Question

高数题目不会做，求解答！

希望有高手快速解答，在线等，解答后马上采纳！

Answer 1

1通分后=x-lnx-1/(lnx*(x-1))
0/0用洛必达=(1-1/x)/((x-1)/x + lnx)，还是0/0，再用一次
=x^-2 /(x^-2 + x^-1) = 1/2

追问

能不能具体一点啊，考试题目，需要具体步骤。谢谢啦！

追答

Answer 2

1. 应为 x→0+
原式 = lim<x→0+>(x-1-lnx)/[(x-1)lnx]
= lim<x→0+>(1-1/x)/[lnx+(x-1)/x]
= lim<x→0+>(x-1)/[xlnx+(x-1)] = -1/(0-1) = 1.
这里利用了 lim<x→0+>xlnx = lim<x→0+>lnx/(1/x)
= lim<x→0+>(1/x)/(-1/x^2) = lim<x→0+>(-x) = 0.
2. 原式 = lim<x→0> 分子/(100x^3)
= lim<x→0>ln(1+100x)sin100x/(300x^2)
= lim<x→0>(100x)(100x)/(300x^2) = 100/3.
3. y = x^100*e^(-100x)
dy = [100x^99e^(-100x)-100x^100*e^(-100x)]dx
= 100x^99(1-x)e^(-100x)dx