Question

lim (x²/x²-1)的x次方 x趋于无穷的极限是e吗，为什么我算到是1

Answer 1

lim [(x2-1)/(x-1)]·e^[1/(x-1)] x→1? =lim [(x+1)(x-1)/(x-1)]·e^[1/(x-1)] x→1? =lim (x+1)·e^[1/(x-1)] x→1? =2·e^(+∞) =+∞ lim [(x2-1)/(x-1)]·e^[1/(x-1)] x→1? =lim [(x+1)(x-1)/(x-1)]·e^[1/(x-1)] x→1? =lim (x+1)·e^[1/(x-1)] x→1? =2·e? =2 [(x2-1)/(x-1)]·e^[1/(x-1)]在x=1处两侧极限不相等 lim [(x2-1)/(x-1)]·e^[1/(x-1)] 不存在 x→1

追问

我是说它的极限值是e吗？

Answer 2