Evaluate the limit$.(2$ pts each$)$

$($a$)\underset{x{0}^{+}}{lim}ta{n}^{-1}(\frac{1}{x})$

$($b$)\underset{x}{lim}{e}^{x-x^2}$

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

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

$($f$)\underset{x}{lim}{e}^{-x}sinx$