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2015年秋季入学测试机考《专升本理科》复习资料

北京航空航天大学现代远程教育

《高等数学》

一、

单项选择题：

1. 函数 3

--=

x x y 的定义域是（）（A ）(2,)+∞

（B ） [2,]+∞ （C ）(,3)(3,)-∞+∞

（D ） [2,3)(3,)+∞

2. 函数 22)1(-=x x y 在区间 (0,1) 内（）（A ）单调增加（B ）单调减少（C ）不增不减（D ）有增有减

3. 下列函数中，是奇函数的是（）

（A ）4

y x x =- （B ）2

y x x =- （C ）22x

x y -=-

（D ）22x

y -=+

4. 已知函数 2,0

()1,0ax b x f x x x +

，则(0)f 的值为（）

（A ）a b + （B ）b a - （C ）1 （D ）0

5. 设函数z=f(x,y)的定义域为D={(x,y)|0≤x≤1,0≤y≤1}，则函数f(x 2,y 3)的定义域为（）

（A ）{(x,y)|0≤x≤1,0≤y≤1} （B ）{(x,y)|－1≤x≤1,0≤y≤1} （C ）{(x,y)|0≤x≤1,－1≤y≤1} （D ）{(x,y)|－1≤x≤1,－1≤y≤1} 6. 下列集合中为空集的是（）

（A ）{x|e x =1} （B ）{0} （C ）{(x, y)|x 2+y 2=0} （D ）{x| x 2+1=0,x ∈R} 7. 函数f(x)==π

?≥<)4(f ,1|x |,01|x ||,x sin |则（）

（A ）0

（B ）1 （C ）

（D ）－

2 8. 设f(x+2)=x 2-2x+3,则f[f(2)]= （）

（A ）3 （B ）0 （C ）1

（D ）2

9. 二元函数f(x,y)=ln(x －y)的定义域为（）

（A ） x －y>0 （B ） x>0, y>0 （C ） x<0, y<0 （D ） x>0, y>0及x<0, y<0 10. 函数y=2｜x ｜－1在x=0处（）

（A ）无定义（B ）不连续（C ）可导（D ）连续但不可导 11. 函数y=x －arctanx 在［－1，1］上（）

（A ）单调增加（B ）单调减少（C ）无最大值（D ）无最小值 12. 设n x u lim ∞

→=a,则当n→∞时，u n 与a 的差是（）

（A ）无穷小量（B ）任意小的正数（C ）常量（D ）给定的正数

13. 设f(x)=???

????<>0x ,x 1sin x 0x ,x

sin ,则)x (f lim 0x +

→=（）

（A ）－1 （B ）0 （C ）1 （D ）不存在

14. x

sin

x 3lim x ?∞

→=（）（A ）正无穷（B ）0

（C ）

3 （D ）

2 15. 设函数?

??≤<-≤<-=3x 1,x 21

x 0,1x )x (f 在x=1处间断是因为（）

（A ）f(x)在x=1处无定义

（B ）)x (f lim 1

x -

→不存在（C ）)(lim 1

x f x +

→不存在

（D ）)x (f lim 1

x →不存在

16. 设F(x)=

-x a dt )t (f a

x x

，其中f(t)是连续函数，则)x (F lim a x +→=（）（A ）0 （B ）a （C ）af(a) （D ）不存在

17. 下列积分中不能直接使用牛顿—莱布尼兹公式的是（）

（A ）

?+1

1dx

（B ）

π40

tgxdx

（C ）

dx x

?+ （D ）

π40

ctgxdx

18. =+→)

