Question

Find the limit of {n^3/(n^4+1)} as n →∞

Answer 1

$\displaystyle \begin{aligned} \lim_{n\to\infty} \frac{n^3}{n^4+1} &= \lim_{n\to\infty} \frac{1}{n + \frac{1}{n^3}} \\&= \lim_{n\to\infty} \frac{1}{n + 0} \\&= \lim_{n\to\infty} \frac{1}{n} = 0 \end{aligned}$