Chapter 1.2, Problem 2QCE

Given that ${\lim }_{x\to a}f\left(x\right)=1$ and ${\lim }_{x\to a}g\left(x\right)=2$ , find the limits.

(a) $\underset{x\to a}{\lim }\left[3f\left(x\right)+2g\left(x\right)\right]=\text{\_\_\_\_\_\_\_}$

(b) $\underset{x\to a}{\lim }\frac{2f\left(x\right)+1}{1-f\left(x\right)g\left(x\right)}=\text{\_\_\_\_\_\_\_}$

(c) $\underset{x\to a}{\lim }\frac{\sqrt{f\left(x\right)+3}}{g\left(x\right)}=\text{\_\_\_\_\_\_\_}$