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Thread: Limit

  1. #1
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    Oct 2008
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    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.
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  2. #2
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    Joined
    Oct 2008
    Posts
    16
    I`ve try this exercise, but I donīt use that $\displaystyle a_n<a<b_n$ (I only use that a_n<b_n).
    And (I think) the proposition itīs false if $\displaystyle a<a_n<b_n$.

    Thanks.
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