MHT CET · Maths · Limits
\(\lim _{n \rightarrow \infty} n\left(\sqrt{n^2+9}-n\right)=\)
- A \(\frac{9}{4}\)
- B \(9\)
- C \(\frac{9}{\sqrt{2}}\)
- D \(\frac{9}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{9}{2}\)
Step-by-step Solution
Detailed explanation
\(\lim _{n \rightarrow \infty} n\left(\sqrt{n^2+9}-n\right)\)
\(\lim _{n \rightarrow \infty} \frac{n\left(n^2+9-n^2\right)}{\sqrt{n^2+9}+n}\)
\(\lim _{n \rightarrow \infty} \frac{9}{\sqrt{1+\frac{9}{n^2}}+1}=\frac{9}{2}\)
\(\lim _{n \rightarrow \infty} \frac{n\left(n^2+9-n^2\right)}{\sqrt{n^2+9}+n}\)
\(\lim _{n \rightarrow \infty} \frac{9}{\sqrt{1+\frac{9}{n^2}}+1}=\frac{9}{2}\)
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