2x (x x

2sin lim

0x （）

（A ）1 （B ）0 （C ）正无穷（D ）2

19. 设2x

x e )

mx 1(lim =-→，则m=（）

（A ）

1 （B ）

2 （C ）－2

（D ）2

20. 设x

y -=是无穷大量，则x 的变化过程是（）

（A ） x→0+

（B ） x→0- （C ） x→＋∞ （D ） x→－∞ 21. 函数在一点附近有界是函数在该点有极限的（）

（A ）必要条件（B ）充分条件（C ）充分必要条件（D ）无关条件 22. 设函数f(x)=?????<-≥0

x ,1x 0

x ,e 2x

，则=---→0x )0(f )x (f lim 0x （）（A ）－1

（B ）－∞ （C ）＋∞ （D ）1

23. 1x +→ 时，下列变量中为无穷大量的是（）

（A ）1

-x

（B ）1

12--x x

（C ）

1 （D ）

2--x x 24. 已知函数

2,()1,f x x ?-?

=-? 11001x x x ≤--<<≤< ，则 1

lim ()x f x →- 和 0lim ()x f x →（）

（A ）都存在（B ）都不存在

（C ）第一个存在，第二个不存在

（D ）第一个不存在，第二个存在

25. 设 232,0

()2,0

x x f x x x +≤?=?

->? ，则 0

lim ()x f x +

→=（） (A) 2

（B ） 0

（C ） 1-

（D ） 2-

26. 函数 1,0

()1,0x f x x ≥?=?

，在 0x = 处（）

(A)左连续

（B ）右连续

（C ）连续

（D ）左、右皆不连续

27.

02lim

5arcsin x x

x →=（）

（A ）0 （B ）不存在（C ）

（D ）1

28. ()f x 在点 0x x = 处有定义，是 ()f x 在 0x x =处连续的（）（A ）必要条件（B ）充分条件（C ）充分必要条件

（D ）无关条件

29. 下列极限存在的有（）

（A ）2(1)

lim

x x x x

→∞+

（B ）01

lim

x x →-

（C ）1

lim x

x e →

（D

）x 30. 设 )(x f 在点 0x 处可导，则下列命题中正确的是（）

（A ）

()()

lim

x x f x f x x x →-- 存在（B ）

()()lim

x x f x f x x x →--不存在（C ） 00()()

lim

x x f x f x x

→+

-存在

（D ） 00

()()

lim

x f x f x x

?→-?不存在

31. 设y=2cosx ,则y '=（）

（A ）2cosx ln2 （B ）－2cosx sinx （C ）－2cosx (ln2)sinx

（D ）－2cosx-1sinx

32. 设 (0)0f = ，且 0

()lim

x f x x → 存在，则 0()

lim x f x x

→ 等于（）

（A ）)(x f ' （B ）)0(f '

（C ）)0(f

（D ）

)0(2

f ' 33. 设 1

(2)1

f x x +=

+ ，则 ()f x '=（）（A ）21

(1)x -

（B ）2

(1)x -

（C ）

x + （D ） 11

x -

- 34. 已知函数 2ln y x = ，则 dy =（）

（A ）

dx x

（B ）

（C ）

1x （D ）

1dx x 35. 设 21cos ,0()0,01

tan ,0x x x f x x x x x

==???>? ，则 ()f x 在 0x =处（）（A ）极限不存在（B ）极限存在，但不连续（C ）连续但不可导

（D ）可导

36.

37.

38.

39.

2015年秋季机考《高等数学》复习资料

参考答案

《大学英语》Vocabulary and Structure

1. An argument ______ in the classroom between the children.

A. broke out

B. broke in

C. broke off

D. broke though

2. When she is drunk, she’s ______ of saying rude things.

A. ashamed

B. envious

C. capable

D. independent

3. He has no ______ of winning.

A. occasion

B. chance

C. favors

D. fate

4. Let’s leave early, ______ we’ll get stuck in a traffic jam.

A. unless

B. despite

C. so

D. otherwise

5. Words play an important ______ in our everyday life.

A. character

B. position

C. role

D. duty

6. ______ but a strong man could have lifted it.

