Evaluating $\lim_{s\to0}\sin(s)\,\Gamma(s)$

Question

How do I evaluate: $\displaystyle\lim_{s\to0}\sin(s)\Gamma(s)$

kk, i understand now.

Answer 1

Hint:

$\sin(s)\Gamma(s)=\frac{\sin(s)}{s}s\Gamma(s)$

Answer 2

$\displaystyle\lim_{s\to0}\sin(s)\Gamma(s)=\lim_{s\to0}\frac{\sin(s)}{s}s\Gamma(s)=\lim_{s\to0}\frac{\sin(s)}{s}\lim_{s\to0}s\Gamma(s)=\lim_{s\to0}\frac{\sin(s)}{s}\lim_{s\to0}\Gamma(s+1)=1\cdot\Gamma(1)=1$