题目
9.设a_(n)=int_(0)^1x^nsqrt(1-x^2)dx,b_(n)=int_(0)^(pi)/(2)sin^ntdt,则极限lim_(ntoinfty)[((n+1)a_(n))/(b_(n))]^n=( ).A. 0B. eC. e^-1D. +∞
9.设$a_{n}=\int_{0}^{1}x^{n}\sqrt{1-x^{2}}dx,b_{n}=\int_{0}^{\frac{\pi}{2}}\sin^{n}tdt$,则极限$\lim_{n\to\infty}[\frac{(n+1)a_{n}}{b_{n}}]^{n}=( )$.
A. 0
B. e
C. e^{-1}
D. +∞
题目解答
答案
C. e^{-1}