计算极限n趋向0,lim(x+e^2x)^(1/sinx)

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计算极限n趋向0,lim(x+e^2x)^(1/sinx)计算极限n趋向0,lim(x+e^2x)^(1/sinx)计算极限n趋向0,lim(x+e^2x)^(1/sinx)e^3limx趋向0,li

计算极限n趋向0,lim(x+e^2x)^(1/sinx)
计算极限n趋向0,lim(x+e^2x)^(1/sinx)

计算极限n趋向0,lim(x+e^2x)^(1/sinx)
e^3

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