lim(x趋向0)(e-e^cosx)⼀(√1+x^2的3次方-1)

2025-01-07 03:59:27
推荐回答(1个)
回答1:

先从分子提出一个e,分母(√1+x²)³-1=(1+x²)^(3/2)-1等价无穷小为:(3/2)x²
原式=lim[x→0] e(1-e^(cosx-1)) / [(3/2)x²]
1-e^(cosx-1)等价于-(cosx-1)等价于(1/2)x²
=lim[x→0] e(1/2)x² / [(3/2)x²]
=3e