Results 1 to 4 of 4

Math Help - Maclaurin series error of approximation!?!

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    88

    Maclaurin series error of approximation!?!

    So it says find the Maclaurin series of
    f(x)=e^(2x)
    Then the part I don't get: How many terms of the series are required so that the error of the approximation is at most 0.01 for all x in the interval [−2, 2] ?
    I know the Mac. Series is (2x)^n/n! but how to find the error?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2010
    Posts
    1
    You're in Steve Desjardins' class? Aren't you?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    88
    Quote Originally Posted by uottawakid View Post
    You're in Steve Desjardins' class? Aren't you?
    Yup...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2009
    Posts
    30
    Quote Originally Posted by calculuskid1 View Post
    So it says find the Maclaurin series of
    f(x)=e^(2x)
    Then the part I don't get: How many terms of the series are required so that the error of the approximation is at most 0.01 for all x in the interval [−2, 2] ?
    I know the Mac. Series is (2x)^n/n! but how to find the error?
    If you truncate the MacLaurin series at n - 1 (including the n - 1 term in your approximation), then the error is:

    \Delta f(x) = \frac{x^n}{n!}\frac{d^n}{dx^n}f(\xi),~\xi \in [0, x]

    \xi is here some unknown value between 0 and x.

    \frac{d^n}{dx^n}e^{2x} = 2^n e^{2x}~\Rightarrow~\Delta f(x) = \frac{(2x)^n}{n!}e^{2\xi}

    Demanding a maximum error of \epsilon = 0.01 means that we want:

    \epsilon > \left|\frac{(2x)^n}{n!}e^{2\xi}\right|

    for ALL values of x and \xi in the area x \in [-2, 2],~\xi \in [-2, 2]. The expression has a maximum value at x = \xi = 2. So then we should find the smallest value of n possible for which:

    \epsilon > \frac{4^n}{n!}e^4

    I don't have my calculator for the moment, but I guess you can check for yourself for what n this is true.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. McLaurin Series Error Approximation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 9th 2011, 10:26 AM
  2. Taylor series approximation and error
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 13th 2011, 09:13 AM
  3. Maclaurin Series(approximation)
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 10th 2009, 05:00 AM
  4. Error approximation for an alternating series
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 17th 2009, 01:11 PM
  5. MacLaurin series error estimation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 15th 2009, 01:13 PM

Search Tags


/mathhelpforum @mathhelpforum