2.1.42 Calculation of limits
Condition: Prove the equalities by definition of the limit of the sequence: a) \( \lim _{n \rightarrow \infty} \frac{(-1)^{n}}{n+12}=0 \) b) \( \lim _{n \rightarrow \infty} \frac{7}{2 n^{3}-1}=0 \).
Calculation of various limits, using L'Hopital's rule, remarkable limits, power series, equivalent values of various other methods.