y2kkao
幼苗
共回答了14个问题采纳率:100% 举报
令y=(lnx)/(x+1) + 1/x - lnx/(x-1) - k/x→当x>0,且x≠1时,xlnx/(x-1)<(1-k)/2.令z=xlnx/(x-1)→z'=[x - 1 - (x+1)lnx]/(x-1) 令w=x - 1 - (x+1)lnx→w'=x - 1/x - 2xlnx→w''=1/x - 2lnx - 1→w'''= -2(x+1)/x 易知:当x>0时,w'''<0→w''单调递减.当x=1时,w''=0→当0<x<1时,w''>0→w'单调递增;当x>1时,w''<0→w'单调递减.当x=1时,w'=0→当x>0,且x≠1时,w'<0→w单调递减.当x=1时,w=0→当0<x<1时,w>0→z单调递增;当x>1时,w<0→z单调递减.易得:lim(x→1) xlnx/(x-1)=1/2→当x>0,且x≠1时,xlnx/(x-1)<1/2 由xlnx/(x-1)<(1-k)/2,xlnx/(x-1)<1/2→k≤0 故:k的取值范围是k≤0
1年前
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