Question

这四题 谢谢蟹蟹

高数极限

Answer 1

(1)
lim(x->0) tanx/(sin2x)^3
=lim(x->0) x/(2x)^3
=lim(x->0) 1/(8x^2)
不存在
(2)
lim(x->∞) [ x.sin(1/x) - sinx/x]
=lim(x->∞) x.sin(1/x)
y=1/x
=lim(y->0+) siny/y
=1
(4)
lim(x->1) lnx/(x-1)^2
=lim(x->1) ln[1+(x-1) ]/(x-1)^2
=lim(x->1) (x-1)/(x-1)^2
=lim(x->1) 1/(x-1)^2
不存在
(5)
x/(x-1) = 1+ 1/(x-1)
let
1/y = 1/(x-1)
lim(x->∞) [x/(x-1)]^(2x-1)
=lim(x->∞) [1+ 1/(x-1)]^(2x-1)
=lim(y->∞) (1+ 1/y)^(2(y+1)-1)
=lim(y->∞) (1+ 1/y)^(2y+1)
=lim(y->∞) (1+ 1/y)^(2y)
=e^2

追问

第二题

使用算的

追答

(2)
lim(x->∞) sinx/x =0
//
lim(x->∞) [ x.sin(1/x) - sinx/x]
=lim(x->∞) x.sin(1/x)
令 y=1/x
=lim(y->0+) siny/y
=lim(y->0+) y/y
=1

追问

好的

我晓得了谢谢