求lim(x-无穷){x/(2+x)}^3x的极限
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求lim(x-无穷){x/(2+x)}^3x的极限求lim(x-无穷){x/(2+x)}^3x的极限求lim(x-无穷){x/(2+x)}^3x的极限x/(2+x)=(x+2-2)/(x+2)=1-2
求lim(x-无穷){x/(2+x)}^3x的极限
求lim(x-无穷){x/(2+x)}^3x的极限
求lim(x-无穷){x/(2+x)}^3x的极限
x/(2+x)
=(x+2-2)/(x+2)
=1-2/(x+2)
令1/a=-2/(x+2)
x=-2a-2
所以原式=lim(1+1/a)^(-6a-6)
=lim[(1+1/a)^a]^(-6)*(1+1/a)^(-6)
=e^(-6)
x/(2+x)=(x+2-2)/(x+2)=1-2/(x+2)令1/a=-2/(x+2)x=-2a-2所以原式=lim(1+1/a)^(-6a-6)=lim[(1+1/a)^a]^(-6)*(1+1/a)^(-6)=e^(-6)
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