Results 1 to 4 of 4

Math Help - Singularity #2

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    33

    Singularity #2

    I need help on this one

    f(z) = \sin(\frac{1}{z})

    Is this removable or essential singularity?

    f(z) = \frac {e^{3z} - 1}{z}

    Is this removable or essential singularity?
    Last edited by mr fantastic; July 15th 2009 at 04:38 PM. Reason: Fixed a latex exponent.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by Richmond View Post
    I need help on this one

    f(z) = \sin(\frac{1}{z})

    Is this removable or essential singularity?
    This is an essential singularity because \lim_{z\to0}\sin{\frac{1}{z}} is not defined.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Richmond View Post
    I need help on this one

    f(z) = \sin(\frac{1}{z})

    Is this removable or essential singularity?

    f(z) = \frac {e^{3z} - 1}{z}

    Is this removable or essential singularity?
    Consider the Laurent series of the functions around z = 0 ....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jun 2009
    Posts
    220
    Thanks
    1
    Quote Originally Posted by Richmond View Post
    I need help on this one

    f(z) = \sin(\frac{1}{z})

    Is this removable or essential singularity?
    Did you try it for yourself last time? http://www.mathhelpforum.com/math-he...ngularity.html
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. singularity
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 12th 2011, 08:51 AM
  2. Singularity
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 12th 2010, 07:57 PM
  3. Singularity of 1/z^(1/2) at z = 0?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 19th 2010, 07:45 AM
  4. isolated singularity
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 11th 2010, 10:11 AM
  5. Singularity
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: July 13th 2009, 11:14 AM

Search Tags


/mathhelpforum @mathhelpforum