If a = lim n → ∞ ∑ k = 1 n 2 n n 2 + k 2 and f x = 1 - cos x 1 + cos x , x ∈ 0 , 1 ,…

1. $2\sqrt{2}f\left(\frac{a}{2}\right)=f^{\text{'}}\left(\frac{a}{2}\right)$
2. $f\left(\frac{a}{2}\right)f^{\text{'}}\left(\frac{a}{2}\right)=\sqrt{2}$
3. $\sqrt{2}f\left(\frac{a}{2}\right)=f^{\text{'}}\left(\frac{a}{2}\right)$
4. $f\left(\frac{a}{2}\right)=\sqrt{2}{f}^{\text{'}}\left(\frac{a}{2}\right)$

Solution

Asked in: JEE Main 2022 (26 Jul Shift 1)

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