Question

$\underset{x\to \infty }{lim}\frac{\sqrt{x^2+1}-\sqrt[3]{3x^3+1}}{\sqrt[4]{4x^4+1}-\sqrt[5]{5x^4+1}}$ is equals to

• A. $1$
• B. $0$
• C. $-1$
• D. None of these

Answer 1

The correct option is B $0$

The value of $\underset{x\to \infty }{lim}\frac{\sqrt{x^2+1}-\sqrt[3]{3x^3+1}}{\sqrt[4]{4x^4+1}-\sqrt[5]{5x^4+1}}$ is
$=\underset{x\to \infty }{lim}\frac{\sqrt{1+\frac{1}{x^2}}\sqrt[3]{31+\frac{1}{x^3}}}{\sqrt[]{1+\frac{1}{x^4}}-\sqrt[]{1+\frac{1}{x^5}}}$
$=\frac{1-1}{1-0}=0$