Prove that \begin{equation}\lim_{x\to a}\,f(x)\,g(x)=LK.\end{equation}

Problem: 

If
\begin{equation}
\lim_{x\to a}\,f(x)=L
\end{equation}
and
\begin{equation}
\lim_{x\to a}\,g(x)=K
\end{equation}
then prove that
\begin{equation}
\lim_{x\to a}\,f(x)\,g(x)=LK.
\end{equation}

Answer: 

It is true that \begin{equation}\lim_{x\to a}\,f(x)\,g(x)=LK.\end{equation}