英语周报2021-2022第答案

21.(1)依题意,(x)=lnx,lnx分)故f(x)=2inx(2分)故当x∈(0,1)时,f(x)<0,当x∈(1, ∞)时,f(x)>0(4分)故函数f(x)的单调递减区间为(0,1),递增区间为(1, ∞)(5分)(2)由已知可得函数g(x)的定义域为(0, ∞),且(x)=1-90(6分)由已知得g'(x0)=0,即x3-2 conco-a=0,①由g(x0)=2可得,x3-x0(lnx0)2-2x0 a=0,②联立①②,消去a,可得2x0-(nx0)2-2lnxo-2=0,③分)2lnx22(x-1nx-1)令:(x)=2x-(nx)2-2lnx-2,则(x)=2x-1nx-1≥0易知,故t(x)≥0,∴t(x)在区间(0, ∞)单调递增,11分)注意到t(1)=0,所以方程③有唯一解x0=1,代入①,可得a=1(12分)

第四部分第二节Iwo davs before my birthday last vear. Dad came home earlv. As usual. Ihelped him carry his bags into his study: When I turned to leave. he said: "Hey. wouldyou like to help me clean my comb? It's been a while since I last cleaned"It hit methen why. as a child. helping my dad clean his comb was such a joy. That routinemeant that my dad was home early to spend the evening with Mum and I. It meantwould watch TV with us or play a few video games with me. It meant a happyloving familyI pass the clean comb back to Dad. I noticed the wrinkles next to his eyes.They are more noticeable when he smiles. but his smile is still as heartw arming asbefore. The smile of a father who just wants a good life for his family. Dad carefullyplaces his comb on top of his wallet. After so many years. he still organises hispersonal items in the same careful way. I guess some things never change. And forthat. I'm glad

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