Chapter 11.2, Problem 46PE

(a)

To determine

To calculate: The limit $\underset{x\to 2^{-}}{\lim }f\left(x\right)$ using properties of limits where $f\left(x\right)=\{\begin{array}{c}{x}^2+6\text{ if }x<2\\ x^3+2\text{ if }x\ge 2\end{array}$.

(b)

To determine

To calculate: The limit $\underset{x\to 2^{+}}{\lim }f\left(x\right)$ using properties of limits where $f\left(x\right)=\{\begin{array}{c}{x}^2+6\text{ if }x<2\\ x^3+2\text{ if }x\ge 2\end{array}$.

(c)

To determine

To calculate: The limit $\underset{x\to 2}{\lim }f\left(x\right)$ using properties of limits where $f\left(x\right)=\{\begin{array}{c}{x}^2+6\text{ if }x<2\\ x^3+2\text{ if }x\ge 2\end{array}$.