Question

lim的数学问题

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Answer 1

33.
选B
lim(1-3x)^(1/x)=lim{[1+(-3x)]^[1/(-3x)]}(-3)=e^(-3)
.
选B
x²-x-2>0
(x+1)(x-2)>0
x<-1或x>2
.
选C
f(x³)=e^(x³)
27.
选B
lim[sin(x-1)/(x²-1)]=lim[(x-1)/(x+1)(x-1)]=lim[1/(x+1)]=1/2
17.
选D
x→-∞，2^x→0， 3-2^x→3
5.
选A
函数定义域为R，f(-x)=-x+sin(-x)=-x-sinx=-(x+sinx)=-f(x)
.
选D
f(3)=3+2=5
f[f(3)]=f(5)=5²=25

30.
选C
lim[1+ 1/(2x)]^x=lim[[1+1/(2x)]^(2x)]^(1/2)=e^(1/2)
8.
选C
n→∞，1/n→0，3-1/n→3
29.
选D
lim(1-2/x)^x=lim[[1+1/(-½x)]^(-½x)]^(-2)=e^(-2)