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2016年成人高考专升本高数二考试真题及答案

2016年成人高考专升本高数二考试真题及答案
2016年成人高考专升本高数二考试真题及答案

2016年成人高考专升本高数二考试真题及答案

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,把所选项前的字母填在题后的括号内。

? ? ?

答案:C

2.

? ? ?

答案:C

3.设函数y=2+sinx,则y/=

? ? +cosx ?

答案:A

4.设函数y=e x-1+1,则dy=

? ? C.(e x+1)dx ? D.(e x-1+1)dx

答案:B

5.

? ? ?

答案:B

6.

A.π/2+1 ?

B.π/2 ?

C.π/2-1 ?

答案:A

7.

+4x ? +4 ? +4x ? +4

答案:D

? ? ?

答案:C

9.设函数z=x2+y,则dz=

+dy ? +dy ? +ydy ? +ydy

答案:A

10.

2 ? ? 2 ?

答案:D

二、填空11-20小题。每小题4分,共40分。把答案填在题中横线上。答案:-1/3

12.设函数y=x2-ex,则y/=

答案:2x-e x

13.设事件A发生的概率为,则A的对立事件非A发生的概率为

答案:

14.曲线y=lnx在点(1,0)处的切线方程为

答案:y=x-1

15.

答案:ln|x|+arctanx+C

16.

答案:0

17.

答案:cosx

18.设函数z=sin(x+2y),则αz/αx=

答案:cos(x+2y)

19.已知点(1,1)是曲线y=x2+alnx的拐点,则a=

答案:2

20.设y=y(x)是由方程y=x-e y所确定的隐函数,则dy/dx=

答案:1/(1+e y)

三、解答题:21-28题,共70分。解答应写出推理、演算步骤。

21.(本题满分8分)

22.(本题满分8分)

设函数y=xe2x,求y/

解:y/=x/e2x+x(e2x)/=(1+2x)e2x.

23.(本题满分8分)

24.(本题满分8分)

25.(本题满分8分)

26.(本题满分10分)

27.(本题满分10分)

设函数f(x,y)=x2+y2+xy+3,求f(x,y)的极点值与极值。28.(本题满分10分)

(Ⅰ)求常数α;

(Ⅱ)求X的数学期望EX及方差DX。

解:(Ⅰ)因为+α++=1,所以α=.

(Ⅱ)EX=0×+10×+20×+30×=16

DX=(0-16)2×+(10-16)2×+(20-16)2×+(30-16)2×=124.

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