A. One

B. No one

C. Any

D. Not one

7. I didn’t hear ______ because there was too much noise where I was sitting.

A. what did he say

B. what he said

C. what was he saying

D. what he says

8. They tried to book the tickets five days earlier. They ____ them ten days earlier.

A. would have booked

B. must have booked

C. might have booked

D. should have booked

9. He will continue the work ______ tries to stand over him.

A. no matter how

B. no matter he

C. no matter who

D. no matter whom

10. You would not feel tired this morning if you ______to bed at a reasonable hour

last night.

A. would go

B. went

C. had gone

D. go

11. After the trip, we all felt our holiday was______ cheap.

A. shockingly

B. amazingly

C. wonderingly

D. annoyingly

12. ____, and you will see a high building.

A. Turning to the left

B. To turn to the left

C. Having turned to the left

D. Turn to the left

13. The old system has died and a new one has sprung up to _____ its place.

A. keep

B. take

C. change

D. give

14. The three Chinese journalists were ____ killed in the missile attack.

A. however

B. whoever

C. whichever

D. whatever

15. The most important thing is for NATO to meet the Chinese requests and ____ full

responsibility for the attack.

A. bring

B. give

C. take

D. carry

16. His son was found guilty, which brought _____ to the whole family.

A. interest

B. flame

C. impression

D. disgrace

17. You ought to ______ your food properly before swallowing it.

A. lick

B. chew

C. bite

D. eat

18. I______ up some English while on my holiday abroad.

A. took

B. picked

C. looked

D. brushed

19. Now many employers have _____ to regard a master's degree as minimum

training.

A. insisted

B. managed

C. come

D. give

20. Hardly when the bell .

A. did I close the door; had rung

B. had I closed the door; rang

C. I had closed the door; rang

D. I closed the door; rang

21. Do you suppose you can ______ to get me a passport?

A. try

B. attempt

C. manage

D. tempt

22. The knife you are cutting the bread with is ______ stainless steel.

A. made by

B. made of

C. made from

D. made in

23. I wonder why they ______ you so much money for such a book.

A. asked

B. requested

C. required

D. charged

24. I don’t think anybody ______ apart from himself.

A. matches

B. matters

C. makes

D. misses

25. My house is different ______ your house in several ways.

A. than

B. in

C. from

D. to

26. I wish I ______ a bird.

A. was

B. were

C. am

D. will be

27. I didn’t hear ______ because there was too much noise where I was sitting.

A. what did he say

B. what he said

C. what was he saying

D. what he says

28. The vehicle in ______ astronauts descend（降落）to the Moon’s surfac e is one of

the most exciting items.

A. that

B. where

C. it

D. which

29. He will continue the work ______ tries to stand over him.

A. no matter how

B. no matter he

C. no matter who

D. no matter whom

30. Who doubts ______ it is true?

A. why

B. what

C. that

D. when

31. The fact _____ shows that he was not serious about the meeting.

A. which he didn’t turn up

B. that he didn’t turn up

C. why he didn’t turn up

D. for him not to turn up

32. With most of the housework _____, Mrs Smith decided to have a rest.

A. done

B. doing

C. have done

D. being done

33. Imagine yourself as a winner, ______ will be of great help to your future success.

A. and

B. it

C. which

D. that

34. It is necessary that the task _____ before Friday.

A. is accomplished

B. will be accomplished

C. be accomplished

D. to be accomplished

35. The telephone _____ for almost a minute. But no one answers it.

A. rang

B. is ringing

C. had rung

D. has been ringing

36. It's believed that you work, result you'll get.

A. the harder. . . the better

B. the more hard. . . the more better

C. the harder. ... a better

D. more hard . . . more better

37. Young people may grow quickly in some ways and more slowly in .

A. the other

B. some other

C. others

D. these others

38. We won't give up we should fail ten times.

A. even if

B. since

C. whether

D. until

39. He'll be an astronaut by the time he thirty.

A. is

B. had been

C. will be

D. is going to be

2015年秋季机考《大学英语》复习资料

参考答案