Does f(x) Approach Zero as x Approaches Infinity?

[Math_Frank]

Homework Statement

Given the odd integral

\int_{a}^{b} f(x) dx How do I prove that

f(x) -> 0 for x \to \infty??

The Attempt at a Solution

Is it? For the above to be true, then there exist an \epsilon > 0 such that

|\int_{a}^{b} f(x) dx-0| \leq \epsilon?

I am stuck here!

Am I going the right way?

Sincerely
Frank

 

[NateTG]

What you've written doesn't really make sense. What is this question from and about?

 

[Math_Frank]

What you've written doesn't really make sense. What is this question from and about?

The Question is

Given the integeral

f(t) = \int_{t}^{2t} e^{-x^2} dx then prove that if f(x) \to 0 then

n \to \infty

Isn't that convergens or it simply existence of the limit?

 

[NateTG]

The Question is

Given the integeral

f(t) = \int_{t}^{2t} e^{-x^2} dx then prove that if f(x) \to 0 then

n \to \infty

Isn't that convergens or it simply existence of the limit?

Where does n come from?

Do you mean "\lim_{x \rightarrow \infty} f(x)=0" when you write "f(x) \to 0"

 

[Math_Frank]

Where does n come from?

Do you mean "\lim_{x \rightarrow \infty} f(x)=0" when you write "f(x) \to 0"

Yes.

 

[NateTG]

You need to show both existence and convergence of the limit.