Question

Prove that : lim n→∞

(2n³+5n)/(4n³+n²) = 1/2

Answer 1

$\lim_{n\to\infin}\frac{2n^3+5n}{4n^3+n^2}=\lim_{n\to\infin}\frac{2n^3(1+\frac{5}{2n^2})}{4n^3(1+\frac{1}{4n})}= \lim_{n\to\infin}\frac{2(1+0)}{4(1+0)}=\frac{1}{2}$