Prove that if \begin{equation} \lim_{x\to\infty}\,f(x)=L \end{equation} and $L\neq 0$ then \begin{equation} \lim_{x\to\infty}\,\frac{1}{f(x)}=\frac{1}{L}. \end{equation}
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Lesson Parent:
Problem:
Prove that if
\begin{equation}
\lim_{x\to\infty}\,f(x)=L
\end{equation}
and $L\neq 0$ then
\begin{equation}
\lim_{x\to\infty}\,\frac{1}{f(x)}=\frac{1}{L}.
\end{equation}
Answer:
It is true that \begin{equation} \lim_{x\to\infty}\,\frac{1}{f(x)}=\frac{1}{L}. \end{equation}
