Chapter 1.2, Problem 1ES

Given that $\underset{x\to a}{\lim }f\left(x\right)=\text{2, }\underset{x\to a}{\lim }g\left(x\right)=-\text{4, }\underset{x\to a}{\lim }h\left(x\right)=\text{0}$ find the limits.

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

(b) $\underset{x\to a}{\lim }\left[h\left(x\right)-3g\left(x\right)+1\right]$

(c) $\underset{x\to a}{\lim }\left[f\left(x\right)g\left(x\right)\right]$

(d) $\underset{x\to a}{\lim }{\left[g\left(x\right)\right]}^2$

(e) $\underset{x\to a}{\lim }\sqrt[3]{6+f\left(x\right)}$

(f) $\underset{x\to a}{\lim }\frac{2}{g\left(x\right)}$