Question

数学，求极限

Answer 1

后面三个不太会，😔

Answer 2

(1)lim(x->0) sin3x/x=lim(x->0) 3x/x =3
(2)lim(x->0) tan2x/(3x)=lim(x->0) 2x/(3x) =2/3
(3)lim(x->0) sin5x/sin2x=lim(x->0) 5x/(2x) =5/2
(4)lim(x->0) x(x+3)/sinx=lim(x->0) (x+3) =3
(5)lim(x->0-) sinx/|x|=lim(x->0-)sinx/(-x) = -1
(6)
let
1/y = 2/x
lim(x->∞)( 1- 2/x)^(2x)
=lim(y->∞)( 1- 1/y)^(4y)
=e^(-4)
(7)
(3x+5)/(3x) = 1 + 5/(3x)
let
5/(3x)= 1/y
lim(x->∞) [(3x+5)/(3x)]^(-x)
=lim(x->∞) [1 + 5/(3x)]^(-x)
=lim(y->∞) [1 + 1/y]^(-5y/3)
=e^(-5/3)
(8)
let
y=3x
lim(x->0) (1+3x)^(1/x)
=lim(y->0) (1+y)^(3/y)
=e^3