Limit

**asub1** · April 13th 2009, 10:26 AM

Hi. I need some help.

Let $f:\mathbb{R}\longrightarrow{}\mathbb{R}$ and $f`(a)=\lim_{h\to 0}{f(a+h)-f(a)\over h}$

prove that
* for $a_n<a<b_n$
* $\{a_n\}, \{b_n\}\subseteq{}\mathbb{R}-\{a\}$
* $lim\{a_n\}=lim \{b_n\}=a<br />$

$\Rightarrow{}$

$<br /> lim {f(b_n)-f(a_n)\over b_n-a_n}= f'(a)<br />$

Thanks.

**asub1** · April 13th 2009, 10:29 AM

I`ve try this exercise, but I don´t use that $a_n<a<b_n$ (I only use that a_n<b_n).
And (I think) the proposition it´s false if $a<a_n<b_n$ .

Thanks.

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