The correct option is D 4 lim_ n→∞ #160; (√( n ^ 2 +1 ) + n )^ 2 /√( n ^ 6 + l ) #160; lim_ n→∞ #160; #160;n^2(1+√(1+1n^2))^2n^2√(1+1n^6 ...

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Factorization Method Form to Remove Indeterminate Form

limn→∞√n2+1+n...

Question

$lim n \to \infty \frac{(\sqrt{n^{2} + 1} + n)^{2}}{\sqrt[3]{n^{6} + l}} =$

1

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\frac{1}{2}

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\frac{1}{3}

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4

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Solution

The correct option is D $4$
$lim n \to \infty \frac{(\sqrt{n^{2} + 1} + n)^{2}}{\sqrt[3]{n^{6} + l}}$
$lim n \to \infty \frac{n^{2} (1 + \sqrt{1 + \frac{1}{n^{2}}})^{2}}{n^{2} \sqrt[3]{1 + \frac{1}{n^{6}}}}$
$= (2)^{2}$
$= 4$

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