JEE Main 202226 Jul, Morning shiftMathematicsMediumIntegral Calculus369× since 2002If a=limn→∞∑k=1n2nn2+k2a = \mathop {\lim }\limits_{n \to \infty } \sum\limits_{k = 1}^n {{{2n} \over {{n^2} + {k^2}}}}a=n→∞limk=1∑nn2+k22n and f(x)=1−cosx1+cosxf(x) = \sqrt {{{1 - \cos x} \over {1 + \cos x}}}f(x)=1+cosx1−cosx, x∈(0,1)x \in (0,1)x∈(0,1), then :AOption A. 22f(a2)=f′(a2)2\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)22f(2a)=f′(2a)BOption B. f(a2)f′(a2)=2f\left( {{a \over 2}} \right)f'\left( {{a \over 2}} \right) = \sqrt 2f(2a)f′(2a)=2COption C. 2f(a2)=f′(a2)\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)2f(2a)=f′(2a)DOption D. f(a2)=2f′(a2)f\left( {{a \over 2}} \right) = \sqrt 2 f'\left( {{a \over 2}} \right)f(2a)=2f′(2a)CheckSkip · show solution
