求lim(3-2x/1-2x)^x的三次方的极限,x→∞
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求lim(3-2x/1-2x)^x的三次方的极限,x→∞
![求lim(3-2x/1-2x)^x的三次方的极限,x→∞](/uploads/image/z/3983291-35-1.jpg?t=%E6%B1%82lim%283-2x%EF%BC%8F1-2x%29%5Ex%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9%E7%9A%84%E6%9E%81%E9%99%90%2Cx%E2%86%92%E2%88%9E)
没过程胡说什么的?
lim(x→∞) [(3 - 2x)/(1 - 2x)]^x
= lim(x→∞) [(2 + (1 - 2x))/(1 - 2x)]^x
= lim(x→∞) [1 + 2/(1 - 2x)]^x
= lim(x→∞) [1 + 2/(1 - 2x)]^[(1 - 2x)/2 • 2x/(1 - 2x)]
= e^lim(x→∞) 2x/(1 - 2x)
= e^lim(x→∞) 2/(1/x - 2)
= e^[2/(0 - 2)]
= e^(- 1)
= 1/e
lim(x→∞) [(3 - 2x)/(1 - 2x)]^x
= lim(x→∞) [(2 + (1 - 2x))/(1 - 2x)]^x
= lim(x→∞) [1 + 2/(1 - 2x)]^x
= lim(x→∞) [1 + 2/(1 - 2x)]^[(1 - 2x)/2 • 2x/(1 - 2x)]
= e^lim(x→∞) 2x/(1 - 2x)
= e^lim(x→∞) 2/(1/x - 2)
= e^[2/(0 - 2)]
= e^(- 1)
= 1/e
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