2.1.82 Calculation of limits
Condition: Calculate the limits: a) \( \lim _{x \rightarrow \infty} \frac{3 x^{4}+x^{2}-6}{2 x^{4}-x-2} \), b) \( \lim _{x \rightarrow 0} \frac{x}{\sqrt{1+3 x-1}} \) c) \( \lim _{x \rightarrow 0} \frac{5 x}{\arctan x} \), d) \( \lim _{x \rightarrow 0}(1+2 x)^{1 / x} \).
Calculation of various limits, using L'Hopital's rule, remarkable limits, power series, equivalent values of various other methods.