2.1.84 Calculation of limits

Condition: Calculate the limits of functions without using differential calculus. a) \( \lim _{x \rightarrow \infty} \frac{-2 x^{2}+7 x+2}{x^{2}-5 x} \) b) \( \lim _{x \rightarrow 0.5-0} \frac{2 x-1}{\ln (0.5-x)} \) c) \( \lim _{x \rightarrow 4} \frac{\arcsin (4-x)}{\ln (x-3)} \) d) \( \lim _{x \rightarrow 0}\left(1+3 x^{2}\right)^{\frac{1}{2 x^{2}}} \)