Question $1$

Evaluate the following:

$($i$)\underset{xk}{lim}\frac{x^3-k{x}^2}{x^2-k^2}$ where $k$ is a $($real$)$ constant,

$($ii$)\underset{x-3}{lim}\frac{x^2+2x-3}{x^3+x^2-2x+12},$

$($iii$)\underset{x16}{lim}\frac{4-\sqrt[\phantom{2}]{x}}{16x-x^2},$

$($iv$)$ Is there a number a such that $\underset{x-2}{lim}\frac{3x^2+ax+a+3}{x^2+x-2}$ exists? For such if any$),$ find $\underset{x-2}{lim}\frac{3x^2+ax+a+3}{x^2+x-2}.$