Results 1 to 3 of 3

Math Help - Continuous Functions?

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    2

    Continuous Functions?

    Prove that the function satisfies the Cauchy Riemann Equations at z = 0, but is not differentiable at z = 0.

    f(z) = i, if y=x^2 and z not equal to 0 or 0, if y not equal to x^2 or z=0

    I can prove that the CRE hold, but am having problems with the second part. Solutions tell me that I can observe that f is not continuous at z=0, but why is this so?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by cm7251 View Post
    Prove that the function satisfies the Cauchy Riemann Equations at z = 0, but is not differentiable at z = 0.

    f(z) = i, if y=x^2 and z not equal to 0 or 0, if y not equal to x^2 or z=0

    I can prove that the CRE hold, but am having problems with the second part. Solutions tell me that I can observe that f is not continuous at z=0, but why is this so?

    Thanks.
    I'm sorry, but could you you possibly rephrase this. I am having trouble understanding what it means z\ne0\text{ or }0?

    Maybe another member will swoop in though.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    2
    Sorry.

    The function is defined in two ways;
    1) f(z) = 0, if z = 0 or  y\ne x^2
    2) f(z) = i, if  z\ne0 and y = x^2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Continuous Functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 22nd 2011, 11:07 AM
  2. Continuous Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 24th 2010, 03:56 AM
  3. Why are the functions f and g continuous?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 3rd 2009, 08:01 PM
  4. Continuous functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 1st 2009, 11:48 AM
  5. Continuous functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 26th 2008, 10:57 AM

Search Tags


/mathhelpforum @mathhelpforum