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Math Help - Absolute Error and Relative Error

  1. #1
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    Absolute Error and Relative Error

    How do you find absolute and relative error?

    For example, one of my homework problems:

    Find the linear approximation to f(x)=ex at x=0 and use it to appoximate e0.1. My answers were x+1 and 1.01. I also had to use x+1 to approximate e-0.25 which I got 0.75. I also have to find the absolute and relative error. How would I do this? And which is closer to its corresponding actual value? Why?
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  2. #2
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    Re: Absolute Error and Relative Error

    Absolute error is (correct value - estimate), and relative error is (correct value - estimate)/(correct value). For example, if you estimate a distance as 500 miles and the actual value is 505 miles, your absolute error is 5 miles, and your relative error is 5/505 = 0.99%.

    Approximations (linear or otherwise) are typically less accurate when they're further away from the known value. So I would expect the relative error to be greater at -0.25 than at 0.1. I didn't do the calculation, though.

    - Hollywood
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