# Calculus

posted by .

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 -

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 -

Now how would you describe the graph of this function when say N=5, N=10, and N=100?

And what does it mean does the graph confirm the limiting behavior of the integral's value?

• Calculus -

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

## Similar Questions

1. ### calculus

consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value …
2. ### calculus

consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value …
3. ### calculus II

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}?
4. ### 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}?
5. ### Calculus

I'm supposed to find the average value of the function over the given interval. f(x) = sin(nx), interval from 0 to pi/n, where n is a positive integer. I know the average value formula, and I know that the integral of that function …
6. ### College Algebra

1.Answer the following for the given quadratic function. f(x) = -2x^2 - 8x - 13 (a) does the graph of f open up or down?
7. ### Math Graph

In polar coordinates, the graph r=sin(θ)/cos^2(θ) represents the function y=(a_n)*x^n+(a_(n−1))*x^(n−1)+…+a_0 in Cartesian coordinates, where n is a positive integer and (a_i) are real numbers. What is the value …
8. ### math

When p is an odd positive integer, then the graph of the power function f(x)=x^p is similar to the graph of y=?
9. ### pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2
10. ### pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2

More Similar Questions