What does Red Chief say to terrorize his kidnappers?

The Red Chief terrorizes Bill the most, and he tells him, "I'll fix you . . . No man ever yet struck the Red Chief but what he got paid for it. You better beware!" This is an undefined threat, but what is more terrifying to the kidnappers, once they've had the boy for a day, is that Red Chief is really enjoying his time with them away from home and has no desire to return to his parents. He tells them, "I never had such fun in all my life."
The kidnappers end up black and blue from the blows Red Chief inflicts on them and realize that their plan has backfired when their ransom note is countered by Red Chief's father; he asks for $250 to take the boy off their hands. Bill and Sam, the kidnappers, conclude that it is a good deal and are only too happy to hand over the boy and the money before leaving town.

Red Chief terrorizes his kidnappers by sitting in the entrance of the cave where they are hiding out and asking one of the kidnappers if he dares to enter Red Chief's camp. He also calls Sam, one of the kidnappers, a spy and tells him that his braves will roast Sam alive when they return. In addition to prattling on continuously, Red Chief also lets out blood-curdling war cries and tries to scalp Bill, the other kidnapper. One of the most terrifying things that Red Chief tells his kidnappers is that he's having so much fun that he doesn't want to go home. He says this before he decides to become Black Scout and ride Bill like a horse. In the end, the kidnappers wind up paying Red Chief's father to take him back, as Red Chief, though just a child, is such a terror. 

Calculus of a Single Variable, Chapter 3, 3.1, Section 3.1, Problem 43

f(x)=x^4-2x^3+x+1
f'(x)=4x^3-6x^2+1
Now to find the absolute extrema of the function, that is continuous on a closed interval, we have to find the critical numbers that are in the interval and evaluate the function at the endpoints and at the critical numbers.
Now to find the critical numbers, solve for x for f'(x)=0.
4x^3-6x^2+1=0
(2x-1)(2x^2-2x-1)=0
2x-1=0
x=1/2
2x^2-2x-1=0
x=(2+-sqrt(4+8))/4
x=(1+-sqrt(3))/2
Now let us evaluate the function at the critical numbers and at the end points of the interval(-1,3) ,
f(-1)=(-1)^4-2(-1)^3+(-1)+1
f(-1)=1+2=3
f(3)=3^4-2*3^3+3+1=31
f(1/2)=(1/2)^4-2*(1/2)^3+(1/2)+1=21/16
f((1+sqrt(3))/2)=3/4
f((1-sqrt(3))/2)=3/4
So, Absolute maximum=31 at x=3
Absolute minimum =3/4 at x=(1+-sqrt(3))/2

Why does Launcelot want to leave Shylock?

It's not entirely clear why Launcelot wants to leave Shylock, and he is torn internally about whether to go or stay. He states:

"Budge," says the fiend. "Budge not," says my conscience."Conscience," say I, you counsel well." "Fiend," say I, "youcounsel well." To be rul'd by my conscience, I should stay withthe Jew my master, who—God bless the mark!—is a kind of devil;and, to run away from the Jew, I should be ruled by the fiend,who—saving your reverence!—is the devil himself.

It seems that Launcelot wants to leave Shylock because he is a Jew, and in the anti-Semitic world in which Launcelot lives, it bothers him to be "ruled by the fiend" (i.e., a Jew). His head tells him that he should leave Shylock's service but his conscience, interestingly enough, tells him he should stay. Apparently, his conscience understands that he should disregard his employer's religion and remain loyal to him.
However, Launcelot also seems to have issues with his employer. These lead him to help Jessica and Lorenzo elope, actions which are certainly a betrayal of Shylock's trust. In the end, Launcelot does leave Shylock and enters the employ of the fortunate Bassanio who, we are led to believe, is a kinder master.
In summary, it appears that Launcelot wants to leave primarily because Shylock is a Jew, a reason he knows, in his heart of hearts, is wrong. However, he does leave.

Launcelot, Shylock's servant, debates with himself whether to leave his master's service. He's torn between what he calls "the fiend at my elbow" urging him to run off, and his conscience, which with equal insistence tries to persuade Launcelot to stay put. Just to make things even more confusing for the indecisive servant, he reckons he's not just caught between a devil and his better self, but between two devils. If Launcelot leaves Shylock's employ then he'll be following the devil; but then if he chooses to remain then he'll continue to serve someone he openly regards as being a devil. Launcelot doesn't mention any specific grievances he may have against Shylock, so it's a fair assumption that he harbors prejudice towards his master on account of his being a Jew.

Does anyone know a poem that relates to anger (2nd stage of grief) in terms of loss of a loved one? Preferably one with 10-20 lines.

A lot of poetry that we see deals with deep emotions, but, surprisingly (at least to me), anger is not one of the more common emotions we find in popular poetry. So, if you want to find a poem about anger specifically related to loss, we'll have to do a little digging.
Wilfred Owen fought as a soldier in World War I and became a famous anti-war poet. The content of the poems may not be exactly what you're looking for, but you could take a look at his poems titled "Dulce Et Decorum Est" and "Anthem for Doomed Youth," as they are about his anger related to the death of his fellow soldiers in war.
You could also look at "On Pain" by Khalil Gibran, and "Eurydice" by H.D. There's also "Those Winter Sundays," by Robert Hayden, but that one's more about the poet being angry with himself for not being aware of the sacrifices his father made for him in life.

