meningococcal in our nose and if we sneeze we can...

Finding examples of "unity and diversity" in the sense that we use these terms today is difficult when looking at the foundational history of the United States. Many of the Founders were, of course, slaveholders, and most saw no place for Native Americans in the nation's future. One striking way in which the United States, as established by its Constitution, did advocate for diversity was its early commitment to religious freedom. The Constitution banned religious tests as a precondition for holding office, and the state of Virginia led the way in establishing what amounted to total religious freedom. This principle was further established in the First Amendment. Yet anti-Catholicism would be rampant in response to waves of Irish immigration in the antebellum period, and most Americans, including many of the founding generation, believed the nation to be an Anglo-Saxon Protestant one. So even this commitment to diversity was severely limited. As for unity, the nation'...

In the story, the trust between two brothers is an important theme. It is alluded to when Henry goes to fight in the Vietnam War and leaves his trusted red Oldsmobile in Lyman's care. When Henry was alive, both brothers often took road trips together in the Oldsmobile. They were happy to travel, and enjoyed great adventures together. After Henry became a Marine, he stayed away for three years fighting in the war. Before he left, he gave Lyman his keys to the Oldsmobile. His actions demonstrated his great trust in his brother. He told Lyman to treat the car as his own. While he was gone, Lyman took good care of the car; he kept it in pristine condition for Henry's return. After Henry returned from the war, however, he was a different man. He became a loner, and he was always mean and easily irritated. Lyman reports that it was difficult to get Henry to laugh, and when he did laugh, it often sounded more like a man who was choking. Although Lyman had kept his brother's trust ...

Ma Joad of The Grapes of Wrath  and Catherine of A Farewell to Arms  are similar in their beliefs in the power of love and in their inner strength in the face of tragedy. However, they differ in their sense of traditional Christian values and the sense of family and human brotherhood. Ma Joad's one aim in life is to preserve her family and ensure its survival. But, she also believes in helping others. As they begin their exodus from Oklahoma, Ma tells her son Tom, “You got to have patience. Why, Tom—us people will go on livin’ when all them people is gone. Why, Tom, we’re the people that live. They ain’t gonna wipe us out. Why, we’re the people—we go on.” (Ch. 13) After Ma stresses the point that people will always survive, and in humanity lies hope rather than in things like food and shelter, she exemplifies this concept as the family has a Mr. and Mrs. Wilson join them on their journey after Al and Tom repair their car. On the other hand, Catherine Barkley loves Frederic for prot...

`dy/dt=t^2/sqrt(3+5t)` `y=intt^2/sqrt(3+5t)dt` Apply integral substitution :`u=sqrt(3+5t)` `du=1/2(3+5t)^(1/2-1)(5)dt` `du=5/(2sqrt(3+5t))dt` `=>dt/sqrt(3+5t)=2/5du` `u=sqrt(3+5t)` squaring above, `u^2=3+5t` `=>5t=u^2-3` `t=(u^2-3)/5` `t^2=1/25(u^2-3)^2` `t^2=1/25(u^4-6u^2+9)` `y=intt^2/(sqrt(3+5t))dt` `=int1/25(u^4-6u^2+9)(2/5)du` `=int2/125(u^4-6u^2+9)du` Take the constant out, `=2/125int(u^4-6u^2+9)du` Apply the sum and power rule, `=2/125(intu^4du-int6u^2du+int9du)` `=2/125(u^5/5-6u^3/3+9u)` `=2/125(u^5/5-2u^3+9u)` Substitute back `u=sqrt(3+5t)` `=2/125(1/5(3+5t)^(5/2)-2(3+5t)^(3/2)+9(3+5t)^(1/2))` simplify the above and add a constant C to the solution, `=2/125(3+5t)^(1/2)(1/5(3+5t)^2-2(3+5t)+9)+C` `=2/125sqrt(3+5t)(1/5(9+25t^2+30t)-2(3+5t)+9)+C` `=2/125sqrt(3+5t)((9+25t^2+30t-10(3+5t)+45)/5)+C` `=2/125sqrt(3+5t)((9+25t^2+30t-30-50t+45)/5)+C` `=2/125sqrt(3+5t)((25t^2-20t+24)/5)+C` `y=2/625(25t^2-20t+24)sqrt(3+5t)+C`

The United States Constitution is the document that set up our entire system of government.  It tells us the distribution of power amongst the three branches of government and the distribution of power between the federal government and the state governments.  It sets forth the rights and duties of federal government.  It also sets forth the ways that Americans are protected from the government.  In some ways, it could be thought of as the Bible of American government.  It has, in my opinion, created the most successful democracy of all time, recent and current events notwithstanding. The way the Constitution works is that anyone who thinks that the government is acting in a way that violates it has the right to go to court and seek relief from that violation.  Sometimes it is one branch of government accusing another branch of government of violating the Constitution. Sometimes it is a private organization or a private citizen making that claim. The court decides whether or not that i...

