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  1. #1
    Member Miss's Avatar
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    Challenge. (1)

    Hello

    Problem:
    Find a limit definition for $\displaystyle f''(x)$ similar for $\displaystyle f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$, Your limit should not have any $\displaystyle f'$. i.e., it must be in terms of $\displaystyle f$ only.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Miss View Post
    Hello

    Problem:
    Find a limit definition for $\displaystyle f''(x)$ similar for $\displaystyle f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$, Your limit should not have any $\displaystyle f'$. i.e., it must be in terms of $\displaystyle f$ only.
    define

    $\displaystyle g(x)=\frac{f(x+h)-f(x)}{h}$

    Then

    $\displaystyle \lim_{h \to 0}\frac{g(x+h)-g(x)}{h}=\lim_{h \to 0}\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}$
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