2.1.30 Calculation of limits
\( \underline{\text { Condition: }} \) Find the limits: a) \( \lim _{x \rightarrow 0} \frac{\tan \pi x+2}{x^{2}+2 x-3} \) b) \( \lim _{x \rightarrow 3} \frac{\sin ^{2} \frac{\pi x}{3}}{x^{2}-4} \) c) \( \lim _{x \rightarrow+\infty} \frac{16-x^{4}}{x^{4}-2 x+3} \), d) \( \lim _{x \rightarrow-1} \frac{5 x^{2}+3 x-2}{x^{2}-1} \).
Calculation of various limits, using L'Hopital's rule, remarkable limits, power series, equivalent values of various other methods.