已知函数f（x）=x﹣1﹣alnx（a∈R）．
（1）若曲线y=f（x）在x=1处的切线方程为3x﹣y=3，求实数a的值；
（2）若f（x）的值域为[0，+ ∞），求a的值．
解：（1）求导函数，可得f'（x）=1﹣
∴f'（1）=1﹣a
∵曲线y=f（x）在x=1处的切线方程为3x﹣y=3，
∴1﹣a=3
∴a=﹣2；
（2）f'（x）=1﹣
=
（x＞0）
当a≤0时，f'（x）＞0恒成立，
∴f（x）在（0，+ ∞）上单调递增，而f（1）=0
∴x∈（0，1）时，f（x）＜0与f（x）≥0恒成立矛盾
∴a≤0不合题意
当a＞0时，f（x）在（0，a）上单调递减，在（a，+ ∞）上单调递增
∴f（x）≥f（a）=a﹣1﹣alna=0
∴a=1．
| 完形填空。 | ||||
| A very little boy was spending his Saturday morning playing in his sandbox. He had with him a plastic pail (桶) and a shiny, red plastic shovel (铲). In the 1 of creating roads and tunnels in the sand, he 2 a large rock in the middle of the sandbox. The boy dug around the rock, 3 to move it off the dirt. At first, he wanted to carry it out of the sandbox with his hands; however, it was too heavy. Later, with much 4 , he pushed the rock across the sandbox by 5 his hands. When the boy got the rock to the 6 of the sandbox, he found that he couldn't roll it up and 7 the little wall. 8 , the little boy pushed, but every time he thought he had made some 9 , the rock tipped (翻滚) and then fell back into the sandbox. The little boy pushed and pushed, but his only 10 was to have the rock roll back. Finally he 11 tears. All this time the boy's father watched from his living room window 12 the drama was unfolded. The moment the tears fell, a large 13 appeared across the sandbox. It was the boy's father. Gently but 14 , he said, "Son, why didn't you use all the strength that you had?" Defeated, the boy 15 back,"I did! I did! I used all the strength that I had!" "No, you didn't. You didn't ask me for help." The father 16 down, picked up the rock and dropped it off the sandbox. Do you have "rocks" in your life that need to be 17 ? Are you discovering that you don't have 18 it takes to lift them? There is someone who is willing to give us the 19 we need. Maybe, it's sometimes a good idea to ask others for 20 when we meet difficulties we can't overcome. | ||||
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