t的二次方分之e的t次方的极限怎么算?..

题目

t的二次方分之e的t次方的极限怎么算?..

答案

(t->0-) lim exp(t)/t² = (t->0-) lim 1/t² = +∞
(t->0+) lim exp(t)/t² = (t->0+) lim 1/t² = +∞
e^t/t² 在 t->0 处无极限
(t->+∞) lim exp(t)/t² = (t->+∞) lim exp(t)/(2t) = (t->+∞) lim exp(t)/2 = +∞
(t->-∞) lim exp(t)/t² = (t->-∞) lim exp(t)/(2t) = (t->-∞) lim exp(t)/2 = 0
e^t/t² 在 t->∞ 处无极限