QUESTION $1$

$($a$)$ Determine the following limits $($if they exists$)$

$($i$)\underset{x-3^{-}}{lim}\frac{(x^2-9)}{|x-3|}$

$($ii$)\underset{y0}{lim}\frac{sin5y}{sin8y}$

$($iii$)\underset{t4}{lim}\frac{1-\sqrt[\phantom{2}]{t}}{1-t}$

$($iv$)\underset{x-}{lim}\frac{x^3+2x^2-x+10}{2x^2-x+3}$

$($v$)\underset{x-2}{lim}\frac{x+2}{x^2-x-6}$