用洛必达法则求极限:x→0 lim[(xcotx-1)⼀x^2]

2024-11-18 22:54:15
推荐回答(1个)
回答1:

用洛必达法则求极限:分子,分母同时求导
x→0lim[(xcotx-1)/x^2]
=x→0lim[(cot(x) - x*(cot(x)^2 + 1))/2x]
=x→0lim[(cot(x) - x*(cot(x)^2 + 1))/2x]
=x→0lim[2*x*cot(x)*(cot(x)^2 + 1) - 2*cot(x)^2 - 2]/2
将x=0代入答案应该是-1/3