Limit Reciprocal Rule Proof

Reciprocal Rule

Let $M,c\in R$ and $g$ is defined at an Punctured Interval. If ${\lim }_{x\to c}g(x)=M$ then ${\lim }_{x\to c}\frac{1}{g(x)}=\frac{1}{M}$ provided $M\ne 0$.

Proof