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Math Help - loss of significance

  1. #1
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    loss of significance

    Loss of significance errors can be avoided by rearranging the function being evaluated. I must rearrange these functions to avoid loss of sig.

    a) f(x) = (1-cosx)/x^2

    b) f(x) = (cube root (1+x)) - 1

    I havn't a clue... any advice?

    Thanks for any help.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by jzellt View Post
    Loss of significance errors can be avoided by rearranging the function being evaluated. I must rearrange these functions to avoid loss of sig.

    a) f(x) = (1-cosx)/x^2

    b) f(x) = (cube root (1+x)) - 1

    I havn't a clue... any advice?

    Thanks for any help.
    I'll do (a).

    Loss of significance occurs at x=0. Note that \frac{1-\cos x}{x^2}=\frac{1-\cos x}{x^2}\cdot\frac{1+\cos x}{1+\cos x}=\frac{1-\cos^2 x}{x^2\left(1+\cos x\right)}=\left(\frac{\sin x}{x}\right)^2\cdot\frac{1}{1+\cos x}.

    Now note that as x\to 0, \frac{\sin x}{x}\to 1. Thus, \left(\frac{\sin x}{x}\right)^2\cdot\frac{1}{1+\cos x}\sim \frac{1}{1+\cos x}.
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  3. #3
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    Thanks, but how do you know to multiply by 1 + cosx / 1 + cosx?

    For the second question, would I multiply by (cube root(1-x)) / cube root(1-x))?
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