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JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\mathop {\lim }\limits_{x \to \infty } \,\left( {\frac{n}{{{n^2}\, + {1^2}}} + \frac{n}{{{n^2} + {2^2}}} + \frac{n}{{{n^2} + {3^2}}} + ...\frac{1}{{5n}}} \right)\) is equal to
- A \(\frac{\pi }{4}\)
- B \(tan^{-1}\,\,(3)\)
- C \(\frac{\pi }{2}\)
- D \(tan^{-1}\,\,(2)\)
Answer & Solution
Correct Answer
(D) \(tan^{-1}\,\,(2)\)
Step-by-step Solution
Detailed explanation
\(\mathop {\lim }\limits_{x \to \infty } \sum\limits_{r = 1}^{2n} {\frac{n}{{{n^2} + {r^2}}}} \) \(\mathop {\lim }\limits_{x \to \infty } \sum\limits_{r = 1}^{2n} {\frac{1}{{\left( {1 + \frac{{{r^2}}}{{{n^2}}}} \right)}}} \) Using \(D.I.\) as limit of sum, we get…
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