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Thread: Challenge. (1)

  1. March 6th 2010, 02:25 PM #1
    Miss
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    Challenge. (1)

    Hello

    Problem:
    Find a limit definition for f''(x) similar for f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}, Your limit should not have any f'. i.e., it must be in terms of f only.
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  2. March 6th 2010, 03:37 PM #2
    TheEmptySet
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    Quote Originally Posted by Miss View Post
    Hello

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

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

    Then

    \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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