问题
问答题
设y=f(x)(x≥0)连续可微，且f(0)=1．现已知曲线y=f(x)，x轴，y轴及过点(x，0)且垂直于x轴的直线所围成的图形的面积与曲线y=f(x)在[0，x]上的一段弧长相等，求f(x)．
答案
参考答案：
解析： 由题设可知
上式两边对x求导得
分离变量得
两边积分得
将f(0)=1代入上式可得C=1，
故
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设y=f(x)(x≥0)连续可微，且f(0)=1．现已知曲线y=f(x)，x轴，y轴及过点(x，0)且垂直于x轴的直线所围成的图形的面积与曲线y=f(x)在[0，x]上的一段弧长相等，求f(x)．
参考答案：
解析： 由题设可知
上式两边对x求导得
分离变量得
两边积分得
将f(0)=1代入上式可得C=1，
故
| 阅读理解。 |
| Billy had a nice shop in the main street of a small town. He sold jewellery, watches, clocks and so on. All went well some years, and then a thief stole a lot of jewellery from his shop twice in one month at night. Three weeks passed, yet the police still didn't catch the thief. So Billy decided to try to do something about it himself. He bought a good camera and fixed it up in his shop and put some cheap jewellery in front of it for the thief, so that it could take a photo of anyone who stole the jewellery. A few nights later the thief came, but he did not touch any of the cheap jewellery that Billy had put out for him. He took the camera, which was worth 1500 dollars. |
| 1. At first all was getting on with Billy. |
[ ] |
| A. successfully B. badly C. quickly D. unhappy |
| 2. Within one month ______. |
[ ] |
| A. Billy began to sell camer B. Billysold all the things in his shop C. a thief stole all the things in Billy's shop D. a thief stole much of Billy's jewellery |
| 3. Billy bought a camera in order to . |
[ ] |
| A. take pictures for those who came to his shop B. find out the thief with its help C. become even richer D. make his shop large |
| 4. In the end of this story, . |
[ ] |
| A. Billy caught the thief B. the thief stole the expensive camera C. the thief took the camera and jewellery D. the thief took the jewellery |
| 5. The thief in the story was very . |
[ ] |
| A. stupid B. sad C. bright D. old |