Chapter 11.9, Problem 44E

(a)

To determine

To calculate: The $\underset{x\to {30}^{-}}{\lim }R\left(x\right)$ where $R\left(x\right)=\left\{\begin{array}{l}19.50+.31290x\text{ if }x\le \text{30,}\\ \text{24}\text{.2979+}\text{.15297}x\text{ if }x>30\end{array}\right\}$.

(b)

To determine

To calculate: The $\underset{x\to {30}^{+}}{\lim }R\left(x\right)$ where $R\left(x\right)=\left\{\begin{array}{l}19.50+.31290x\text{ if }x\le \text{30,}\\ \text{24}\text{.2979+}\text{.15297}x\text{ if }x>30\end{array}\right\}$.

(c)

To determine

To calculate: The $\underset{x\to 30}{\lim }R\left(x\right)$ where $R\left(x\right)=\left\{\begin{array}{l}19.50+.31290x\text{ if }x\le \text{30,}\\ \text{24}\text{.2979+}\text{.15297}x\text{ if }x>30\end{array}\right\}$.

(d)

To determine

To calculate: The value of $R\left(x\right)$ at $x=30$ where $R\left(x\right)=\left\{\begin{array}{l}19.50+.31290x\text{ if }x\le \text{30,}\\ \text{24}\text{.2979+}\text{.15297}x\text{ if }x>30\end{array}\right\}$.

(e)

To determine

Whether the $R\left(x\right)$ is continuous at $x=30$ or not, where $R\left(x\right)=\left\{\begin{array}{l}19.50+.31290x\text{ if }x\le \text{30,}\\ \text{24}\text{.2979+}\text{.15297}x\text{ if }x>30\end{array}\right\}$.

(f)

To determine

Whether the $R\left(x\right)$ is differentiable at $x=30$ or not, where $R\left(x\right)=\left\{\begin{array}{l}19.50+.31290x\text{ if }x\le \text{30,}\\ \text{24}\text{.2979+}\text{.15297}x\text{ if }x>30\end{array}\right\}$.