Evaluate the limit of y=(2x^2-x-3)/(x+1), x-->-1 using L'Hopital theorem.

We'll verify if the limit exists, for x =
-1.

We'll substitute x by -1 in the expression of the
function.

lim y = lim
(2x^2-x-3)/(x+1)

lim (2x^2-x-3)/(x+1) =  (2+1-3)/(-1+1) =
0/0

We've get an indetermination
case.

We could solve the problem in 2 ways, at
least.

We'll apply L'Hospital
rule:

lim f(x)/g(x) = lim
f'(x)/g'(x)

f(x) = 2x^2-x-3 => f'(x) =
4x-1

g(x) = x+1 => g'(x) =
1

lim (2x^2-x-3)/(x+1) = lim
(4x-1)

lim (2x^2-x-3)/(x+1) = 4*(-1) - 1 =
-5

In The Cider House Rules explain the significance of the moments of courage that present themselves.Thanks for your help.

I would say that the search for courage might rest with
Homer.  I think that a case could also be made for Dr. Larch, but Homer embodies courage
in a couple of ways.  Homer's desire for freedom and his willingness to embrace an
uncertain future where living life to its fullest is vitally important is an act of
courage for it is without fear or abandon.  When Homer decides to leave the orphanage,
there is little fear in his actions, while he lacks the knowledge to fully grasp what
lies ahead.  At the same time, I think that Homer represents courage when he embraces
and understands that he must become what he used to detest.  His stand on abortion, as
principled as it was, is something that he learns to place in a different context.  When
performing the abortion on Rose Rose, there is courage evident for he is confronting
what he originally opposed.  I think that in this light there is a sense of courage, as
Homer is able to embrace change and understand that being right and doing right might be
two different things at times.

What is the message that S.E Hinton wants to convey about violence in The Outsiders ?provide textual evidence :)

S.E. Hinton's The Outsiders can be
interpreted to have a few different messages about violence. I think the first and most
important message is that violence, especially between teens, is senseless and almost
never ends well. This is illustrated through the deaths of Bob, Johnny, and Dally. In
the first instance, Ponyboy was defending himself when he killed Bob, but because of his
gang he was unable to see Bob as a person, only as a Soc. It is only later when Ponyboy
begins to understand who Bob truly was as a human being. Johnny and Dally die on their
own terms, but both of their deaths are a result of Ponyboy's initial misstep. At the
end of the novel, it is clear that all of the characters have started to realize that
violence creates more troule than good. In the story, these teenagers act like adults,
and then realize that they are still kids who have committed very mature acts, and are
challenged to face the repercussions.

Another message could
be that, with determination, it is possible to escape a life of violence. At the novel's
end, despite Ponyboy's involvement in the gang throughout his life, the reader is left
to believe that he will go on to be successul in school, perhaps go to college, and
escape his prior poverty and crime.

Why did Louis XIV revoke the Edict of Nantes?

Now-days, the government relies on schools and TV to
inform, guide, propagandize, and mold the opinions and attitudes of the people.  In
Louis XIV's time, those functions were performed by the Church.  The king could issue a
decree and the priests would all read it in their churches.  The Catholic Church and
monarchy had evolved together.  They supported one
another.

In England, King James I told Puritian petitioners
who wanted the episcopal Church of England altered into a presbyterian church, "A
Scottish presbytery agreeth as well with monarchy as God and the devil."  This was
probably also the feeling of Louis XIV.  (Some historians have said that the American
War of Independence was a Presbyterian rebellion. Presbyterian churches are governed by
the people of each individual church; the Catholic church is governed by a Pope and
Cardinals, much like a country was governed by a king and his
ministers.)

Donald Kagan, et al, in their textbook
The Western Heritage since 1648 (1979), give it as Louis's reason,
that a country could not be under one law and one king unless it was also under one
religious system. They also say that until the time of his death, Louis thought he had
done a great thing for which "God was indebted to him."

