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.