lim(1-3x)^(1/x) =lim(1-3x)^(1/-3x)*(-3) =e^(-3) =1/e^3 怎么化简的
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lim(1-3x)^(1/x) =lim(1-3x)^(1/-3x)*(-3) =e^(-3) =1/e^3 怎么化简的?
![lim(1-3x)^(1/x) =lim(1-3x)^(1/-3x)*(-3) =e^(-3) =1/e^3 怎么化简的](/uploads/image/z/18198000-0-0.jpg?t=lim%EF%BC%881-3x%29%5E%281%2Fx%29+%3Dlim%EF%BC%881-3x%29%5E%281%2F-3x%29%2A%28-3%29+%3De%5E%28-3%29+%3D1%2Fe%5E3+%E6%80%8E%E4%B9%88%E5%8C%96%E7%AE%80%E7%9A%84)
lim(x→0)(1-3x)^(1/x)=lim(x→0) [(1-3x)^(1/(-3x)]^(-3)
(-3x)=u,x→0,-3u→0
lim(x→0)(1-3x)^(1/(3x)=lim(u→0)(1+u)^(1/u)=e
lim(x→0)[(1-3x)^(1/(-3x)]^(-3)=e^(-3)
(-3x)=u,x→0,-3u→0
lim(x→0)(1-3x)^(1/(3x)=lim(u→0)(1+u)^(1/u)=e
lim(x→0)[(1-3x)^(1/(-3x)]^(-3)=e^(-3)
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