JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f ( x )=\frac{ x }{\left(1+ x ^{ n }\right)^{\frac{1}{ n }}}, x \in R -\{-1\}, n \in N , n > 2\). If \(f ^{ n }( x )= (fofof \ldots \ldots\) upto \(n\) times) \(( x )\), then \(\operatorname{Lim}_{n \rightarrow \infty} \int \limits_0^1 x^{n-2}\left(f^n(x)\right) d x\) is equal to \(...............\).
- A \(2\)
- B \(4\)
- C \(0\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=\frac{x}{\left(1+x^n\right)^{1 / x}}, x \in R-\{-1\}, n \in N, n > 2\) \(F^n(x)=\text { (fofof... upto } n \text { times) }(x) \text {, }\) then \(\lim _{n \rightarrow \infty} \int \limits_0^1 x^{n-2}\left(f^n(x)\right) d x\)…
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