$\underset{x→∞}{\lim}\frac{(1+x+x^2)}{x.(\ln\ x)^3}$ is equal to
Answer & explanation
Correct answer: option 4
$\underset{x→∞}{\lim}\frac{(1+x+x^2)}{x.(\ln\ x)^3}=\underset{t→0^+}{\lim}\frac{t^2+t+1}{t^2.\frac{1}{t}.(\ln(\frac{1}{t}))^3}=\underset{t→0^+}{\lim}\frac{1+t+t^2}{-t.(\ln t)^3}=+∞$,
as $-t.(\ln t)^3→0$ when $t→0^+$