1. ## Limit

Hi. I need some help.

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

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

$\displaystyle \Rightarrow{}$

$\displaystyle lim {f(b_n)-f(a_n)\over b_n-a_n}= f'(a)$

Thanks.

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

Thanks.