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问题 填空题
已知函数f(x)=
-x2+6x+e2-5e-2，x≤e
x-2lnx，x＞e
（其中e为自然对数的底数，且e≈2.718）若f（6-a2）＞f（a），则实数a的取值范围是______．
答案

∵f(x)=

-x2+6x+e2-5e-2，x≤e
x-2lnx，x＞e

∴当x≤e时y=-（x-3）2+e2-5e+7∴x≤e时函数单调递增 当x＞e时y'=1-

2
x
＞0恒成立，故x＞e时函数单调递增，

∵f（e）=e-2=e-2lne∴函数在R上为增函数．

∴由f（6-a2）＞f（a）得6-a2＞a，

解得-3＜a＜2

故答案为-3＜a＜2

探究题

西安的秦始皇陵兵马俑是世界上的一大奇观，已经出土兵马俑7000多件。假设有个美国商人提出以5000万美元的高价收购一件兵马俑，此时文物局来征求你的意见，请你从多方面、多角度思考，写一篇短文，阐明自己的观点和理由。（150字左右）

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改错题

I had a interesting dream last night. I dreamedthat I took part in a race. At first, I could not to run very fast and fell behind. So I didn’t lose heart and keptrunning. All the students on the playground cheer me on, “ Come on!” I was so encouraging that I ran faster and fast till I caught up all the other runners. I felt as if flying like a superman. In the end, I got to the finishing line first.I won the race. I felt very proudly of myself. Many of my classmate threw me up into the air. Just at that timeI woke up and found me still in bed!
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