x趋向于无穷,求x乘以In（x/x-1）的极限
问题描述：
x趋向于无穷,求x乘以In（x/x-1）的极限
答
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
答
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