Question

Calcule os limites do infinito:
$\lim_{x\to \infty} ( \sqrt[3]{ \frac{3x^7-4x^5}{2x^7+1}} )$

Answer 1

$\boxed{\boxed{ \lim_{x \to \infty} \sqrt[3]{ \frac{3x^7-4x^5}{2x^7+1} } }}$

colocando x^7 em evidencia no numerador e no denominador
 $\lim_{x \to \infty} \sqrt[3]{ \frac{x^7*\left(3- \frac{4}{x^2} \right)}{x^7*\left(2+ \frac{1}{x^7}\right) } }\\\\\\\ \lim_{x \to \infty} \sqrt[3]{ \frac{\left(3- \frac{4}{x^2} \right)}{\left(2+ \frac{1}{x^7}\right) } }= \sqrt[3]{ \frac{3-0}{2+0} }= \sqrt[3]{ \frac{3}{2} }$