\[\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - {e^{ - x}}}}{{\sin x}}\]

\[\mathop {\lim }\limits_{x \to - \frac{\pi }{2}} \left( {\frac{{1 + \sin 13x}}{{1 + \sin 17x}}} \right)\]