Let f: R → R be a differentiable function such that f(0)=0, f(π/2)=3 and f^'(0)=1. If g(x)=∫_x^π/...

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Let f: R → R be a differentiable function such that f(0)=0, f(π/2)=3 and f^'(0)=1.
If g(x)=∫_x^π/2[f^'(t) cosec t- t cosec t f(t)] d t for x ∈(0, π/2], then lim _x → 0 g(x)=
(2017 Adv.)

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