Results 1 to 3 of 3

Math Help - Taylor series.

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    35

    Taylor series.

    Let .
    Find the MacLaurin polynomial of degree 7 for .

    Use this polynomial to estimate the value of


    I don't really understand what it means by degree 7..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,695
    Thanks
    450
    \sin{u} = u - \frac{u^3}{3!} + \frac{u^5}{5!} - \frac{u^7}{7!} + ...

    so ...

    \sin(8t^2) = 8t^2 - \frac{(8t^2)^3}{3!} + \frac{(8t^2)^5}{5!} - \frac{(8t^2)^7}{7!} + ...

    \sin(8t^2) = 8t^2 - \frac{8^3t^6}{3!} + \frac{8^5t^{10}}{5!} - \frac{8^7t^{14}}{7!} + ...

    since you only need a 7th degree approximation for F(x) ...

    F(x) \approx \int_0^x 8t^2 - \frac{8^3t^6}{3!} \, dt<br />

    F(x) \approx \frac{8x^3}{3} - \frac{8^3x^7}{7 \cdot 3!}

    finish up by determining the approximation for F(.67)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    35
    i went to ((8t)^(14))/(14*13!)

    i was counting to 7

    anyway, thank you for the help
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Getting stuck on series - can't develop Taylor series.
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: October 5th 2010, 08:32 AM
  2. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  3. Formal power series & Taylor series
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 19th 2009, 09:01 AM
  4. Taylor Series / Power Series
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 4th 2009, 01:56 PM
  5. Replies: 9
    Last Post: April 3rd 2008, 05:50 PM

Search Tags


/mathhelpforum @mathhelpforum