TS EAMCET · Maths · Definite Integration
\(\lim _{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots+\frac{1}{n} \sec ^2 1\right]=\)
- A \(\frac{1}{2} \sec (1)\)
- B \(\frac{1}{2} \operatorname{cosec}(1)\)
- C \(\tan (1)\)
- D \(\frac{1}{2} \tan (1)\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2} \tan (1)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots+\frac{n}{n^2} \sec ^2 \frac{n^2}{n^2}\right] \\ = & \lim _{n \rightarrow \infty} \sum_{r=1}^n\left[\frac{1}{n}\left(\frac{r}{n} \sec…
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