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Math Help - Linear Approximation and Error Problem

  1. #1
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    Linear Approximation and Error Problem

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




    I need the and the error in Linear Approximation, please help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Quiz0n View Post
    Estimate the quantity using Linear Approximation and find the error using a calculator.




    I need the and the error in Linear Approximation, please help!
    Look at the first term:

    <br />
\frac{1}{\sqrt{95+3}}= \frac{1}{\sqrt{95}}\frac{1}{\sqrt{1+3/95}}<br />

    ..... = \frac{1}{\sqrt{95}} [1-(1/2)(3/95) + R]

    where R \approx (3/8)(3/95)^2 is the remainder, or the error in the linear approximation.
    (here I am using a rule of thumb that the error is approximatly the first neglected term, in this case
    this can be made precise)

    So:

    <br />
\frac{1}{\sqrt{98}}-\frac{1}{\sqrt{95}} \approx -(1/2)(3/95^{1.5}) + R/\sqrt{95}<br />

    RonL
    Last edited by CaptainBlack; October 9th 2007 at 01:17 PM.
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  3. #3
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    I need in a numerical form, I got the answer -0.0015 using examples from my textbook, but it's apparently incorrect. Thanks for the help. I still can't figure it out.
    Last edited by Quiz0n; October 9th 2007 at 03:21 PM. Reason: I'm lost!
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Quiz0n View Post
    I need in a numerical form, I got the answer -0.0015 using examples from my textbook, but it's apparently incorrect. Thanks for the help. I still can't figure it out.
    You have a calculator, so you can evaluate what I gave in my earlier post.

    If you are going to give an answer to two significant digits round it correctly
    don't just truncate the answer to two significant digits.

    RonL
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