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$(11$ points$)$ Compute each of the following limits$,$ if it exists.

$($a$)\underset{x1}{lim}\frac{x^2-1}{x-1}$

$($b$)\underset{x-3}{lim}\frac{x^2-x12}{x3}$

$($c$)\underset{x-3}{lim}\frac{x^2-x-12}{x3}$

$($d$)\underset{x0}{lim}\frac{x^{2}x}{x}$

$($e$)\underset{h0}{lim}\frac{(3h{)}^2-9}{h}$

$($f$)\underset{t0}{lim}\frac{\sqrt[\phantom{2}]{2-t}-\sqrt[\phantom{2}]{2}}{t}$

$($g$)\underset{x1}{lim}[\frac{2}{1-x^2}\frac{1}{x-1}]$

$($h$)\underset{s0}{lim}[\frac{1}{s\sqrt[\phantom{2}]{s1}}-\frac{1}{s}]$

$($i$)\underset{x2}{lim}\frac{4x1}{2x-1}$

$($j$)\underset{x2}{lim}\sqrt[\phantom{2}]{4x1}$

$($k$)\underset{y3}{lim}(y^{3}2)(y^2-5y)$