Question

求极限 x趋于0 lim (e^-1)/sinx 1

Answer 1

当x趋于0时
e^x-1=0 sinx=0 是0分之0的形式,所以用洛必塔法则
即对分子分母分别求导
x趋于0 lim (e^-1)/sinx
=x趋于0 lim(e^x-1)'/(sinx)'
= x趋于0 lime^x/cosx
=1/1=1