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Math Help - Linear Approximation

  1. #1
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    Linear Approximation

    Estimate the quantity using Linear Approximation and find the error using a calculator.


    The Linear Approximation is:
    The error in Linear Approximation is:


    I know that:
    <br />
f(x) = 1/(sqrtx)<br />
 , a=95<br />
and the change in x is 4.

    So:

    f'(x)=-1/2(x)^(-3/2)
    f'(a)=-1/2(1/95)^(3/2)
    f'(a)=-.000539988606


    Change in F=f'(a)*Change in x
    So:

    delta f=(4)*(-.000539988606)
    delta f=-.0021599544


    Actual change=f(a+delta x)-f(a)
    =f(95+4)-f(95)
    =-.0020940537

    Error in Approximation= absolute value of (delta f - actual change)
    = (-.0021599544-(-.0020940537))
    =.000065900717


    **Updated with right answers for those that may need help.**
    Last edited by jwebb19; November 12th 2007 at 08:11 PM. Reason: Solved
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  2. #2
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    Solved the problem. Updated original post for those that may need help in the future.
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