求极限lim(1+3x）^(2/sinx),x趋向于0

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设lim(1+3x）迅并^(2/sinx)=a
lim[(1+3x）^1/(3x)]^(6x/sinx)=a
lnlim[(1+3x）^1/(3x)]^(6x/sinx)=lna
limln(1+3x）^1/(3x)]^(6x/亩袜迹sinx)=lna
lim(6x/sinx)ln(1+3x）^1/(3x)]=lna
lim(6x/sinx)*limln(1+3x）^1/(3x)]=lna
6*lnlim(1+3x）^1/(3x)]=lna
6*lne=lna
lna=6
a=e^6
好奇妙，我竟解好明出来了！

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lim(1+3x）改毕祥散^(2/sinx)
=lim e^ln((1+3x）核宴芹^(2/sinx))
=lim e^[2ln(1+3x）/sinx]
=lim e^(2*3x/x)
=e^6

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