Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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lim x → ∞ √ x 2 − 1 2 x + 1 - Mathematics

MCQ

\[\lim_{x \to \infty} \frac{\sqrt{x^2 - 1}}{2x + 1}\] 

Options

  • 1

  • 0

  • −1 

  • 1/2 

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Solution

1/2 

\[\lim_{x \to \infty} \frac{\sqrt{x^2 - 1}}{2x + 1}\]
\[ = \lim_{x \to \infty} \frac{\sqrt{1 - \frac{1}{x^2}}}{2 + \frac{1}{x}}\]
\[\text{ Dividing the numerator and the denominator by x, we get }: \]
\[ = \frac{\sqrt{1 - 0}}{2 + 0}\]
\[ = \frac{1}{2}\]

Hence, the correct answer is d.

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Q 13 | Page 78
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