# Singularity #2

• Jul 15th 2009, 01:42 PM
Richmond
Singularity #2
I need help on this one

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

Is this removable or essential singularity?

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

Is this removable or essential singularity?
• Jul 15th 2009, 02:16 PM
VonNemo19
Quote:

Originally Posted by Richmond
I need help on this one

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

Is this removable or essential singularity?

This is an essential singularity because $\displaystyle \lim_{z\to0}\sin{\frac{1}{z}}$ is not defined.
• Jul 15th 2009, 03:37 PM
mr fantastic
Quote:

Originally Posted by Richmond
I need help on this one

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

Is this removable or essential singularity?

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

Is this removable or essential singularity?

Consider the Laurent series of the functions around z = 0 ....
• Jul 15th 2009, 03:38 PM
pomp
Quote:

Originally Posted by Richmond
I need help on this one

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

Is this removable or essential singularity?

Did you try it for yourself last time? http://www.mathhelpforum.com/math-he...ngularity.html