Question

求极限，详细过程

高等数学 大学数学

Answer 1

(1)

lim(x->0) sin(2x)/sin(3x)=lim(x->0) (2x)/(3x) =2/3
(2)
lim(x->0) x.cot2x
=lim(x->0) x/tan2x
=lim(x->0) x/(2x)
=1/2
(3)
lim(x->∞) x^2 .sin(2/x^2)
=lim(x->∞) x^2 .(2/x^2)
=2
(4)
lim(x->0) (1-cosx)/(xsinx)
=lim(x->0) (1/2)x^2/x^2
=1/2
(5)
lim(x->∞) (1 +3/x)^(x+1)= e^3
(6)
lim(x->∞) [(1+x)/x]^(2x)
=lim(x->∞) [1+ 1/x]^(2x)
=e^2
(7)
lim(x->0) (1-x)^(1/x) =e^(-1)
(8)
lim(x->∞) ( 1- 1/x)^(x+2) = e^(-1)

追问

7和8的详细过程有吗