问题 问答题

设在半平面x>0中,有力

构成的力场,其中k为常数,

.证明在此力场中,场力所做的功与所取路径无关,而只与起点、终点有关,并计算由点(1,1)到点(2,2)场力所做的功.

答案

参考答案:由题设知,沿曲线L场力所做的功为
[*]
因当x>0时,P(x,y),Q(x,y)及其一阶偏导数均连续,且[*],故在此力场中,场力所做的功与所取路径无关,而只与起点、终点有关.
为了求由点(1,1)到点(2,2)场力所做的功,可取连接此两点的直线段:y=x(1≤x≤2)作为积分路径,于是有
[*]

解析:

[分析]: 按第二型曲线积分,写出沿曲线L场力所做的功的表达式,欲证场力做的功与所取路径无关,只要验证[*]即可.最后南曲线积分算出所做的功.

单项选择题
阅读理解

.

Books, software, and videos, no matter what you are looking for, if you turn on a computer and log (登录) on the Internet, you are sure to find something.

E-books are all over the Internet; some are free, and some are not. E-books are basically electronic books you can read without having to carry heavy books and look through all the pages. Now authors not only sell regular books in bookstores but also sell e-books on the Internet. Some e-books are sold on CDs, too.

You can get all types of software right from the Internet. After you download it, you have it. It is so convenient that you can get it even without leaving the house. These are the advantages we have in today’s high-tech world.

We can find videos of different people. There are so many websites with videos that it would take you some time to actually go through them all. The cool thing about videos is that some people have their own websites or their own spaces where they can upload videos of their families or of different events and allow other people to view them. It is amazing.

The Internet is an exciting place and it plays a big part in our lives today. You can even pay your bills on the Internet if that’s what you want to do. The marketing industry is also doing a lot better because of the Internet. Companies can communicate very quickly with each other over the Internet.

60. What can we know about the videos online according to the passage?

A. They are making human rights harder to protect.

B. They can include a lot of personal information.

C. They allow viewers to get to know each other more easily.

D. It’s a waste of time to watch videos online.

61. It can be inferred from the passage that _______.

A. people have to pay to download software

B. people usually pay their bills on the Internet these days

C. the Internet allows people to communicate more quickly

D. a lot of people still like paper books

62. The purpose of the passage is to______.

A. suggest that people start reading e-books on the Internet

B. advise people to form good computer habits

C. introduce many uses of the Internet

D. discuss problems people have online