lim [ln (1+nx)]/x=lim
(1/x)*ln(1+nx)
We'll use the power property of the
logarithm:
lim [ln (1+nx)]/x=lim
ln[(1+nx)^(1/x)]
The limit will override the logarithm and
we'll go near the function (1+nx)^(1/x).
ln lim
(1+nx)^(1/x) = ln lim [(1+nx)^(1/nx)]*n
ln lim
(1+nx)^(1/x)=ln e^n
ln lim (1+nx)^(1/x)=n*ln
e
ln lim
(1+nx)^(1/x)=n
But, from hypothesis, lim [ln
(1+nx)]/x=3, so n=3.
In my opinion, this story portrays marriage as an
institution that is harmful to women. It is saying that women who are married tend to
lose their personalities and their ability to have a life separate from their
husbands.
We can see this in the way that Louise Mallard
reacts to the "death" of her husband. When she believes that he is dead, she comes to
realize that now she is "free." She sees that there will come a series of years that
"would belong to her absolutely." During these years, she would be able to "live for
herself."
If this is what she is thinking when she thinks
her husband is dead, it implies that her married life is the opposite of all these
things.
The story, "The Fall of the House of Usher" by Edgar Allan Poe,
deals with two themes: evil and madness.
It seems as if Roderick
Usher is going insane. He is weighed down by worry, depression and hysteria. However, I have felt
when reading this that the undercurrents in the story tie the themes together, and that the evil
practiced in the house is responsible for Roderick's ensuing madness, among other things.
(Learning he has buried his sister alive also feeds Roderick's disconnect with a healthy mental
state.)
It has been suggested that the close ties that exist between
Roderick and his sister Madeline are based on an incestuous relationship. This was not an
uncommon practice among "great" families of England, especially the royal houses, in order to
keep power within that family.
If this is the evil that exists, it
explains the insanity as well, as incestuous relationships can cause physical and mental defects
in the offspring of such a joining, and as the House of Usher is dissolving away, one has the
sense that this brother and sister may be the result of a long line of ancestors who also were
involved in this practice.
Poe, then, may be speaking to the issue
of incest within families, as well as the issue of mental illness. (The mentally ill were not
well-cared for at that time, as little was understood about the
brain.)
Poe himself dealt with serious depression, and many of the
characters he writes about (e.g., "The Tell-Tale Heart" and "The Cask of Amontillado") are
insane.
First, we'll have to re-write the given fraction in a right way,
using the brackets:
f(x)
=[(2x+4)/(3x-1)]^3
We'll use the chain rule considering that the
function f(x) is the result of composing 2 functions:
f(x) =
u(v(x))
u(v) = v^3 => u'(v) =
3v^2
v(x) = (2x+4)/(3x-1) => v'(x) = [(2x+4)'*(3x-1) -
(2x+4)*(3x-1)']/(3x-1)^2
v'(x) = [2(3x-1) -
3(2x+4)]/(3x-1)^2
v'(x) = (6x - 2 - 6x -
12)/(3x-1)^2
v'(x) =
-14/(3x-1)^2
u(v(x)) =
3*[(2x+4)/(3x-1)]^2*[-14/(3x-1)^2]
f'(x) =
-42(2x+4)^2/(3x-1)^4
The derivative of the given function
is:
f'(x) =
-168(x+2)^2/(3x-1)^4
The mood of the story is how the author makes the reader
feel.
The mood of John Updike's "A & P" is that of
wonder, at first, and later, of sadness and
resignation.
Sammy is the name of the narrator of the
story. He describes the day when three girls come to the grocery store where he works in
their bathing suits. One of the girls he describes as queen-like: in the way she walks,
carries herself and turns her head.
This may simply be his
perception, but he is as taken with her as any boy his age is taken with a pretty girl:
he follows her progress through the store, noticing even how her feet hit the floor as
she walks. To him, this unnamed girl is simply
amazing.
When the three girls make their way to the front
of the store, Sammy is lucky enough to wait on them. After he rings up their purchase,
the manager chastises the girls for entering the store in bathing suits instead of
regular street clothes.
After the girls leave, Sammy feels
he must speak up for them, defend them for some reason, even though they have already
left. It is here that the mood begins to change. Sammy defends the girls on principle.
The manager, a friend of the family explains the rule, but Sammy cannot and will not
listen: he quits on the spot.
Even as he leaves, he knows
that he will regret the move. He also knows, somehow in his heart, that things will
never be the same for him. He has turned a corner that has taken him from his innocent
youth, one step closer to being a man. The deed has been done, which makes him kind of
sad, but he is resigned to it, almost as if he knows this is the natural way of
things.
In A Long Way Gone, Ishmael Beah is finally
put into rehabilitation, but he and the other boys do not take to it easily. The boys have been
exposed to harsh drugs for so long that it is not easy for them to recover. In addition to their
physical bodies being addicted to drugs, Ishmael and his friends have become addicted to
destructive behaviors and mentalities. Ishmael had been praised by the other soldiers for his
stealthy tactics during raids, and over time, Ishmael came to enjoy the praise of his elders. The
boys were taught to see their countrymen as enemies, and they were brainwashed into accepting
hatred into their lives. This hatred did not immediately leave the boys once they entered
rehabilitation. In fact, a fight breaks out at the rehabilitation center and the boys resort to
the manners that they learned as child soldiers. It takes much time before Ishmael is able to
leave these behaviors and beliefs behind.
I think one of the biggest similarities you can draw is the way
in which religion is portrayed in this future world. I am in no way saying that every religion in
our world can be compared to the beliefs of David's father and family, but this novel presents us
with a religious creed that is rigidly adhered to, no matter what the cost or price that needs to
be paid. Mothers are willing to let their children die through deformities. Thus, adherence to
this creed has dehumanised the world. It is as if religious belief is preventing mankind from
embracing and adapting to the changes in the world. The woman from Sea Land is definite about
what such an approach will mean for humanity:
"They have become history without being aware of it. They
are determined still that there is a final form to defend: soon they will attain the stability
they strive for, in the only form it is granted--a place among the
fossils..."
There is a sense in which,
unless religious beliefs allow themselves freedom to adapt and change to a constantly
transforming world, they consign themselves a place in the garbage of
history.
