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    Hi, im really confused as to how to work out what values a taylor expansion is valid for. could someone please give me some help.

    heres an example.

    this is a maclaurin expansion (a=0) for

    expansion up to  x^2 is

    2x-2 x^2

    the answer says expansion is valid for mod 2x <1 so mod x<1/2

    i dont understand why this is.
    thank you

    The expansion involves higher and higher powers of x. For 2x<1, the higher powers will be fractional and so will decrease in magnitude (e.g. 0.5^2 = 0.25) For 2x>1 this is not the case: higher order temrs will be larger than 1, meaning the series will diverge to infinity.
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