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

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

\[\begin{array}{l} {\text{Вычислите:}} \hfill \\ \mathop {\lim }\limits_{a \to 0 + } \left( {{a^{\frac{5}{3}}}\int\limits_a^{\frac{\pi }{2} - a} {\frac{{dx}}{{{{\left( {1 - \sin x} \right)}^{\frac{4}{3}}}}}} } \right) \hfill \\ \end{array}\]

\[\mathop {\lim }\limits_{x \to \frac{1}{2}} \frac{{{{\arcsin }^{\frac{1}{2}}}x - {{\left( {\frac{\pi }{6}} \right)}^{\frac{1}{2}}}}}{{{x^{\frac{1}{2}}} - {{\left( {\frac{1}{2}} \right)}^{\frac{1}{2}}}}}\]