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Question

Question: ![](https://cdn.pureessence.tech/canvas_556.png?top_left_x=995&top_left_y=600&width=300&height=300)\...

nasin2(n!)n+1\frac{n^{a}\sin^{2}(n!)}{n + 1}, (0 < a < 1) =

A

1

B

+

C

0

D

None of these

Answer

0

Explanation

Solution

limnα\lim _ { n \rightarrow \alpha } na1+sin2(n!)(1+1n)\frac{n^{a - 1} + \sin^{2}(n!)}{\left( 1 + \frac{1}{n} \right)}= (α)a1.[0,1]1\frac{(\alpha)^{a - 1}.\lbrack 0,1\rbrack}{1}= 0 × [0, 1]

(Q 0 < a < 1 Ž aa–1 Ž a –ve = 0) = 0