答:题目有错误吧?
lim(x→ -∞) (1-x)^x=0
lim(x→ +∞) (1-x)^x= ∞题目是这样的,下列各式中正确的是 A lim(x→ +∞) xsin 1/x=1 B lim(x→ 0) xsin 1/x=1 C lim(x→ +∞) (1-x)∧x=eD 一定是错的,我就不打了答:
A)
lim(x→+∞) xsin(1/x)
=lim(x→+∞) sin(1/x) /(1/x)
=1
B)错误
lim(x→0) xsin(1/x)
=lim(x→0) sin(1/x) / (1/x)
=0
1/x是无穷大,sin(1/x)有界
C)错误
lim(x→+∞) (1-x)^x= ∞
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