Question

求lim(3-2x／1-2x)^x的三次方的极限,x→∞

Answer 1

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