2.1.52 Calculation of limits
condition: Find the limits: a) \( \lim _{x \rightarrow \infty}\left(\frac{2 x+3}{2 x+4}\right)^{x+5} \) b) \( \lim _{x \rightarrow 0}\left(\frac{\arcsin x}{2} \cdot \cot \frac{\pi x}{2}\right) \).
Calculation of various limits, using L'Hopital's rule, remarkable limits, power series, equivalent values of various other methods.