Results 1 to 4 of 4

Math Help - Taylor Series problem, approximate and actual value.

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Malaysia
    Posts
    3

    Taylor Series problem, approximate and actual value.

    i) Derive the two variable second order Taylor series approximation,
    below, to f(x,y) = x3 + y3 5xy centred at (a,b) = (3,5).
    (ii) Calculate and state this approximate value at (x,y) = (5,7).
    (iii) Calculated and state the actual value of f(x,y) at (5,7).
    (iv) Calculated and state the error, Q(x,y) - f(x,y) at (5,7).

    This is a simple one,
    i've managed to work out part (i) and (ii) , provided my working isn't wrong.
    anyway, i'll show you what i've done.
    for (a,b) = (3,5) , f(x,y) = 77+2(x-3) + 60(y-5) + 1/2!(18)(x-3)^2 + 1/2!(22)(x-3)(y-5) + 1/2!(70)(x-3)(y-5) + 1/2!(30)(y-5)^2 .....

    so before I move on, I need to check if part(ii) has the same procedure as part(i)?? they changed the variable from (a,b) to (x,y) so do I still just sub in x,y = 5,7 like how i subbed in a,b = 3,5 for part i?

    part (iii) whats the difference between an actual and approximate value and how do u go about calculating it? does it have anything to do with truncation errors?

    (iv) i guess you just subtract part (iii) and (ii)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Re: Taylor Series problem, approximate and actual value.

    Try to expand your series expansion at (3,5) and see if you get the original f(x,y)!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Malaysia
    Posts
    3

    Re: Taylor Series problem, approximate and actual value.

    didn't i already do that??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Question Re: Taylor Series problem, approximate and actual value.

    I meant have you expanded, factored, and simplified this:
    f(x,y) = 77+2(x-3) + 60(y-5) + 1/2!(18)(x-3)^2 + 1/2!(22)(x-3)(y-5) + 1/2!(70)(x-3)(y-5) + 1/2!(30)(y-5)^2 .....
    Last edited by MaxJasper; October 17th 2012 at 07:15 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: September 1st 2012, 01:08 PM
  2. Taylor series problem
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 23rd 2011, 04:43 PM
  3. Replies: 2
    Last Post: June 2nd 2010, 09:48 AM
  4. Replies: 1
    Last Post: April 26th 2010, 03:22 PM
  5. approximate with Taylor remainder
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 17th 2008, 08:37 AM

Search Tags


/mathhelpforum @mathhelpforum