Results 1 to 4 of 4

Math Help - Problem rewriting function as a power series

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    41

    Problem rewriting function as a power series

    Using known power series representations find
    limit as x => 0 of (1 - e^(x^4)) / (x^2 * sin (x^2))

    I cannot figure out how to rewrite this in any way that involves (1 / (1 - x)) which is how we rewrote most functions as power series in examples.

    How can i rewrite this function as a power series?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by crymorenoobs View Post
    Using known power series representations find
    limit as x => 0 of (1 - e^(x^4)) / (x^2 * sin (x^2))

    I cannot figure out how to rewrite this in any way that involves (1 / (1 - x)) which is how we rewrote most functions as power series in examples.

    How can i rewrite this function as a power series?
    You only need to use the first few terms of each series:

    \lim_{x \rightarrow 0} \frac{1 - (1 + x^4 + x^8 + ....)}{x^2 (x^2 - x^6/6 + ....)}


    = \lim_{x \rightarrow 0} \frac{-x^4 - x^8 - ....}{x^4 (1 - x^4/6 + ....)} = ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    41
    Oh ok thank you.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    \frac{1-e^{x^{4}}}{x^{2}\sin x^{2}}=\frac{1-e^{x^{4}}}{x^{4}}\cdot \frac{x^{2}}{\sin x^{2}}, and the limit is 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find the power series for the function....
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 13th 2010, 07:07 AM
  2. Power Series&Function Series Questions
    Posted in the Calculus Forum
    Replies: 10
    Last Post: January 19th 2010, 11:38 PM
  3. Power series for tangent function
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: October 24th 2009, 05:41 AM
  4. Rewriting an Analytic function based on its Power Series
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: July 30th 2009, 05:11 PM
  5. Power series representatin of a function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 17th 2009, 09:53 AM

Search Tags


/mathhelpforum @mathhelpforum