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Thread: Estimate the Given Number

  1. #1
    Junior Member
    Sep 2008

    Estimate the Given Number

    I'm having some trouble with the following problems.

    Use a linear approximation (or differentials) to estimate the given number.

    1. (8.06)^(2/3)
    2. 1/1002

    My book doesn't go over the process of how to do these problems. Thanks for any help.
    Last edited by dm10; Oct 26th 2008 at 08:59 AM.
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  2. #2
    Global Moderator

    Nov 2005
    New York City
    Quote Originally Posted by dm10 View Post
    Let f(x) = (8+x)^{2/3} then f(h) \approx f(0) + hf'(0)

    Now f'(x) = \tfrac{2}{3}(8+x)^{-1/3} \implies f'(0) = \tfrac{2}{3}\cdot 8^{-1/3} = \tfrac{1}{3}

    This means, f(h) \approx 2 + \tfrac{h}{3}

    Now let h=.06

    The other problem is similar.
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