x趋向于无穷,求x乘以In(x/x-1)的极限
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x趋向于无穷,求x乘以In(x/x-1)的极限
x趋向于无穷,求x乘以In(x/x-1)的极限
x趋向于无穷,求x乘以In(x/x-1)的极限
x/(x-1)
=1+1/x
1/x→0
所以ln{1+1/x)~1/x
所以原式=lim(x→∞)x*1/x=1
lim{√[(X+P)(X+Q)]-X},X→+∞
=lim{√[(X+P)(X+Q)]-X}*{√[(X+P)(X+Q)]+X}/{√[(X+P)(X+Q)]+X},X→+∞
=lim[(X+P)(X+Q)-X²]/{√[(X+P)(X+Q)]+X},X→+∞
=lim[(P+Q)X+PQ]/{√[(X+P)(X+Q)]+X},X→+∞,分子分母同除以X得
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lim{√[(X+P)(X+Q)]-X},X→+∞
=lim{√[(X+P)(X+Q)]-X}*{√[(X+P)(X+Q)]+X}/{√[(X+P)(X+Q)]+X},X→+∞
=lim[(X+P)(X+Q)-X²]/{√[(X+P)(X+Q)]+X},X→+∞
=lim[(P+Q)X+PQ]/{√[(X+P)(X+Q)]+X},X→+∞,分子分母同除以X得
=lim[P+Q+PQ/X]/{√[(1+P/X)(1+Q/X)]+1},X→+∞
=[P+Q+0]/{√[(1+0)(1+0)]+1}
=(P+Q)/2
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