Results 1 to 3 of 3

Math Help - Using the degree six Taylor polynomial approximate the value of f(1).

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    57

    Using the degree six Taylor polynomial approximate the value of f(1).

    We know that e^x = n=0, infinite (x^n)/n!. Using this knowledge find the power series of the function f(x)=(e^x + e^-x)/2. Using the degree six Taylor polynomial approximate the value of f(1).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,406
    Thanks
    1294
    Quote Originally Posted by ewkimchi View Post
    We know that e^x = n=0, infinite (x^n)/n!. Using this knowledge find the power series of the function f(x)=(e^x + e^-x)/2. Using the degree six Taylor polynomial approximate the value of f(1).
    So where are you stuck?

    Replace x with -x and you have the Taylor series for e^{-x}.


    Then substitute the two series into f(x) and simplify...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2010
    Posts
    57

    Did I get it right?

    After integration, I got x + (x^3)/6 + (x^5)/120 + (x^7)/5040

    I plugged in 1 and got

    5923/5040.

    Is that right?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Second degree taylor polynomial help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 19th 2010, 11:32 AM
  2. Taylor Polynomial of degree 2
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 15th 2010, 03:51 PM
  3. Replies: 3
    Last Post: May 25th 2010, 03:16 PM
  4. Replies: 1
    Last Post: April 26th 2010, 03:22 PM
  5. Third-degree Taylor polynomial
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 31st 2010, 12:18 AM

Search Tags


/mathhelpforum @mathhelpforum