2.1.67 Calculation of limits

Condition: Calculate the indicated limits without using L'Hopital's rule: a) \( \lim _{x \rightarrow \infty} \frac{3 x^{3}-x+2}{3 x^{2}-2 x^{3}+1} \) b) \( \lim _{x \rightarrow 3} \frac{x^{2}-9}{6 x^{2}-16 x-6} \) c) \( \lim _{x \rightarrow 0} \frac{\sqrt{x+2}-\sqrt{2}}{\sqrt{x+3}-\sqrt{3}} \), d) \( \lim _{x \rightarrow 0} \frac{1-\cos 2 x}{3 x \cdot \sin x} \) e) \( \lim _{x \rightarrow+\infty} x(\ln (2 x-1)-\ln (2 x-3)) \).