计算lim(1+3x)^3/x x趋向0
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计算lim(1+3x)^3/xx趋向0计算lim(1+3x)^3/xx趋向0计算lim(1+3x)^3/xx趋向0如图.lim(x->0)(1+3x)^(3/x)=lim(3x->0)[(1+3x)^
计算lim(1+3x)^3/x x趋向0
计算lim(1+3x)^3/x x趋向0
计算lim(1+3x)^3/x x趋向0
如图.
lim(x->0) (1+3x)^(3/x)
=lim(3x->0)[(1+3x)^(1/3x)]^9
=e^9
lim(1+3x)^(3/x)=lime^[ln(1+3x)^(3/x)]=lime^[3/xln(1+3x)]
又lim3/xln(1+3x)=lim[3ln(1+3x)]/x=lim9/(1+3x)=9
所以lim(1+3x)^3/x=e^9
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