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2016年成人高考专升本考试《高等数学》真题及标准答案

2016年成人高考专升本考试《高等数学》真题及标准答案
2016年成人高考专升本考试《高等数学》真题及标准答案

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(总分150, 考试时间150分钟)

一、选择题:1~10小题,每小题4分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的。

1.

A 0B 1C 2D 3

该问题分值: 4

答案:C

2.

A -1

B 0

C 1

D 2

该问题分值: 4

答案:C

3. 设函数y=2+sinx,则y/=

A cosx

B -cosx

C 2+cosx

D 2-cosx

该问题分值: 4

答案:A

4. 设函数y=ex-1+1,则dy=

A exdx

B ex-1dx

C (ex+1)dx

D (ex-1+1)dx

该问题分值: 4

答案:B

5.

A 1

B 3

C 5

D 7

该问题分值: 4

答案:B

6.

A π/2+1

B π/2

C π/2-1

D 1

该问题分值: 4

答案:A

7.

A 4x3+4x

B 4x3+4

C 12x2+4x

D 12x2+4

该问题分值: 4

答案:D

8.

A -1

B 0

C 1

D 2

该问题分值: 4

答案:C

9. 设函数z=x2+y,则dz=

A 2xdx+dy

B x2dx+dy

C x2dx+ydy

D 2xdx+ydy

该问题分值: 4

答案:A

10.

A 1/2

B 1

C 3/2

D 2

该问题分值: 4

答案:D

填空题

填空11-20小题。每小题4分,共40分。

11.

该问题分值: 4

答案:-1/3

12. 设函数y=x2-ex,则y/=

该问题分值: 4

答案:2x-ex

13. 设事件A发生的概率为0.7,则A的对立事件非A发生的概率为该问题分值: 4

答案:0.3

14. 曲线y=lnx在点(1,0)处的切线方程为

该问题分值: 4

答案:y=x-1

15.

该问题分值: 4

答案:ln|x|+arctanx+C

16.

该问题分值: 4

答案:cosx

17.

该问题分值: 4

答案:cosx

18. 设函数z=sin(x+2y),则αz/αx=

该问题分值: 4

答案:cos(x+2y)

19. 已知点(1,1)是曲线y=x2+alnx的拐点,则a=

该问题分值: 4

答案:2

20. 设y=y(x)是由方程y=x-ey所确定的隐函数,则dy/dx=

该问题分值: 4

答案:1/(1+ey)

解答题

21-28题,共70分。解答应写出推理、演算步骤。

21.

该问题分值: 8

答案:

22. 设函数y=xe2x,求y/

该问题分值: 8

答案:

y/=x/e2x+x(e2x)/=(1+2x)e2x

23.

该问题分值: 8

答案:

24.

该问题分值: 8

答案:

25.

该问题分值: 8

答案:

26. 求曲直线,直线x=1和x轴所围成的有界平面图形的面积为S,及该平面图形绕x轴旋转一周所得旋转体的体积为V。

该问题分值: 10

答案:

27. 设函数f(x,y)=x2+y2+xy+3,求f(x,y)的极点值与极值。

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