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Analysis problem using the Lagrange Remainder Theorem

  1. Jun 27, 2011 #1
    1. The problem statement, all variables and given/known data
    Prove that for every pair of numbers x and h, [itex]\left|sin\left(x+h\right)-\left(sinx+hcosx\right)\right|\leq\frac{h^{2}}{2}[/itex]


    3. The attempt at a solution
    Let f(x)= [itex]\left|sin\left(x+h\right)-\left(sinx-hcosx\right)\right|[/itex]?
    and then to center the taylor polynomial around 0 let h=0? I'm not sure how to get the taylor polynomial for this so that it can be compared to [itex]\frac{h^{2}}{2}[/itex]
     
  2. jcsd
  3. Jun 27, 2011 #2

    micromass

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    Hi shan1732! :smile:

    Try to calculate the Taylor polynomial of the sine around x.
     
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