# Thread: Example of limit of a function

1. ## Example of limit of a function

Find an example of a function $f0,1) \rightarrow \mathbb {R} " alt="f0,1) \rightarrow \mathbb {R} " /> that is differentiable with $f'(x)$ not bounded, and that $\lim _{x \rightarrow 0^+ } f(x)$ do not exist.

Umm... I can't really think of any examples. Since $f(x)= \frac {1}{x}$ has a bounded derivative.

$f(x)= \frac {1}{x}$ has a bounded derivative.
3. the derivative is $-x^{(-2)} = - \frac {1}{x^2}$, yeah, it is not bounded below, hell. Thanks.