limx→∞(x-1/x+3)^x

扭曲的奇葩 1年前 已收到1个回答 举报

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lim(x→∞)(x-1/x+3)^x

=lim(x→∞)[1-4/(x+3)]^x

=lim(x→∞)[1-4/(x+3)]^[-(x+3)/4*(-4)-3]

=lim(x→∞)[1-4/(x+3)]^[-(x+3)/4*(-4)]*lim(x→∞)[1-4/(x+3)]^(-3)

=lim(x→∞)[1-4/(x+3)]^[-(x+3)/4*(-4)]

=e^(-4)

1年前

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