Chapter 2.2, Problem 55E

a.

To determine

To calculate: The limit $\underset{x\to b}{\lim }\left(f\left(x\right)+g\left(x\right)\right)$ if ${\lim }_{x\to \text{ b}}f\left(x\right)=7$ and ${\lim }_{x\to \text{ b}}g\left(x\right)=-3$.

b.

To determine

To calculate: The limit $\underset{x\to b}{\lim }\left(f\left(x\right)\cdot g\left(x\right)\right)$ if ${\lim }_{x\to \text{ b}}f\left(x\right)=7$ and ${\lim }_{x\to \text{ b}}g\left(x\right)=-3$.

c.

To determine

To calculate: The limit $\underset{x\to b}{\lim }4g\left(x\right)$ if ${\lim }_{x\to \text{ b}}f\left(x\right)=7$ and ${\lim }_{x\to \text{ b}}g\left(x\right)=-3$.

d.

To determine

To calculate: The limit $\underset{x\to b}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$ if ${\lim }_{x\to \text{ b}}f\left(x\right)=7$ and ${\lim }_{x\to \text{ b}}g\left(x\right)=-3$.