If f(x)= Lim _ n e x tan (1/n) log (1/n) and f(x) d x [3] ^ 11 x x = g(x) + c then
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If \(f(x)=\operatorname{Lim}_{n \rightarrow \infty}\)ex tan (1/n) log (1/n) and \(\int \frac{f(x) d x}{\sqrt[3]{\sin ^{11} x \cos x}}=\)g(x) + c then
- \(\operatorname{g}\left(\frac{\pi}{4}\right)=\frac{3}{2}\)
- g (x) is continuous for all x
- \(g\left(\frac{\pi}{4}\right)=\frac{-15}{8}\)
- g (x) is non-differentiable at infinitely many points
Answer
(C) g ( 4 )= -15 8, (D) g (x) is non-differentiable at infinitely many points
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