Results 1 to 2 of 2

Math Help - TEST Preparations; Integrals.

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    TEST Preparations; Integrals.

    Let F(x)=e^{-x^2}\int_0^x e^{t^2}dt

    I have proved the following(I don't know if this will be useful):

    F'(x)+2xF(x)=1

    Now, I need to find for which values of a we get:
    lim_{x\to 0}\frac{F(x)}{x^a}=1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Expand the function F(x) is a Taylor series at zero.

    You should get something like F(x) \approx x-\frac{2}{3}x^3+\mathcal{O}(x^5)

    This gives

    \frac{F(x)}{x^a}\approx x^{1-a}-\frac{2}{3}x^{3-a}+\mathcal{O}(x^{5-a})

    I hope this helps.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrals - test tomorrow
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 15th 2009, 01:41 PM
  2. Replies: 1
    Last Post: February 17th 2009, 12:37 PM
  3. comparison test for improper integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 20th 2009, 05:21 PM
  4. Maths exam preparations help please!!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 4th 2008, 05:20 PM
  5. Test at 7pm, stuck on Trig Integrals.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 4th 2008, 12:36 PM

Search Tags


/mathhelpforum @mathhelpforum