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Let f(x)= lim as h->0 of ((x+h)^2-x^2)/ h. For what value of x does f(x)= 4?

  • Math -

    (x+h)^2-x^2 = x^2 + 2 x h + h^2 - x^2
    or in other words 2 x h + h^2
    or h (2 x + h)
    divide that by h
    2x+h
    limit as h ---> 0 is
    2 x
    so
    f(x) = 2 x as h--->0
    4 = 2 x
    x = 2

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