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?

Question

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?

Answer 1

If you graph the function for those N, you will be able to see what the graph does.
Does changing N change the limit?

I am wondering why you are asking others this question: Did you graph it?

Answer 2

But how can you tell the limit?

Answer 3

On the graph? YOu look at the graph as x > limits. Look at the same graph for various N.