复习资料2013秋

第一部分 数学：

一、计算题

（一）计算下列极限：

1、121lim 2

-++∞>-n n n n = n n n n 1211lim 22-++∞>-=1 2、x

x x 11lim 0-+>- =x x x 21lim 0>-(其中x x 21~11-+) =21 （注：本题也可用洛必达法则、或分子有理化）

3、x x x x x x sin cos sin lim 20->-=30cos sin lim x x x x x ->-=2

03sin cos cos lim x x x x x x +->-=31 （二）求下列函数的导数：

1、)1ln(2x x y ++=，221)1(x x x x y ++'

++='=22211

111x x x x x +=++++

2、解：等式两边分别对x 求导得 y e y y x y '='+22

移项得 x y y e y 2)2(='- ， 所以 y

e x y y 22-=' （三）要从一根截面是半径为R 的圆木中锯出截面是矩形的柱子，问怎样距法可以使废弃的木料最少。

解：设截得矩形柱子的截面矩形边长分别为y x ,，满足2224R y x =+

要使废弃的余料最少，即使截得的截面面积最大，设截面面积为S ， 224x R x xy S -==，求导得222

2244x R x x R S ---='令其等于零，

解得R x 2=，所以锯成截面边长为R 2的正方形使得废弃的余料最少。

（四）求函数2)2(x x y -=的单调区间与极值。 解：该函数的递增区间为)32,(-∞、),2(+∞，递减区间为)2,32(极大值为27

32)32(=

f ，极小值为0)2(=f

（五）求由曲线1,2==x x y 及x 轴所围成的平面图形面积。

解：由曲线1,2==x x y 及x 轴所围成的平面图形面积设为A

3

131103102===

⎰x dx x A

第二部分 英语： I.Multiple choice

Fill in the blanks with proper words

1. Daisy is introducing Sally to Smith.

Daisy: Good morning, Smith. Could I of your time?

Smith: Oh, it's you, Daisy! What can I do for you?

Daisy: May I my friend Sally to you, Smith? She's an

student in our college. She speaks good English. And also she is good at

.

Sally: How do you do, Smith?

Smith: Pleased to meet you, Sally. I have about you from Daisy.

Would you like to work for two months in my ?

Sally: Of course I'd love to. I really want to get some real through my

work here.

Smith: Ok, please come to work at 8:00 tomorrow morning.

Sally: . Goodbye!

pany

B. introduce

C.operating

D.a little

E.heard

F.take a few minutes

G.See you tomorrow

puter

I.outstanding

J.experience

F B I C H E D A J G

2. A are talking about their neighbour, Mr. Wang.

Wife: , do you know anything about our new neighbour , Mr. Wang?

Husband: Nothing that he goes to work at 7:30 every morning.

Wife: He is quite special.

Husband: Special? What's special about him?

Wife: Well, for one thing, he is Wang Li's .Mrs. Li has told me that.

Husband: What else?

Wife: He's from a village three years ago with only 20 yuan in his

but now ...

Husband: What has happened?

Wife: He has his company with about 200 . It's reported that he has built a new school for his poor .

Husband: A story!

A.boyfriend

B.Darling

C.pocket

D.couple

E.hometown

F.set up

G.rags-to-riches

H.except

I.employees

J.distant

D B H A J C F I

E G

3. Wang Fang shows a photo of her family to Dianna.

Dianna: How many are there in your family?

Wang: There are five. Look at the photo. The old sitting in the middle are my parents.

Dianna: Oh, your parents! They smile so happily.

Wang: You're right. My mother was an English teacher in a middle school, and my father was a doctor. Now both of them are from work.

Dianna: Your English must be from your mother, I think.

Wang: Maybe. When I was little, she liked to teach me English.

Dianna: A wise mother! Who is the man ?

Wang: He's my elder brother.

Dianna: He looks so . What is he doing now?

Wang: He works in a big company in Shanghai as a .

Dianna: Who is the girl on the right? Is that you?

Wang: No, that's my younger sister. She is studying in Los Angeles.

Dianna: So the girl her must be you.

Wang: Yes, you're right.

Dianna: You are still as lovely as you were.

Wang: Thank you, by the way, I'd like to see my parents this weekend. Would you like to go with me? My mother is preparing my . Have a taste, OK? Dianna: Oh, I'd love to. I'll be glad to meet your parents. It seems you really have a happy family.

A.inherited

B.favorite dishes

C.on the left

D.handsome and energetic

E.fluent

F.next to

G.members

H.couple

I.manager

J.retired

G H J E A C D I F B

4. Kate and her brother Bill are talking about their cousin Nancy and her husband Steve. Bill: Kate, Nancy and Steve are .

Kate: It's really a . I've heard that they , but they've always afterward.

Bill: Things are not working out this time. They are getting a soon.