1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Doubt regarding Taylor's theorem

  1. Aug 5, 2014 #1

    utkarshakash

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    In Taylor's series, the Lagrange form of remainder is given by
    [itex]R_n = \dfrac{f^{n+1}(t)(x-a)^{n+1}}{(n+1)!} \\ t \in [a,x][/itex]

    whereas my book states that it is given by
    [itex]\dfrac{h^n}{n!} f^n (a+ \theta h) \\ \theta(0,1) [/itex]

    I don't see how these two are interrelated. Can anyone explain ?
     
  2. jcsd
  3. Aug 5, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    How is ##h## defined in the expression from your book? Obviously, if ##h = x-a## then your book's expression is the same as the Lagrange version, because if ##\theta \in [0,1]## then ##a + \theta h## is a number in ##[a,x]##.
     
  4. Aug 5, 2014 #3

    utkarshakash

    User Avatar
    Gold Member

    But the book's version has nth derivative. Shouldn't it be n+1?
     
  5. Aug 5, 2014 #4

    Mark44

    Staff: Mentor

    It would be helpful to include some of the accompanying text in your book. It's possible that your text is giving the remainder after the terms of degree n - 1, while the more usual form you also show gives the remainder after terms of degree n.
     
  6. Aug 5, 2014 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I agree with Mark44. One form gives the remainder after an (n+1)-term polynomial (where the powers of (x-a) go from 0 to n) while the other (perhaps) gives the remainder after an n-term polynomial (where the powers go from 0 to n-1).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Doubt regarding Taylor's theorem
  1. Taylors Theorem (Replies: 3)

  2. Taylor theorem (Replies: 0)

  3. Taylors theorem (Replies: 14)

  4. Taylor theorem (Replies: 0)

  5. Taylor's Theorem (Replies: 1)

Loading...