What is the information on chapters 18–20 and others in The Westing Game?

In chapter 18 of The Westing Game, Turtle and Flora grow closer, and Turtle begins addressing Flora by the nickname "Baba." At Turtle's insistence, they unload all other stock and put their money into Westing Paper Products, which begins to climb in value. Sandy compiles information on Baumbach, Amber, Deere, and Pulaski to share with Judge Ford. Theo instructs Doug to follow Otis Amber, and Doug jogs all over town to keep track of him. Angela quietly reveals that she doesn't want plastic surgery to fix her cheek, and Turtle instructs her not to talk to anyone about the bomb. Dr. Deere brings Chris to the hospital to see a neurologist about his condition.
Chapter 19, encompassing all of Thursday, begins with Turtle and Flora anxiously monitoring their stock. Otis suggests to Crow that James Hoo is the bomber, and she is suspicious of Hoo until he gives her insoles of his own invention that relieve her aching feet, proving to her that he is good and could not be the bomber. Sandy and the judge review his notes on Crow and the Wexler family and realize that Sydelle Pulaski was mistakenly included in the list of heirs. Chris finds an envelope containing clues (WITH and MAJESTIES) in his bathrobe and delivers it to Angela as a gift from Theo; the words were actually put there by Crow, unbeknownst to Theo.
In chapter 20, Turtle instructs Flora to sell all the stock after Westing Paper Products reaches its highest peak in fifteen years. Doug follows Otis around but can't find Theo, and his feet find relief thanks to the insoles his father invented. Following a hunch regarding their last clue, Theo experiments with fertilizer in the chemistry lab at school and causes an explosion, which makes the bomb squad suspicious of him. Sandy completes his notes on the Theodorakis family after Judge Ford questions George Theodorakis, who once had a romantic relationship with Violet Westing. Sandy and the judge conclude that the former wife of Sam Westing must be one of the heirs and that her life is in danger, since she is likely the person he would most want to punish.
For more information on The Westing Game, including detailed chapter summaries for the entire book, see the link below.

sum_(n=1)^oo (2n^2-1)/(3n^5+2n+1) Use the Limit Comparison Test to determine the convergence or divergence of the series.

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)^oo(2n^2-1)/(3n^5+2n+1)
Let the comparison series be sum_(n=1)^oon^2/n^5=sum_(n=1)^oo1/n^3
a_n/b_n=((2n^2-1)/(3n^5+2n+1))/(1/n^3)
a_n/b_n=(n^3(2n^2-1))/(3n^5+2n+1)
a_n/b_n=(2n^5-n^3)/(3n^5+2n+1)
lim_(n->oo)a_n/b_n=lim_(n->oo)(2n^5-n^3)/(3n^5+2n+1)
=lim_(n->oo)(n^5(2-n^3/n^5))/(n^5(3+(2n)/n^5+1/n^5))
=lim_(n->oo)(2-1/n^2)/(3+2/n^4+1/n^5)
=2/3>0
The comparison series sum_(n=1)^oo1/n^3 is a p-series with p=3
As per p-series test sum_(n=1)^oo1/n^p is convergent if p>1 and divergent if 0Since the comparison series sum_(n=1)^oo1/n^3 converges, so the series sum_(n=1)^oo(2n^2-1)/(3n^5+2n+1) as well ,converges by the limit comparison test.

In The Things They Carried, what are the main character's traits, strengths, or weaknesses? As the story progresses, to what degree do his/her traits become more or less prominent, and how does that work out for the character (does it have good effects or bad effects)?

The main character in The Things They Carried, Tim O'Brien, has the strength of observation and of empathy with the soldiers around him. His weakness is that he joined the army out of fear of seeming like a coward. Over time, he develops greater and greater strength as a writer by observing the men around him--soldiers such as Jimmy Cross, who loves a girl named Martha back home who can never love him back. Tim O'Brien (the author) says of Tim O'Brien (the main character): 




"I feel guilty sometimes. Forty-three years old and I'm still writing war stories. My daughter Kathleen tells me it's an obsession, that I should write about a little girl who finds a million dollars and spends it all on a Shetland pony. In a way, I guess, she's right: I should forget it. But the thing about remembering is that you don't forget."

Therefore, Tim O'Brien's strengths as a writer and observer become strengthened over time as he lives through Vietnam and then spends the years after the war writing about what he witnessed and experienced. His weaknesses diminish, as it's clear that both fighting in the war and writing about it require courage (and he is therefore not a coward).
His writing has good effects, as it helps him make sense of his past. As he writes in the story "The Rainy River" of the shame he's had to live with for years, "by putting the facts down on paper, I'm hoping to relieve at least some of the pressure on my dreams." In other words, writing is cathartic for him and helps him shake some of the demons that trouble him, and writing also helps him remember and honor the soldiers who fought with him.