求极限x→无穷大lim(1-2/3x)^(x+1)麻烦具体

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求极限x→无穷大lim(1-2/3x)^(x+1)麻烦具体
求极限x→无穷大lim(1-2/3x)^(x+1)麻烦具体

求极限x→无穷大lim(1-2/3x)^(x+1)麻烦具体
知道无穷lim(1+1/x)^x=e吧(不知道就追问一下)
lim(1-2/3x)^(x+1)
=lim(1-2/3x)^x 乘lim(1-2/3x)
=lim(1-2/3x)^x
设1/t=-2/3x x=-2t/3
=lim(1+1/t)^t(-2/3)
=e^(-2/3)

令-2/3x=1/t,t→无穷大
x=-3/2t
lim(1-2/3x)^(x+1)
=lim(1+1/t)^[t*(-3/2t+1)/t]
=e^(-3/2)

1.乘出来就知道了,结果是无穷。