计算极限n趋向0,lim(x+e^2x)^(1/sinx)
问题描述：
计算极限n趋向0,lim(x+e^2x)^(1/sinx)
答
limx趋向0,lim(x+e^2x)^(1/sinx)
=limx趋向0,lim(1+x+e^2x-1)^(1/sinx)
=limx趋向0[(1+x+e^2x-1)^(1/(x+e^2x-1)]^[(x+e^2x-1)/sinx)]
=e^limx趋向0[(x+e^2x-1)/sinx)]
=e^limx趋向0[(x+e^2x-1)/x)]
=e^limx趋向0[(x+e^2x-1)/x)]
=e^3
答
e^3