Example of limit of a function

**tttcomrader** · October 20th 2008, 02:38 PM

Find an example of a function $f<img src=$ 0,1) \rightarrow \mathbb {R} " alt="f

0,1) \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.

**Opalg** · October 21st 2008, 01:37 AM

Originally Posted by tttcomrader

$f(x)= \frac {1}{x}$ has a bounded derivative.

Does it?

**tttcomrader** · October 21st 2008, 05:29 AM

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

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