题目

lim _(xarrow 0)((x+{e)^x)}^dfrac (1{x)}.

$%5Clim%5Climits_%7Bx%5Crightarrow%200%7D%5Cleft%28x%2Be%5E%7Bx%7D%5Cright%29%C2%A0%5E%7B%5Cfrac%7B1%7D%7Bx%7D%7D$ .

题目解答

答案

由题意，

原式 $%3De%5E%7B%5Clim%5Climits_%7Bx%5Crightarrow%200%7D%5Cfrac%7B%5Cln%20%5Cleft%28x%2Be%5E%7Bx%7D%5Cright%29%7D%7Bx%7D%7D%3De%5E%7B%5Clim%5Climits_%7Bx%5Crightarrow%200%7D%5Cfrac%7B1%2Be%5E%7Bx%7D%7D%7Bx%2Be%5E%7Bx%7D%7D%7D%3De%5E%7B2%7D$