求极限(x→0)lim((x^1/3)sin(1/x))我知道(x→0)lim((1/x)sinx)=1①(x→∞)lim((1/x)sinx=0②上面的具体怎么求,

Question

求极限(x→0)lim((x^1/3)sin(1/x))
我知道(x→0)lim((1/x)sinx)=1 ①
(x→∞)lim((1/x)sinx=0 ②
上面的具体怎么求,

Answer 1

极限(x→0)lim((x^1/3)sin(1/x))
极限(x→0)lim((x^1/3)sin(1/x))
-lim((x^1/3)=0<=lim((x^1/3)sin(1/x))=<0
所以
极限(x→0)lim((x^1/3)sin(1/x))=0