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数学专升本考试试题

数学专升本考试试题
数学专升本考试试题

高等数学(二)命题预测试卷(二)

'、选择题(本大题共 5个小题,每小题4分,共20分。在每个小题给出的选

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)

A .

B . 1 In 2

2

C . 1

D . In 2

5?设u _ xy z

u 等于(

)

x

A . z

zxy

B . xy z 1

C . y z 1

D . y z

x 为

)

4.若 f (

h

x

1、填空题:本大题共

10个小题, ,则 1

1 ?下列函数中,当 x —■ 1时,与无穷小量 (1 x )相比是高阶无穷小的是(

A . ln( 3 =x) C . cos(x 1) 2.曲线 y 3护:

A . 处处单调减小

C . 具有最大值

x 3 - 2x 2 x

D . x 2

1

B ?处处单调增加 D ?具有最小值

3?设f (x )是可导函数,且 lim

x

f ( x o + 2h)

f (x0

)= 1,贝U f (X 0 )为( ) h

1

[f ( x)dx 10个空,每空4分,共40分,把答案填在

6. 设 z —e xy 一 yx

则'Z

&

(1,2 )

x f ( x) _

_

In x ,则 f (3厂

则f (」)_ ______ +2在⑴“)内是(

x

题中横线上。

1

10. lim (1 _ 1 ) x

2x

1

x sin 2x

dx -

1

1 cos

2 x

、解答题:本大题共 13小题,共90分,解答应写出推理、演算步骤。

斗0

x

的间断点.

计算lim ,x

2x 2 1

x 一 0

16.

(本题满分

6 分)

17.

(本题满分

6 分)

11 .函数 f (x) - 1 (e 八

e x )的极小值点为

12

.若

lim

2

x ax 一 4

,则

曲线y arctanx 在横坐标为

1点处的切线方程为

函数y 二

?0

sin tdt 在 X r

处的导数值为

求函数f (x )

arcta n 0

18. (本题满分6分)

x) x 计算lim In arcs in x (1

x 0

1

23 ?(本题满分6分)

若f ( x )的一个原函数为 xln x ,求 x f ( x )dx .

19 ?(本题满分6分)

设函数f (x)

Xe x

_

ln(1 x)

x 0 ,求 f ( x) ? -1 x 0

20 ?(本题满分6分)

求函数y -sin ( x y )的二阶导数.

21 ?(本题满分6分)

求曲线f (x ) _x 4

2x 3

的极值点.

22 ?(本题满分6分)

x 3

计算

dx ?

24?(本题满分6分)

1

已知k dx _ _1,求常数k的值.

1 x

2 2

25.(本题满分6分)

求函数f (x, y) - y 3 _x 2 6 x _12 y用5的极值.

26 ?(本题满分10分)

求fJ( x2+y)dxdy,其中D是由曲线y =x 2与x=?y 2所围成的平面区域.

D

27.(本题满分10 分)

、 2 a a

设f ( x) N - J f ( x)dx,且常数a 于-1,求证:f (x)dx

0 0

28 ?(本题满分10分)

求函数y —ln

X的单调区间、极值、此函数曲线的凹凸区间、拐点以及渐近x

线并作出函数的图形.

3 ——a

3(a 1)

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高等数学专升本试卷 考试说明: 1、考试时间为150分钟; 2、满分为150分; 3、答案请写在试卷纸上,用蓝色或黑色墨水的钢笔、圆珠笔答卷,否则无效; 4、密封线左边各项要求填写清楚完整。 一. 选择题(每个小题给出的选项中,只有一项符合要求.本题共有5个小题,每小题4分,共20分) 1函数1 arccos 2 x y +=的定义域是 ( ) .A 1x < .B ()3,1- .C {}{}131x x x

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