# Math Help - Singularity #2

1. ## 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?

2. Originally Posted by Richmond
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.

3. Originally Posted by Richmond
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 ....

4. Originally Posted by Richmond
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