$$\eqalign{ \mathop {\lim }\limits_{x \to 0} \frac{{\ln \frac{{\sqrt {x + 1} + 1}}{2}}}{{{\mathop{\rm arctg}\nolimits} 4x}} } $$

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