Results 1 to 5 of 5

Math Help - Taylor's Theorem

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    225

    Taylor's Theorem

    Consider the forward difference approx. to f'

    f'(0)= f(h)-f(0) / h

    Let the error be E = f'(0)- (f(h)-f(0) / h)

    Derive a formula for E by Taylor expanding f about x0=0 and using the Remainder thm.

    So far I have f(x)=f(x0) + f'(x0)h+f''(x0)h^2 /2 + f'''(c)h^3 /6

    So the error will be f'''(c)h^3 /6 for some c in the interval

    What do I do now?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,310
    Thanks
    687

    Re: Taylor's Theorem

    shouldn't it be f(h) = f(0) + f'(0)h + f"(c)h^2/2, for some c in (0,h)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    225

    Re: Taylor's Theorem

    You're right. But my error term is the same, f'''(0)h^3 /6

    My error is supposed to be of the form K1h+k2h^2 and I'm not sure how to get there...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,310
    Thanks
    687

    Re: Taylor's Theorem

    if f(h) = f(0) + f'(0)h + f"(0)h^2/2 + f'''(c)h^3/6, then

    then

    f(h) - f(0) = f'(0)h + f"(0)h^2/2 + f'''(c)h^3/6

    [f(h) - f(0)]/h = f'(0) + f"(0)h/2 + f'''(c)h^2/6

    f'(0) - [f(h) - f(0)]/h = -f"(0)h/2 - f'''(c)h^2/6
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Aug 2008
    Posts
    225

    Re: Taylor's Theorem

    I was making a very stupid mistake. Thanks for helping!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. taylor's theorem
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: February 9th 2010, 08:11 AM
  2. taylor's theorem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 24th 2009, 06:14 AM
  3. Taylor's Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 28th 2009, 08:27 AM
  4. taylor's theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 2nd 2009, 07:36 PM
  5. Taylor's Theorem
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 23rd 2009, 07:52 AM

Search Tags


/mathhelpforum @mathhelpforum