2.1.40 Calculation of limits

Condition: Using the 2nd remarkable limit, calculate the limits: a) \( \lim _{x \rightarrow \infty}\left(\frac{x+3}{x-2}\right)^{2 x+1} \), b) \( \lim _{x \rightarrow \infty}\left(1+\tan ^{2} \sqrt{x}\right)^{\frac{3}{x}} \), c) \( \lim _{x \rightarrow \infty} x(\ln (2+x)-\ln x) \), d) \( \lim _{x \rightarrow 0} \frac{1}{x} \ln \sqrt{\frac{1+x}{1-x}} \).