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Math Help - Taylor series approximation and error

  1. #1
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    Taylor series approximation and error

    The question:

    For small values of s, how good is the approximation cos x \approx x ?

    By "small values", how small does the question want x to be? Less than 1? Less than 0.1? Less than 0.01?

    Also, how do I proceed to get an approximation of the error? After expressing cos x in terms of its Taylor series, at a point c=0, I get the error term in terms of O(x^2).

    Any help to extend my reasoning would be much appreciated.
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  2. #2
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    Quote Originally Posted by shailen.sobhee View Post
    The question:

    For small values of s, how good is the approximation cos x \approx x ?

    I assume you mean "For small values of x".

    As an approximation, not too good ... as x gets close to 0 , cos x approaches 1
    ...
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