Question

当x大于0时,xsin(1/x)的极限是多少?

Answer 1

0 ≤ |xsin(1/x)| = |x||sin(1/x)| ≤ |x|

∵ lim(x->0) x = 0

∴ 由夹逼定理：

lim(x->0) xsin(1/x) = 0