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Math Help - Limit

  1. #1
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    Oct 2008
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    Limit

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

    Thanks.
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