x趋近于1时,求[1⼀(1-x)]-[3⼀(1-x^3)]的极限 求详解 谢谢咯

2025-03-05 06:31:51
推荐回答(3个)
回答1:

原式=lim(x2+x-2)/(1-x3)
=lim(x+2)/(x2+x+1)
=lim3/3
=1
【欢迎追问,满意采纳,谢谢合作】

回答2:

J = 1/(1-x) - 3/(1-x^3) = (x^2+x-2)/(1-x^3) //: 通分
lim(x->1) J
= lim(x->1) (x^2+x-2)/(1-x^3) //: 为:0/0 ,用洛必达法则;
= lim(x->1) (2x+1)/(-3x^2)
= 3/(-3)
= -1

回答3:

解:
原式=lim(x->1)(x²+x-2)/(1-x³) 分子分母都趋近于0,用罗比达
=lim(x->1)(2x+1)/(-3x²)
=-1
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