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Question: Answered & Verified by Expert
$\lim _{n \rightarrow \infty} n\left(\sqrt{n^2+9}-n\right)=$
MathematicsLimitsMHT CETMHT CET 2022 (06 Aug Shift 1)
Options:
  • A $\frac{9}{4}$
  • B $9$
  • C $\frac{9}{\sqrt{2}}$
  • D $\frac{9}{2}$
Solution:
2101 Upvotes Verified Answer
The correct answer is: $\frac{9}{2}$
$\lim _{n \rightarrow \infty} n\left(\sqrt{n^2+9}-n\right)$
$\lim _{n \rightarrow \infty} \frac{n\left(n^2+9-n^2\right)}{\sqrt{n^2+9}+n}$
$\lim _{n \rightarrow \infty} \frac{9}{\sqrt{1+\frac{9}{n^2}}+1}=\frac{9}{2}$

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