Differentiation Question 144
Question: $ \underset{x\to \infty }{\mathop{\lim }}\frac{n^{p}{{\sin }^{2}}(n!)}{n+1},0<p<1 $ is equal to
Options:
A) 0
B) $ \infty $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Given limit can be written as $ \underset{n\to 0}{\mathop{\lim }}\frac{{{\sin }^{2}}(n!)}{{n^{1-p}}(1+1/n)}(0<p<1) $
$ =\frac{Somerealnumberin[0,1]}{\infty }=0 $
$ (\because 1-p>0) $
BETA
