Homework Help: calculus

Posted by Paul on Wednesday, February 24, 2010 at 11:13am.

Posted by Paul on Friday, February 19, 2010 at 3:57am.

I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? And what happens to the graph and to the value of the integral as N approaches infinity? Does the graph confirm the limiting behavior of the integral's value?

* Calculus - Damon, Friday, February 19, 2010 at 10:07am

well, e^0 is 1
and e^.5 = 1.64
and e^1 is 2.72
so it is a sine wave with increasing amplitude as you approach 1 and frequency increasing with N
The integral of e^ax sin bx dx is
[e^ax/(a^2+b^2)] [a sin bx -b cos bx}here a = 1 and b = N
so
[e^x/(1+N^2)] [sin Nx - N cos Nx]
as N gets big
this looks like
e^x (-N cos Nx)/N^2
or
(-e^x/N)(cos Nx)
e^x is that small constant and cos Nx ranges between -1 and + 1 so as N gets big this goes to zero like 1/N

* Calculus - Paul, Wednesday, February 24, 2010 at 11:12am

But how did you arrive at "as N gets big this looks like e^x(-NcosNx)/N^2?????

calculus - bobpursley, Wednesday, February 24, 2010 at 11:36am
Professor Damon is describing the integral, not the function.

Have you graphed this function? For various N?
calculus - Paul, Wednesday, February 24, 2010 at 12:11pm
Yes I have, but I don't understand why the integral would go to zero. And the description of the interval.
calculus - Paul, Wednesday, February 24, 2010 at 12:18pm
is it because every interval of one the integrals approach 1?
calculus - Paul, Wednesday, February 24, 2010 at 12:18pm
I meant to say zero
calculus - Paul, Wednesday, February 24, 2010 at 12:20pm
But then would this confirm the limiting behavior of the graph because at every interval up to infinity it would approaching zero?

Answer this Question

Related Questions

Calculus - I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a...
calculus II - I have the function f(x)=e^x*sinNx on the interval [0,1] where N ...
Algebra-still need some help - Homework Help Forum: Algebra Posted by Jena on ...
Algebra- is my answer right - The function g is defined by g(x)=3x^2+6. Find g(...
calculus - consider the function f(x) = e^x(sinNx) on the interval [0,1] where N...
calculus - consider the function f(x) = e^x(sinNx) on the interval [0,1] where N...
Physics- repost - Posted by jude on Saturday, February 6, 2010 at 2:20am. Given ...
FOR MATHMATE - Media services charges $40 for a phone and 20/mth for its economy...
English - Posted by rfvv on Friday, July 2, 2010 at 1:00am. 1. What does she ...
calculus - I have posted this question earlier and had the answer given to me ...

For Further Reading

First Name:
School Subject:
Answer: