2.1.50 Calculation of limits

Condition: Find the limits of functions without using L'Hopital's rule. a) \( \lim _{x \rightarrow \infty} \frac{(7-x)^{4}-(9-x)^{4}}{(2-x)^{3}-(1+x)^{3}} \) b) \( \lim _{x \rightarrow 1} \frac{2 x^{2}-x-1}{x^{3}+2 x^{2}-x-2} \) B) \( \lim _{x \rightarrow 0} \frac{\cos 2 x-1}{x \tan 3 x} \), d) \( \lim _{x \rightarrow 0} \frac{6^{2 x}-7^{-2 x}}{\sin 3 x-2 x} \) e) \( \lim _{x \rightarrow \infty}\left(\frac{10 x+2}{10 x-7}\right)^{x-3} \).