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March 29, 2017

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f*(x) = lim as h -> 0 [f(x+h)-f(x-h)]/ h

write an equation that expresses the relationship between the functions f*(x) and f`

I know that f` is [f(x+h)-f(x)]/h but i have no clue how to write an equation to relate the two!!!

  • calculus - ,

    f(x+h)-f(x-h) =

    f(x+h) - f(x) + f(x) - f(x-h)

    lim as h -> 0 [f(x+h)-f(x-h)]/ h =


    lim as h -> 0 [f(x+h)-f(x)]/ h +

    lim as h -> 0 [f(x)-f(x-h)]/ h

    lim as h -> 0 [f(x)-f(x-h)]/ h

    also equals the derivative of f if the functon is differentiable.

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