Prove that if \begin{equation}\lim_{x\to a-}\,f(x)=L\quad\mbox{and}\quad\lim_{x\to a+}\,f(x)=L\end{equation} then \begin{equation}\lim_{x\to a\,}\,f(x)=L.\end{equation}
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Lesson Parent:
Problem:
Prove that if \begin{equation}\lim_{x\to a-}\,f(x)=L\quad\mbox{and}\quad\lim_{x\to a+}\,f(x)=L\end{equation} then \begin{equation}\lim_{x\to a\,}\,f(x)=L.\end{equation}
Answer:
It is true that if \begin{equation}\lim_{x\to a-}\,f(x)=L\quad\mbox{and}\quad\lim_{x\to a+}\,f(x)=L\end{equation} then \begin{equation}\lim_{x\to a\,}\,f(x)=L.\end{equation}
