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Finding Taylor series about some point

  1. May 19, 2009 #1
    In this: http://www.math.tamu.edu/~fulling/coalweb/sinsubst.pdf

    It says that to find the Taylor series of sin(2x + 1) around the point x = 0, we cannot just substitute 2x+1 into the Maclaurin series for sinx because 2x + 1 doesn't approach a limit of 0 as x approaches 0.

    It says we have to find the Taylor series for sinx about x = 1, and then we can substitute 2x + 1 into it.

    Why is this?
  2. jcsd
  3. May 19, 2009 #2


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    Science Advisor

    The Taylor series for sinu around 1 will be a series of powers of (u-1). Substitute 2x+1 for u and you will have a series in powers of 2x.
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