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Homework Help: Maclaurin Expansion

  1. May 21, 2010 #1
    Hi, I recently sat my Maths examination and there was a Maclaurin expansion question that I made an attempt at but I think it was wrong, it would be good if I could get help on this, it's too late to be of any real help but it will help me understand where I went wrong:

    Obtain the first three non-zero terms in the Maclaurin expansion of (1 + sin2x)

    What I done here was, let f(x) = (1 + sin2x) and differentiated until I got three non-zero terms when plugging in x = 0. But I'm not sure if this is "expandable" or whether I need to change sin2x into something that can be expanded.

    Did I do the right thing or did I make a mistake?
  2. jcsd
  3. May 21, 2010 #2
    The first term is 1.
  4. May 21, 2010 #3


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    Staff Emeritus
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    What you describe sounds like one of several correct ways to attack the problem. Of course, I cannot tell if you executed the attack correctly.
  5. May 21, 2010 #4


    Staff: Mentor

    A quicker way (and one probably alluded to by Hurkyl) is to take a couple of terms of the Maclaurin series for sin(x), square them, and then add 1.
  6. May 21, 2010 #5
    Or use the trig formula

    \sin^{2} x = \frac{1 - \cos{2 x}}{2}

    and use the Maclaurin series for the cosine.
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