Question

# How to find removable singularity?

Open in App
Solution

## Step 1: Explaining how to find removable singularity:A removable singularity of a function is a point ${z}_{0}$ where the function $\mathrm{f}\left({\mathrm{z}}_{0}\right)$ appears to be undefined. We can remove this singularity by redefining the function, then we can say we remove the singularity.Step 2: Writing example:$\mathrm{f}\left(\mathrm{z}\right)=\frac{{\mathrm{z}}^{2}-1}{\mathrm{z}-1}$ at $\mathrm{z}=1$the function is undefined.$\mathrm{f}\left(\mathrm{z}\right)$ has a removable singularity.$\mathrm{f}\left(\mathrm{z}\right)=\frac{\left(\mathrm{z}-1\right)\left(\mathrm{z}+1\right)}{\left(\mathrm{z}-1\right)}\mathbf{}\left[\because \left({\mathrm{a}}^{2}-{\mathrm{b}}^{2}\right)=\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}-\mathrm{b}\right)\right]\phantom{\rule{0ex}{0ex}}\mathrm{f}\left(\mathrm{z}\right)=\left(\mathrm{z}+1\right)$Now the function has no singularity as we removed it.Hence, in this way, we can find removable singularity.

Suggest Corrections
0
Related Videos