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1)

Let f:R→ R be a differentable function such that f(0)=0,  f(π2)=3 and f ' (0)=1

  if g(x)=π20f(t)cosec tf(t)cot tcosec tf(t)]dt

  for   xϵ(0,π2], then limx0g(x)=


A) 4

B) 2

C) 1

D) 3

Answer:

Option B

Explanation:

g(x)=π2xf(t)cosec tf(t)cot tcosec tf(t)]dt

g(x)=f(π2)cosec π2f(x)cosec x

   g(x)=3f(x)sinx

limx0g(x)=limx0(3sinxf(x)sinx)

=limx03cosxf(x)cosx

311=2