Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2011 / 5 / ii / Solution

A removable singularity at $a$ is an isolated singularity for which one can assign a value at $a$ to obtain a holomorphic function on the whole disc. Equivalently its Laurent series has no negative powers. A finite limit $L$ supplies the extension value $f(a)=L$.