The value of $\lim_{x \rightarrow \infty}\frac{\sqrt{1 + x^{4}} - (1 + x^{2})}{x^{2}}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
$\lim_{x \rightarrow \infty}\frac{\sqrt{1 + x^{4}} - (1 + x^{2})}{x^{2}} = \lim_{x \rightarrow \infty}\frac{\sqrt{1 + \frac{1}{x^{4}}} - \left( 1 + \frac{1}{x^{2}} \right)}{1}$
$= \frac{1 - 1}{1} = 0$

Q. The value of $\lim_{x \rightarrow \infty}\frac{\sqrt{1 + x^{4}} - (1 + x^{2})}{x^{2}}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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