lim(x→0)(1/x)*(e^-1/x)的值要步骤,
1个回答

当x从左边趋向0

lim(x→0⁻) (1/x)e^(- 1/x),令y = - x,y→0⁺

= lim(y→0⁺) 1/(- y) * e^(1/y)

= lim(y→0⁺) - [e^(1/y)]/y → 负无穷大

当x从右边趋向0

lim(x→0⁺) (1/x)e^(- 1/x),令y = 1/x,y→+∞

= lim(y→+∞) ye^(- y)

= lim(y→+∞) y/e^y,e^y上升比y快

= 0

左右极限不相等,lim(x→0) (1/x)e^(- 1/x) 不存在.