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Question
The value of \[\lim_{x \to \infty} \frac{\sqrt{1 + x^4} + \left( 1 + x^2 \right)}{x^2}\] is
Options
−1
1
2
none of these
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Solution
2
\[\lim_{x \to \infty} \frac{\sqrt{1 + x^4} + \left( 1 + x^2 \right)}{x^2}\]
\[ = \lim_{x \to \infty} \sqrt{\frac{1}{x^4} + 1} + \frac{1}{x^2} + 1\]
\[ = 2\]
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