Prove that \begin{equation} \lim_{x\to\infty}\,\frac{1}{x^n}=0. \end{equation}

Problem: 

Prove that
\begin{equation}
\lim_{x\to\infty}\,\frac{1}{x^n}=0
\end{equation}
where $n=1,2,3,\cdots$.

Answer: 

It is true that \begin{equation} \lim_{x\to\infty}\,\frac{1}{x^n}=0. \end{equation}