Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By hollywood

Math Help - Derivative of a complex function using limit definition

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    116
    Thanks
    1

    Derivative of a complex function using limit definition

    Find the derivative of f(z)=5z^2-10z+8 using the following definition:

    f'(z_0)=\lim_{z\to z_0}\frac{f(z)-f(z_0)}{z-z_0}

    I started with

    f'(z_0)=\lim_{z\to z_0}\frac{5z^2-10z+8-(5z_0^2-10z_0+8)}{z-z_0}

    which simplifies a bit to

    f'(z_0)=\lim_{z\to z_0}\frac{5z^2-10z-5z_0^2+10z_0}{z-z_0}

    but where do you go from there? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Derivative of a complex function using limit definition

    Quote Originally Posted by Ragnarok View Post
    Find the derivative of f(z)=5z^2-10z+8 using the following definition:

    f'(z_0)=\lim_{z\to z_0}\frac{f(z)-f(z_0)}{z-z_0}

    I started with

    f'(z_0)=\lim_{z\to z_0}\frac{5z^2-10z+8-(5z_0^2-10z_0+8)}{z-z_0}

    which simplifies a bit to

    f'(z_0)=\lim_{z\to z_0}\frac{5z^2-10z-5z_0^2+10z_0}{z-z_0}

    but where do you go from there? Thanks!
    \frac{5z^2-10z-5z_0^2+10z_0}{z-z_0}=\frac{5(z^2-z_0^2)-10(z-z_0)}{z-z_0}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2010
    Posts
    980
    Thanks
    236

    Re: Derivative of a complex function using limit definition

    Try this:

    f'(z_0)=\lim_{z\to z_0}\frac{5z^2-5z_0^2-10z+10z_0}{z-z_0}

    f'(z_0)=\lim_{z\to z_0}\frac{5(z+z_0)(z-z_0)-10(z-z_0)}{z-z_0}

    - Hollywood

    Awww - Plato, you beat me!
    Thanks from Ragnarok
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Apr 2010
    Posts
    116
    Thanks
    1

    Re: Derivative of a complex function using limit definition

    Ah thank you! I forgot my difference of squares factorization.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative using a limit definition
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 6th 2012, 09:17 AM
  2. Derivative of complex function using definition
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 9th 2011, 04:55 AM
  3. [SOLVED] limit definition of derivative
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 3rd 2011, 01:53 PM
  4. limit definition of a derivative?
    Posted in the Calculus Forum
    Replies: 8
    Last Post: December 5th 2009, 09:57 PM
  5. derivative using limit definition
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 5th 2008, 08:18 AM

Search Tags


/mathhelpforum @mathhelpforum