Derivatives · Exercise 116

With the use of a graphing utility, use numerical or 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

$f\left(x\right)=\{\begin{array}{cc}\frac{1}{x}-3,\text{i}f& x\le 2\\ x^3+1,if& x>2\end{array}a=2$

OpenStax, Precalculus 2e · §12.4 Derivatives · Exercise 116