calculus

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?????

  1. 0
  2. 1
asked by Paul
  1. Professor Damon is describing the integral, not the function.

    Have you graphed this function? For various N?

    posted by bobpursley
  2. Yes I have, but I don't understand why the integral would go to zero. And the description of the interval.

    posted by Paul
  3. is it because every interval of one the integrals approach 1?

    posted by Paul
  4. I meant to say zero

    posted by Paul
  5. But then would this confirm the limiting behavior of the graph because at every interval up to infinity it would approaching zero?

    posted by Paul

Respond to this Question

First Name

Your Response

Similar Questions

  1. English

    Posted by rfvv on Friday, July 2, 2010 at 1:00am. 1. What does she look like? She looks sad. 2. What is she like? She looks happy. 3. How does she look? She looks surprised. 4. What does her appearance look like? She looks upset.
  2. Algebra- is my answer right

    The function g is defined by g(x)=3x^2+6. Find g(5y) Algebra - drwls, Friday, February 4, 2011 at 11:07am 3*(5y)^2 + 6 = __? Algebra - Janet, Friday, February 4, 2011 at 3:56pm I get 75y+6
  3. Physics- repost

    Posted by jude on Saturday, February 6, 2010 at 2:20am. Given a square of sidelength a = 5 cm. We place a charged particle at each corner, three of them carry + 2 nC of charge and one carries the same amount of negative charge.
  4. FOR MATHMATE

    Media services charges $40 for a phone and 20/mth for its economy plan. It says to find a model that determines the total cost, C(t), of operationg a media Services phone for t months. I think the answer should be in this equation
  5. Algebra-still need some help

    Homework Help Forum: Algebra Posted by Jena on Thursday, February 3, 2011 at 7:32pm. Find the domain of the function. f(x)=(sqrt x+6)/(-2x-5) Write your answer as an interval or union of intervals. Algebra - David, Thursday,
  6. accounting

    On February 1, 2010, Par5 paid property taxes on its warehouse for the calendar year 2010 in the amount of $385,000. In the first week of June 2010, Par5 made unanticipated major repairs to its warehouse at a cost of $3,000,000.
  7. physics

    I have another question for the problem below, so What is the speed of the car just before it lands safely on the other side? would it be the same 38.6 meters/sec A 10,000N car comes to a bridge during a storm and finds the bridge
  8. physics

    I have another question for the problem below, so What is the speed of the car just before it lands safely on the other side? would it be the same 38.6 meters/sec A 10,000N car comes to a bridge during a storm and finds the bridge
  9. physics

    I have another question for the problem below, so What is the speed of the car just before it lands safely on the other side? would it be the same 38.6 meters/sec A 10,000N car comes to a bridge during a storm and finds the bridge
  10. Math Fractions

    Posted by Mary Mac on Friday, May 9, 2008 at 10:01am. I have this fraction: 6 2/9 + 1 3/4 - 3 5/6= Okay First I changed the mixed numbers into improper fractions. I got this: 56/9 + 7/4 + 23/6 Then I thought you have to find the

More Similar Questions