Chapter 1.4, Problem 27E

Compute the limits that exist, given that

$\underset{x\to 0}{\lim }f(x)=-\frac{1}{2}$ and $\underset{x\to 0}{\lim }g(x)=\frac{1}{2}$

a. $\underset{x\to 0}{\lim }\left(f(x)+g(x)\right)$

b. $\underset{x\to 0}{\lim }\left(f(x)-2g(x)\right)$

c. $\underset{x\to 0}{\lim }f(x)\cdot g(x)$

d. $\underset{x\to 0}{\lim }\frac{f(x)}{g(x)}$