In Frankenstein, why does Victor turn to the study of mathematics, and what prevents him from continuing this study?Frankenstein chapter 2 and 3

In Chapter 2 of Frankenstein, Victor
begins the study of mathematics, but it is "destiny" that causes him to change his
course of study to natural philosophy:

readability="21">

Before this I was not unacquainted with the more
obvious laws of electricity. On this occasion a man of great research in natural
philosophy was with us, and, excited by this catastrophe, he entered on the explanation
of a theory which he had formed on the subject of electricity and galvanism, which was
at once new and astonishing to me. All that he said threw greatly into the shade
Cornelius Agrippa, Albertus Magnus, and Paracelsus, the lords of my imagination; but by
some fatality the overthrow of these men disinclined me to pursue my accustomed studies.
It seemed to me as if nothing would or could ever be known. All that had so long engaged
my attention suddenly grew despicable. By one of those caprices of the mind, which we
are perhaps most subject to in early youth, I at once gave up my former occupations; set
down natural history and all its progeny as a deformed and abortive creation; and
entertained the greatest disdain for a would-be science, which could never even step
within the threshold of real knowledge. In this mood of mind I betook
myself to the mathematics, and the branches of study appertaining to that
science, as being built upon secure foundations, and so worthy of my
consideration.

It is destiny
that causes him to meet M. Waldman, who develops Victor's passion for the natural
sciences of galvanism, electromagnetism, and alchemy.  Victor might have been a good
mathematician, if he were devoid of passion.  But his passion causes him to pursue his
dreams and the God-like ideal, and so he seeks intuitively to seek the answers to
stopping death through the life sciences.

The Romantics
believed heavily in destiny.  To them, it was the inevitable by-product of their
passions.  So says Victor:

readability="15">

"I would account to myself for the birth of that
passion, which afterwards ruled my
destiny, I find it arise, like a mountain river, from
ignoble and almost forgotten sources; but, swelling as it proceeded, it became the
torrent which, in its course, has swept away all my hopes and
joys.

Victor ends the chapter
thusly:

It was
a strong effort of the spirit of good; but it was
ineffectual. Destiny was too potent, and her immutable laws
had decreed my utter and terrible
destruction.

This brash
idealism will cause Victor to rationalize his abuses of science (playing God and
isolating himself from others, all for the sake of discovery).  His belief in passion
and destiny is reckless.  Perhaps the world would have been safer if he had chosen
mathematics.

Verify if the function has limit if x-->1 f(x)=(x^2-4x+3)/(x-1)

To verify if the limit exists, for x = 1, we'll substitute
x by 1 in the expression of the function.

lim f(x) = lim
(x^2-4x+3)/(x-1)

lim (x^2-4x+3)/(x-1) =  (1-4+3)/(1-1) =
0/0

We notice that we've get an indetermination
case.

We could apply 2 methods for solving the
problem.

The first method is to calculate the roots of the
numerator. Since x = 1 has cancelled the numerator, then x = 1 is one of it's 2
roots.

We'll use Viete's relations to determine the other
root.

x1 + x2 = -(-4)/1

1 + x2
= 4

x2 = 4 - 1

x2 =
3

We'll re-write the numerator as a product of linear
factors:

x^2-4x+3 =
(x-1)(x-3)

We'll re-write the
limit:

lim (x-1)(x-3)/(x -
1)

We'll simplify:

lim
(x-1)(x-3)/(x - 1) = lim (x - 3)

We'll substitute x by
1:

lim (x - 3) =
1-3

lim (x^2-4x+3)/(x-1) =
-2

Compare the love that Romeo feels for Juliet to the love that he felt for Rosaline in Romeo and Juliet.

To compare means noting similarity and difference. In the
case of Romeo's different loves for Juliet and Rosaline, I find some surprising
similarities.

Romeo may have indeed been driven by two
things for both ladies when all was said and done: physical appearance and
attainability. Rosaline had beauty beyond measure (until Romeo met Juliet), yet she had
this feature that made her unattainable, she wanted to be a nun. Thus, dating and sex
were not an option for her. This usually makes a girl less attractive. I almost wonder
if Romeo did not just like the idea that she was out of his
reach.

Juliet was also beautiful, but at first Romeo did
not know how unattainable she was. Upon learning it though, he makes effort all the more
to know for sure that a future relationship was possible with
her.

In terms of difference, many people judge Romeo's
first love as infatuation. It was a crush, with no option to ever exercise feelings and
determine if a love relationship was possible. Some might even say it was lustful
because Romeo's words of adoration about Rosaline generally focused on her physical
beauty and sexual appeal. Romeo's second love, to Juliet, is often judged as true love
because it is a self-sacrificing love. Romeo is willing to give up on the feud and
appeal to Tybalt as a relative. He mourns with Juliet over their separation. Willing to
lose his own life to be with Juliet in heaven or wherever after life, many find Romeo's
suicide romantic.

A final worthy note is Romeo's
selfishness. Of both girls, Romeo wants what he wants and impulsively works to get it at
all costs.