Chapter 11.2, Problem 45PE

(a)

To determine

To calculate: The value of $\underset{x\to 2^{-}}{\lim }f\left(x\right)$ where $f\left(x\right)=\{\begin{array}{c}{x}^2+5\text{ if }x<2\\ x^3+1\text{ if }x\ge 2\end{array}$ using properties of limits.

(b)

To determine

To calculate: The value of $\underset{x\to 2^{+}}{\lim }f\left(x\right)$ where $f\left(x\right)=\{\begin{array}{c}{x}^2+5\text{ if }x<2\\ x^3+1\text{ if }x\ge 2\end{array}$ using properties of limits.

(c)

To determine

The value of $\underset{x\to 2}{\lim }f\left(x\right)$ where $f\left(x\right)=\{\begin{array}{c}{x}^2+5\text{ if }x<2\\ x^3+1\text{ if }x\ge 2\end{array}$ using properties of limits.