Thread: Example of limit of a function

1. Example of limit of a function

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

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

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