12.1 Exercise 37

Use a graphing utility to find graphical evidence to determine the left- and right-hand limits of the function given as $x$ approaches $a .$ If the function has a limit as $x$ approaches $a ,$ state it. If not, discuss why there is no limit.

$\left(x\right) = \left\{\right. \begin{matrix}\frac{1}{x + 1} , & \text{if}\textrm{ } x = - 2 \\ \left(x + 1\right)^{2} , & \text{if}\textrm{ } x \neq - 2\end{matrix} a = - 2$