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Calculus

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1. For a differentiable function f, f' be the funcyion defined by f'(x) lim h->0 =f(x+h)-f(x-h)/(h)
a: Determine f'(x) for f(x)=x
b: Determine f'(x) for f(x)=x^2

  • Calculus - ,

    I will do the 2nd one, ....

    f'(x) = lim ( (x+h)^2 - x^2 )/h , as h --> 0
    = lim (x^2 + 2xh + h^2 - x^2)/h
    = lim (2xh + h^2)/h , as h -->0
    = lim 2x + h , as h --> 0
    = 2x

    for the 1st one, you should get 1

  • Calculus - ,

    Thanks ^.^

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