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lim (x趋近于0) [(3x-1)/(3x+1)]的3X次方
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lim (x趋近于0) [(3x-1)/(3x+1)]的3X次方
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楼主可能要问的是 lim (x趋近于∞) [(3x-1)/(3x+1)]的3X次方
lim (x趋近于∞) [(3x-1)/(3x+1)]^(3X)
=lim [1 + (-2)/(3x+1)]^(3X)
=e^ lim (3X)·ln [1 + (-2)/(3x+1)]
=e^ lim (3X)· (-2)/(3x+1) 【等价无穷小代换】
=e^ lim (-6X)/(3x+1)
=e^(-2)
lim (x趋近于∞) [(3x-1)/(3x+1)]^(3X)
=lim [1 + (-2)/(3x+1)]^(3X)
=e^ lim (3X)·ln [1 + (-2)/(3x+1)]
=e^ lim (3X)· (-2)/(3x+1) 【等价无穷小代换】
=e^ lim (-6X)/(3x+1)
=e^(-2)
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