limx趋近于无穷[(x+3)÷(x-6)]的x次方

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limx趋近于无穷[(x+3)÷(x-6)]的x次方limx趋近于无穷[(x+3)÷(x-6)]的x次方limx趋近于无穷[(x+3)÷(x-6)]的x次方这是1^∞型极限,用重要极限lim(x→∞)

limx趋近于无穷[(x+3)÷(x-6)]的x次方
limx趋近于无穷[(x+3)÷(x-6)]的x次方

limx趋近于无穷[(x+3)÷(x-6)]的x次方

这是1^∞型极限,用重要极限lim(x→∞) [1+(1/x)]^x=e
lim(x→∞) [(x+3)/(x-6)]^x
=lim(x→∞) [1+9/(x-6)]^{[(x-6)/9]*[9x/(x-6)]}
=e^lim(x→∞) [9x/(x-6)]
=e^9