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_(n=2)^oo (-1)^n/(ln(n))^n` , we let: `a_n =(-1)^n/(ln(n))^n.` We set-up the limit as:      `lim_(n-gtoo) |(-1)^n/(ln(n))^n|^(1/n) =lim_(n-gtoo) (1/(ln(n))^n)^(1/n)` Note: `|-1^n| =1` Apply Law of Exponent: `(x/y)^n = x^n/y^n` and `(x^n)^m = x^(n*m)` . `lim_(n-gtoo) (1/(ln(n))^n)^(1/n)=lim_(n-gtoo)(1^(1/n)/(ln(n))^n)^(1/n)`                              `=lim_(n-gtoo) 1^(1/n)/(ln(n))^(n*1/n)`                              `=lim_(n-gtoo) 1^(1/n)/(ln(n))^(n/n)`         ...

There are many ways to interpret Golding's Lord of the Flies . Certainly Golding meant the boys' microcosm of society to symbolize the macrocosm of European or Western society. Looking at the characters in terms of psychologist Carl Jung's archetypes, one can see the following correlations: Ralph represents the Everyman, or the "regular guy." Although he seems to be the hero of the story, he doesn't demonstrate special competence or courage above the other boys, nor does he have the weakness of arrogance which tends to be the downfall of archetypal heroes. Instead, he believes in the equality of everyone. His talents are being real and caring for others and being practical. Jack represents the Ruler, whose core desire is control and who has the qualities of a natural leader. His weakness, of course, is being an autocrat. Piggy stands for the Caregiver or Parent. As the one who is most worried about "what grownups would say," he steps in to help Ralph...

Chapter 3, "Evil Air," is about the effects of malaria in the New World. The disease became endemic in the New World, and Mann traces the consequences of malaria. As Mann writes, the disease "turned the Americas upside down" (page 103). Malaria caused high rates of mortality, and Mann states that the areas that were once the locations of high rates of malaria are still less well developed and poorer today, as Europeans used these areas as "extractive states" (page 103) from which to draw natural resources but not as areas in which to establish permanent institutions. In the latter part of the chapter, Mann develops the argument that malaria was one of the reasons colonial America turned to slavery. After long relying on enslaving Native Americans and becoming an exporter rather than an importer of slaves, colonies such as Virginia turned to chattel slavery and the enslavement of Africans in part because malaria decimated Native American and white populatio...

I think that one example of a multidisciplinary approach to teaching European History would involve integrating literature as a part of instruction. Embracing literature and history is a natural, effective, and interdisciplinary approach to make content come alive.  When we use literature as an embedded part of the instructional process, greater understanding of history emerges.  For example, teaching about European History during World War I gains greater significance when pulling from the literature of the time period.  The historical conditions of the battlefield and trench warfare are so viscerally understood when reading works such as Remarque's  All Quiet on the Western Front .  In this instance, literature allows the pain and alienation of World War I to resonate in the student's mind. Another example of how literature can better enhance the understanding of European History can be seen in teaching Machiavelli's The Prince . Machiavelli's work illuminates the int...

 Given the equation of a line `y = mx + b,` => slope = `dy/dx = m` . Thus, the distance is: `L = int_a^b sqrt(1+(dy/dx)^2) dx  , a<=x<=b`  we know the two points` (x_1,y_1)=(0,0)` `(x_2,y_2)=(8,15)` `m = (y_2- y_1)/(x_2-x_1) = (15-0)/(8-0) = 15/8` so now the length is `L = int_0^8 sqrt(1+(15/8)^2) dx`  `= int_0^8 sqrt(1+(225/64)) dx`  =` int_0^8 sqrt((64+225)/64)) dx` = `int_0^8 sqrt((289)/64)) dx` = `int_0^8 (17/8) dx` = `(17/8) int_0^8 1 dx`   = `(17/8) |_0^8 x`  =` (17/8 )[8-0]` = `17 ` so the distance between the two points = 17

Kira, knowing her mother's cott might be burned while she was at the Field of Leaving, had managed to stash away some personal possessions in the clearing so they wouldn't be destroyed. Matt, Kira finds out, had also rescued some things from the home before it burned. He brings them to her when he meets her at the Council Edifice. As such a young child, and without knowing what Kira might want, Matt had no real basis on which to choose what to save. Yet he chose well. He saved her threading frame , understanding how important that would have been to Kira. He also saved some dried herbs in a basket that Kira's mother had woven from river grass. He even saved some "chunky tubers." From Matt's perspective, food would have been one of the most important items to take, but Kira's food will now all be provided for her. The bundle also contained some of Kira's mother's clothing: a shawl and a skirt. The most important thing Matt rescued, however, was t...