Chapter 2.5, Problem 204E

Using the function from the previous exercise, use the precise definition of limits to show that $\underset{x\to a}{\lim }f\left(x\right)$ does not exist for $a\ne 0$ .

For the following exercises, suppose that $\underset{x\to a}{\lim }f\left(x\right)=L$ and $\underset{x\to a}{\lim }g\left(x\right)=M$ both exist. Use the precise definition of limits to prove the following limit laws: