Let f:R\toR be a differentiable function such that f(0)=0,f(\pi/2)=3 and f'(0)=1.If g(x)=\int^{\pi/2}_{x}[f'(t)\cosec t-\cot t \cosec t f(t)]\dt for x∊(0,\pi/2], then {\lim}_{x\to0}\g(x)=0 [JEE Adv 2017 P1]

Limits, Continuity and Differentiability

Section: Mathematics

Question : 31 of 51

Marks: +1, -0

Let f:R→R be a differentiable function such that
f(0)=0,f(

)=3 and
f′(0)=1.If g(x)=

∫

[f′(t)‌cosec‌t−cot‌t‌cosec‌t‌f(t)]‌dt for x∊(0,

], then

lim

x→0

g(x)=0

[JEE Adv 2017 P1]

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