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Math Help - Approximation

  1. #1
    MHF Contributor Amer's Avatar
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    Approximation

    I have a question in numerical analysis and I do not know where to put it so I post it here ok the question


    Find the largest interval in which p^{*} must lie to approximate p with relative error at most 10^{-4} for each value of p


    a.\pi \quad\quad b.e \quad\quad c.\sqrt{2} \quad\quad d.\sqrt[3]{7}


    I know that relative error = \frac{\mid p-p^*\mid}{\mid p\mid}

    p^* is the approximation to for p

    can anyone tell me how I can solve questions like this ..........

    Thanks
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  2. #2
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    |p - p*| / |p| <= 10^(-4), so |p - p*| <= |p|.10^(-4).
    (a) p = pi.
    |pi - p*| <= pi.*10^(-4) = 3.14159 * 0.0001 = 0.000314
    so pi - 0.000314 <= p* <= pi + 0.000314
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by BobP View Post
    |p - p*| / |p| <= 10^(-4), so |p - p*| <= |p|.10^(-4).
    (a) p = pi.
    |pi - p*| <= pi.*10^(-4) = 3.14159 * 0.0001 = 0.000314
    so pi - 0.000314 <= p* <= pi + 0.000314

    can you explain more

    you sub pi instead of p

    \mid \pi - p^* \mid \leq \pi(10^{-4})=3.14159(\frac{1}{10000})

    I can't understand what you did in the red line
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  4. #4
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    The previous line is saying that the maximum difference between the exact and approximate values is to be about 0.000314. In that case the approximate value has to lie within the approximate range 3.141278 to 3.141907.
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