题目

若曲线y=x2－1与y=1－x3在x=x0处的切线互相垂直,则x0等于 A.                       B.－                    C.                                   D.或0 答案：A 解析:本题主要考查导数的几何意义及两直线垂直的位置关系,即若两直线的斜率都存在,则它们垂直的条件是斜率的乘积等于－1. 因为两直线垂直且导数都存在且分别为y′=2x,y′=－3x2,所以(2x)·(－3x2)=－1, 即x=. Bob Christiansen, who studied the volcanic history of Yellowstone National Park in the 1960s, became puzzled about something that, oddly, had not troubled anyone before: he couldn’t find the park’s volcano. It had been known for a long time that Yellowstone was volcanic in nature—that’s the reason for all its hot springs and other steamy features. But Christiansen couldn’t find the Yellowstone volcano anywhere.Most of us, when we talk about volcanoes, think of the classic cone (圆锥体) shapes of a Fuji or Kilimanjaro,which are created when erupting magma(岩浆) piles up. These can form remarkably quickly. In 1943, a Mexican farmer was surprised to see smoke rising from a small part of his land. In one week he was the confused owner of a cone five hundred feet high. Within two years it had topped out at almost fourteen hundred feet and was more than half a mile across. Altogether there are some ten thousand of these volcanoes on Earth, all but a few hundred of them extinct. There is, however, a second less known type of volcano that doesn’t involve mountain building. These are volcanoes so explosive that they burst open in a single big crack, leaving behind a vast hole, the caldera(火山喷口). Yellowstone obviously was of this second type, but Christiansen couldn’t find the caldera anywhere.Just at this time NASA decided to test some new high-altitude cameras by taking photographs of Yellowstone. A thoughtful official passed on some of the copies to the park authorities and said that they might make a nice blow-up for one of the visitors’centers. As soon as Christiansen saw the photos, he realized why he had failed to spot the caldera: almost the whole park-2.2 million acres—was caldera. The explosion had left a hole more than forty miles across—much too huge to be seen from anywhere at ground level. At some time in the past Yellowstone must have blown up with a violence far beyond the scale of anything known to humans.1.What puzzled Christiansen when he was studying Yellowstone？2.Is Fuji or Kilimanjaro created when erupting magma piles up?3.What does the second paragraph mainly talk about？4.When did Christiansen realize why he had failed to spot the caldera?5.What was the caldera of Yellowstone?