Given that for each a ∈ (0, 1), _ h 0^ + _ h ^ 1-h t^ -a (1-t)^ a-1 d t exists. Let this…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Given that for each a ∈ (0, 1), \(\lim _{h \rightarrow 0^{+}} \int_{h}^{1-h} t^{-a}(1-t)^{a-1} d t\) exists. Let this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).
The value of \(g^{\prime}\left(\frac{1}{2}\right)\) is
The value of \(g^{\prime}\left(\frac{1}{2}\right)\) is
- p/2
- π
- –p/2
- 0
Answer
(D) 0
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