英语周报2020 2021人教新目标版第四期答案

21.(1)解:由题意得函数f(x)的定义域为(-1,+∞)(1分)1 arta+l所以f(x)=a+x+1x+1①若a≥0,则f(x)>0,所以f(x)在区间(-1,+∞)上单调递增;(3分)ai②若a<0,则f(x)=x+1令f(x)>0,得-1 -1--,此时f(x)单调递减综上所述,当a≥0时,f(x)在区间(-1,+∞)上单调递增;当a<0时,f(x)在区间上单调递增,在区间(-1-,+∞上单调递减(5分)(2)证明:当a=-1时,f(x)=-x+n(x+1)-2,由(1)知,f(x)在区间(-1,0)上单调递增,在区间(0,+∞)上单调递减,所以f(x)≤f(0),又f(0)=-2,所以f(x)≤-2(8分)(3)证明:由(2)知,-x+ln(x+1)-2≤-2,即ln(x+1)≈x所以x-1≥nx,当且仅当x=1时取等号令(k∈N,k≥2),则2-1≥1n(k≥2)整理得2lnk≥12>1--1k-1'k(10分)当=2,3,…,n时21n2>1-2-12ln3>1+32ln>1--1-+1上面n-1个式子累加得2lh(2×3●n)>1+-(n≥2),n(n-1)故1n(2×3×…×n)>n≥2)2nn(12分)即∑1n(+1)>-2n2cos a为参

第二节One possible versionWhen Norah heard of her mothers plan, she was terhappy. She couldnt wait to see Dan at once. Hardly hadthey met Dan in his yard when Norah shouted excitedlyShe ran right up to him as if she had known him all of herlife and she was climbing all over him like a monkeyAnd of course every time I turned around. she d comeback over and hug me again, " Dan said. When it was timeto leave, Norah and her mom passed the rose bush by thedoor. Dan picked a big red rose and gave it to Norah, saying, "This is a symbol of our friendship.The mother and her daughter hane been visiting himceely, erer since. Every time they went there, the old andthe young would play games and tell each other secretsorah considers Dan as a family member and Dan has neverbeen alone again. "Norah helped me recover from my sad-ness and gave me something to live for, Dan said, with afresh shave and haircut

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