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How to solve where a maclaurin series intersects a graph

  1. Apr 1, 2013 #1
    I have just finished a unit on constructing taylor and maclaurin polynomials and series.
    However I am really lost on how to find the answer to this problem that i found online for the test review and its going to be on my test, I know how to construct a maclaurin polynomial and have a vague sense of how to use it, but since the polynomial is centered at zero and the two graphs don't intersect at zero, isn't there some degree of error?

    gahh, I don't understand and would really appreaciate a nudge in the right direction..
    Here is the problem:
    http://img534.imageshack.us/img534/7917/problemthree.png [Broken]
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 1, 2013 #2
    Because the series is infinite, you cannot treat it as a polynomial equation. However, the left side is just cos (2x), so you need to solve

    cos(2x)=2x^3.

    This cannot be solved (as far as I know) analytically, the approx. solution is 0.58236.
     
  4. Apr 1, 2013 #3
    thanks much, that makes sense to me now.. Without converting it into cos(2x) though, is that a solvable problem? Like what if you couldn't put that into any abbreviated equation, like sin or cos or e^x or a geometric series?

    is it actually possible to solve where a random maclaurin and a graph intersect.. ?
     
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