c$)\underset{x-3}{lim}\frac{x^2-x-12}{x+3}$ Compute the following limits if they exist

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

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

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

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

$($j$)\underset{x2}{lim}\sqrt[\phantom{2}]{4x+1}$

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

$($l$)\underset{u-2}{lim}\sqrt[\phantom{2}]{u^4-3u+6}$

$($m$)\underset{t0}{lim}\frac{\sqrt[\phantom{2}]{3+t}-\sqrt[\phantom{2}]{3}}{t}$

$15\mathrm{.}2$ Compute $\underset{x}{lim}f(x)$ for each of the following functions $f(x).$

$($a$)f(x)=\frac{3x-2}{x+1}$

$($b$)f(x)=\frac{x^2-1}{x^2+1}$

$($c$)f(x)=\frac{3x}{\sqrt[\phantom{2}]{x^2+8}}$

$($d$)f(x)=\frac{3x}{x^2+1}$