Prove that \[ \lim_{x\to a}\frac{1}{x}=\frac{1}{a} \] for any $a$ in $(0,\infty)$.

Problem: 

Prove that
\[
\lim_{x\to a}\frac{1}{x}=\frac{1}{a}
\]
for any $a$ in $(0,\infty)$.

Answer: 

It is true that \[ \lim_{x\to a}\frac{1}{x}=\frac{1}{a} \] for any $a$ in $(0,\infty)$.