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Limits Continuity and Differentiability question

2017 · Shift 1 · Q28

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2017 · Shift 1 · Q28

Limits Continuity and Differentiability question

2017 · Shift 1 · Q28

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityNumerical+3 / −1

Let f : R

\to

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

f\left( {{\pi \over 2}} \right) = 3

and f'(0) = 1. If

g(x) = \int\limits_x^{\pi /2} {[f'(t)\text{cosec}\,t - \cot t\,\text{cosec}\,t\,f(t)]dt}

for

x \in \left( {0,\,{\pi \over 2}} \right]

, then

\mathop {\lim }\limits_{x \to 0} g(x)

=

Numerical answer

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