21.(本小题满分12分)(I)函数f(x)的定义域为(0+∞).设切点坐标为(x,y0),f(x)=_+1+x+1+lnx=a由题意得,{x,∴2lx-x+=22分(x+1)hnx=a(x-1)令(x)=2hx-x+一,则h(x)+(x-2x2-2x+≤0xh(x)在(O,+∞)上单调递减,∴h(x)=0最多有一个实数根.…………4分又∵加()=0,;=1,…∴=0,∴切点坐标为(1,0).………5分(Ⅱ)当x∈(0)时,g(x)>f(x)恒成立,等价于hxa(x-1)0对任意x∈(0)恒x+1成立6分令F(x)=lnxx+12,则P)12aa【xx2+2(-a)x+1x(x+12x(Er(+i)2ue,F(()=07分①当a≤2,x∈(0,1)时,x2+2(1-a)x+1x2-2x+1>0,∴F(x)>0,F(x)在(,)上单调递增,∴F(x) 2时,令F(x)=0得x=a-1-√(a-1)-1,x=a-1+√(a-12-1由x2>1与x=1得,0 F()=0,不符合题意综上所述,a的取值范围为(-∞,2]2分

书面表达One possible version:NOTICEA sports meeting will be held in the playground of our school from next Thursday to FridayAs you know, the pressure of study is very heavy now, especially for those senior 3. So the purpose of the sports meeting is to letevery student get relaxed, as a result of which we students can live happily and heal thilyEveryone is welcome to take part in it. Those who perform excellently at the sports meeting will get prizes. But don' t take theresults so serously because taking part is more important than the result. Good luck to everyone!

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