Does the Mean Value of a Function Tend to Zero as T Increases to Infinity?

[zetafunction]

let be a function so $$\frac{1}{T}\int_{0}^{T}f(x)dx =0$$

as T--->oo does it man that the function f(x) tends to ' as x--->oo what if 'f' is an oscillating function ??

 

[HallsofIvy]

let be a function so $$\frac{1}{T}\int_{0}^{T}f(x)dx =0$$

as T--->oo does it man that the function f(x) tends to ' as x--->oo

I have no clue what you mean by that. What does ' mean?

what if 'f' is an oscillating function ??

Well, did you try an example? What if f(x)= sin(x)?

The integral oscillates (and is bounded) but the denominator gets larger and larger. The limit is 0.

 

[Nebuchadnezza]

I think "zetafunction" means

$$\lim_{T \to \infty } \frac{1}{T} \int_{0}^{T} f(x) dx$$

Just quote my post, to see how I made it.