2.1.73 Calculation of limits

condition: Find the limits of functions without using L'Hopital's rule. a) \( \lim _{x \rightarrow 1} \frac{\sqrt{x}-1}{x^{2}-1} \) b) \( \lim _{x \rightarrow \pi} \frac{x^{2}-\pi^{2}}{\sin x} \) c) \( \lim _{x \rightarrow \infty} \frac{15 x^{4}-(x+2)^{2}}{(x+1)^{2}-3 x^{4}} \), d) \( \lim _{x \rightarrow 0}\left(\frac{2+x}{2-x}\right)^{\frac{3+x}{x}} \).