Results 1 to 5 of 5

Math Help - Taylor polynomail approximation

  1. #1
    Member
    Joined
    May 2007
    Posts
    150

    Taylor polynomail approximation

    What is/how can I find the taylor polynomial for a semi circle, such as sqrt(25-x^2) ?

    when i calculate the derivatives at 0, i just get 0's so i don't know how I can do it.

    Thanks
    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
    Quote Originally Posted by stones44 View Post
    What is/how can I find the taylor polynomial for a semi circle, such as sqrt(25-x^2) ?

    when i calculate the derivatives at 0, i just get 0's so i don't know how I can do it.

    Thanks
    f(x)=\sqrt{25-x^2} \implies f(0)=5

    f'(x)=\frac{-x}{\sqrt{25-x^2}} \implies f'(0)=0

    I agree that the first derivative is zero,but what about the 2nd?

    You will find that all of the even derivaitves are equal to zero at zero, but not the odd.

    i.e

    f''(x)=\frac{-x^2}{(\sqrt{25-x^2})^3}-\frac{1}{\sqrt{25-x^2}} \implies f''(0)=-\frac{1}{5}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member iPod's Avatar
    Joined
    Jul 2009
    Posts
    87
    \sqrt{25-x^2}=0

    25-x^2=0

    x^2=25

    x=5

    x=-5
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2007
    Posts
    150
    wait...i have that the second derivative = -x^2 * (25-x^2)^-1.5
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    f(x)=(25-x^2)^{1/2}

    f'(x)=-x(25-x^2)^{-1/2}

    Now by the product rule

    f''(x)=-1(25-x^2)^{-1/2}-x^2(25-x^2)^{-3/2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Taylor approximation.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 6th 2010, 04:02 AM
  2. taylor approximation help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 13th 2010, 08:31 AM
  3. Taylor approximation
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 10th 2010, 06:55 AM
  4. taylor approximation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 14th 2009, 06:15 AM
  5. Final Exams: Taylor Polynomail Help!!!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 26th 2005, 01:08 AM

Search Tags


/mathhelpforum @mathhelpforum