2022英语周报第五期答案

21.【命题意图】本题考查导数在研究函数性质中的应用解析】(1)由题意,得f(x)的定义域为(0,+∞)、f(x)=2e显然当a≤0时,(x)>0恒成立,厂(x)无零点(2分)当a>0时,取(x)=f(x)=2e则r(x)=4e2+">0,即f(x)单调递增(4分又(a)>0/(2)=2=-2o所以导函数f(x)存在唯一零点故当a>0时、f(x)存在唯一零点,当a≤0时f(x)无零点(5分)(Ⅱ)由(1)知,当a≤0时、f(x)单调递增,所以f(x)=f(e)=e2-a=e2,所以a=0因为g(x)=1=m-x,函数g(x)的图象在点(1,g(1)处的切线方程为y-3=0以g(1)=1m=0,所以m=1又g(1)=1+1mL+n=3,所以n=2,所以g(x)=1++2(7分)根据题意,要证f(x)≥g(x),即证lnx+1≤e2-2,只需证x(e-2)-lnx令=2-3-:则((x+1-2(2+(2-令F(x)=2-1(x>0),则F(x)=22+1所以F(x)在(0,+∞)上单调递增(8分)4<0()=e=2>0所以F()有唯一的等点(÷)当x∈(0,x)时,F(x)<0,即h(x)<0,h(x)单调递减当x∈(x,+∞)时,F(x)>0,即h(x)>0,h(x)单调递增所以h(x)=h(x2)=xn(e20-2)-lnx又因为F(x)=0.所以=所以M(x)=(-2)-()=1-2+2故f(x)≥g(x)(12分)

第三节One possible version:Paragraph 1On the Christmas of 1995, a drunken lady said some-thing that amoke him and he realized he had found hisdream girl. That was why the guy did not bother to lookfurther when he realized the girl was not coming backRealizing that he had let away someone so important in hislife. he decided to call her immediately. His whole mindwas flooded with fear. He was afraid that she might havefound someone new or no longer had the same feelings anymore. He tried again and again, never giving up. Finallygot through. He expressed his love for her and thewas moved to tears. She was still waiting for him, nevergiving up.Paragraph 2He decided to y to vancouver to join her. It was thehappiest time of their lizes! But their happy time was short-lived.Two days before he was supposed to fly to Vancou-ver. he received a call from her father. She had a head-oncar collision with a drunken driver. Anyone can imagine theheart-broken feelings he had. Why did fate play such cruelames with him? How he hated himself for taking so long togarealize his mistake I That was in 1996

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