1. ## limits problem

Hello

I need to give an example of a function f(x) such that limf(x), as x goes to infinity, exists but limf'(x) does not. Any help?

Thx

2. Originally Posted by AlexHall
Hello

I need to give an example of a function f(x) such that limf(x), as x goes to infinity, exists but limf'(x) does not. Any help?

Thx
$f(x)=\frac{\cos\left(x^{n\geqslant{2}}\right)}{x}$

3. Originally Posted by AlexHall
an example of a function f(x) such that limf(x), as x goes to infinity, exists but limf'(x) does not.
Try $f(x) = (x)\left( {\arctan (x)} \right)$.

4. Originally Posted by Plato
Try $f(x) = (x)\left( {\arctan (x)} \right)$.
Isn't that the converse of this question? The limit of the function is nonexistant but its derivative is finite.