Chapter 1.3, Problem 3QCE

Given that $\underset{x\to +\infty }{\lim }f\left(x\right)=2\text{ and }\underset{x\to +\infty }{\lim }g\left(x\right)=-3$ Find the limits that exist.

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

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

(c) $\underset{x\to +\infty }{\lim }\frac{2f\left(x\right)+3g\left(x\right)}{3f\left(x\right)+2g\left(x\right)}=\text{\_\_\_\_\_\_}$

(d) $\underset{x\to +\infty }{\lim }\sqrt{10-f\left(x\right)g\left(x\right)}=\text{\_\_\_\_\_\_}$