求【(x+1)/(x-1)】的x次方,当x 趋于无穷时的极限
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2012-01-29 · 知道合伙人教育行家
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lim(x趋近于+∞【[(x+1)/(x-1)]^x】
= lim(x趋近于+∞【[(x-1+2)/(x-1)]^x】
= lim(x趋近于+∞【[1+2/(x-1)]^(x-1) * [1+2/(x-1)]】
= lim(x-1趋近于+∞【[1+2/(x-1)]^(x-1) 】*lim(x-1)趋近于+∞【 1+2/(x-1)】
= e^2 * 1
= e^2
= lim(x趋近于+∞【[(x-1+2)/(x-1)]^x】
= lim(x趋近于+∞【[1+2/(x-1)]^(x-1) * [1+2/(x-1)]】
= lim(x-1趋近于+∞【[1+2/(x-1)]^(x-1) 】*lim(x-1)趋近于+∞【 1+2/(x-1)】
= e^2 * 1
= e^2
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