Chapter 1.2, Problem 2ES

Use the graph of $f$ and $g$ in the accompanying figure to find the limits that exist. If the limit does not exist, explain why.

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

(b) $\underset{x\to 0}{\lim }\left[f\left(x\right)+g\left(x\right)\right]$

(c) $\underset{x\to 0^{+}}{\lim }\left[f\left(x\right)+g\left(x\right)\right]$

(d) $\underset{x\to 0^{-}}{\lim }\left[f\left(x\right)+g\left(x\right)\right]$

(e) $\underset{x\to 2}{\lim }\frac{f\left(x\right)}{1+g\left(x\right)}$

(f) $\underset{x\to 2}{\lim }\frac{1+g\left(x\right)}{f\left(x\right)}$

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

(h) $\underset{x\to 0^{-}}{\lim }\sqrt{f\left(x\right)}$