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Thread: Singularity #2

  1. July 15th 2009, 01:42 PM #1
    Richmond
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    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 03:38 PM. Reason: Fixed a latex exponent.
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  2. July 15th 2009, 02:16 PM #2
    VonNemo19
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    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.
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  3. July 15th 2009, 03:37 PM #3
    mr fantastic
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    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 ....
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  4. July 15th 2009, 03:38 PM #4
    pomp
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    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
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