Evaluate the given limits:

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

$($e$)\underset{x{0}^{+}}{lim}{x}^{sinx}$

$($b$)\underset{x}{lim}\frac{e^{3x}-e^{-3x}}{e^{3x}+e^{-3x}}$

$($f$)\underset{x\frac{{}^{-}}{-}}{lim}(1+cosx{)}^{tanx}$

$($c$)\underset{x{0}^{+}}{lim}arctan(\frac{ln(2+x)}{e^x-1})$

$($g$)\underset{x}{lim}xsin(\frac{1}{x})$

$($h$)\underset{x{0}^{+}}{lim}(lnx{)}^x$

$($d$)\underset{x2}{lim}\frac{x^2-x-2}{x^2-4}$