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Proving Lagrange's Remainder from Taylor's Theorem

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data
    I'm interested in the use of the mean value theorem of integration to convert Taylor's theorem into Lagrange's remainder. Though, I'm confused as to how it's used in the conversion. Could someone explain to me how the MVT of integration is used to convert Taylor's theorem into Lagrange's remainder?


    2. Relevant equations
    I"m bad with LaTeX, but it's Taylor's theorem right here: http://upload.wikimedia.org/math/6/d/7/6d70410a12402233d48598420cb7995f.png
    and Lagrange's remainder right here: http://upload.wikimedia.org/math/2/1/2/212f9b5c042521027f93d959faf79798.png

    3. The attempt at a solution
    I reviewed the mean value theorem for integration, but I'm rather clueless as to how it's used to convert Taylor's theorem into Lagrange's remainder.
     
  2. jcsd
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