AP EAMCET · Maths · Definite Integration
\(\lim _{n \rightarrow \infty}\left[\frac{n}{(n+1) \sqrt{2 n+1}}+\frac{n}{(n+2) \sqrt{2(2 n+2)}}\right.\) \(+\frac{n}{(n+3) \sqrt{3(2 n+3)}}+\ldots n\) terms \(]=\int_0^1 f(x) d x\) then \(f(x)=\)
- A \(\frac{1}{(1+x) \sqrt{x^2+2 x}}\)
- B \(\frac{1}{(1+x) \sqrt{x+2}}\)
- C \(\frac{1}{(1+x) \sqrt{x^2+x+1}}\)
- D \(\frac{1}{(1+x) \sqrt{x^2-2 x}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{(1+x) \sqrt{x^2+2 x}}\)
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