求极限、limx→0(xsin1⼀x+(1⼀x )sinx) 求解题过程 答案是1

2024-12-31 01:48:29
推荐回答(2个)
回答1:

xsin1/x是0乘有界量=0 sinx/x是重要极限=1,x~0时,x与sinx是等价的

回答2:

limx→0(xsin1/x+(1/x )sinx)
=limx->0xsin1/x + limx->0sinx/x
(注意sin函数值有限,范围只能是[-1.1])
=0 + limx->0sinx/x
(sinx和x是等价无穷小)
=1