Calculus

Using the definition of derivative state the function, f(x) and the value of a for lim as h->0 of (square root of (121+h) -11)/h

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asked by Ben
  1. if
    f(x) = x^.5
    then
    f(x+h) = (x + h)^.5


    [f(x+h) - f(x)]/h = [(x+h)^.5-x^.5]/h

    binomial expansion of
    (x+h)^.5 = x^.5 + .5 x^-.5 h ..... higher powers of h
    so
    [ x^.5 + .5 x^-.5 h ...-x^.5 ]/h

    or
    .5 x^-.5 + higher powers of h

    = .5 x^-.5 as h --->0

    if x = 121
    f(x) = 121^.5 = 11
    f(x+h) = (121+h)^.5

    df(121)/dx = .5 (121)^-.5 = .5/11

    f(x) = 121

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    posted by Damon

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