Determine the following limit$,$ algebraically. If the limit doesn't exist, describe accurately the left and right hand$-$side behaviors of the function.

$\underset{x-2}{lim}\frac{1-x}{2+x}=$

Determine each limit if it exists, algebraically. Otherwise, indicate if the function is increasing or decreasing without bound.

a$.\underset{x9}{lim}\frac{\sqrt[\phantom{2}]{x}-3}{x-9}=$