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专升本《高数》入学试题库

专升本《高数》入学试题库
专升本《高数》入学试题库

1.函数、极限和连续(53题)

函数(8题) 1.1.1函数定义域 1.函数lg

arcsin 23

x x

y x =+-的定义域是( )

。A A. [3,0)(2,3]-; B. [3,3]-; C. [3,0)

(1,3]-; D. [2,0)(1,2)-.

2.如果函数()f x 的定义域是1

[2,]3-,则1()f x

的定义域是( )。D

A. 1[,3]2-

; B. 1

[,0)[3,)2-?+∞; C. 1[,0)(0,3]2-?; D. 1

(,][3,)2

-∞-?+∞.

3. 如果函数()f x 的定义域是[2,2]-,则2(log )f x 的定义域是( )。B A. 1[,0)(0,4]4-

; B. 1[,4]4; C. 1[,0)(0,2]2- ; D. 1

[,2]2

. 4.如果函数()f x 的定义域是[2,2]-,则3(log )f x 的定义域是( ).D

A. 1[,0)(0,3]3-?;

B. 1[,3]3;

C. 1[,0)(0,9]9-? ;

D. 1[,9]9

.

5.如果)(x f 的定义域是[0,1],则(arcsin )f x 的定义域是( )。C

A. [0,1];

B. 1[0,

]2; C. [0,]2

π ; D. [0,]π. 1.1.2函数关系

6.设()()22

2

21,1x f x x x x

??+??==??-,则()f x =( ).A A .

211x x +-; B. 211x x -+; C. 121x x -+; D. 1

21

x x +-. 7.函数331

x

x y =+的反函数y =( )。B

A .3log (

)1x x +; B. 3log ()1x x -; C. 3log ()1x x -; D. 31log ()x x

-.

8.如果2sin (cos )cos 2x

f x x

=,则()f x =( ).C

A .22121x x +-; B. 22121x x -+; C. 22121x x --; D. 2

2121

x x ++.

极限(37题) 1.2.1数列的极限

9.极限123lim ()2

n n n

n →+∞++++-=( ).B

A .1; B. 12; C. 1

3; D. ∞.

10.极限2123lim 2n n

n

→∞++++=( ).A A .14; B. 14-; C. 15; D. 15

-

11.极限11

1lim 1223(1)n n n →∞??

++

+

=

???+?

?

( ).C

A .-1; B. 0; C. 1; D. ∞.

12.极限221111(1)222lim

111

1333n n

n n

→+∞-+++-=++++( ).A A .49; B. 4

9-; C. 94; D. 94

-

1.2.2函数的极限

13.极限lim

x x

→∞=( ).C A .

1

2; B. 1

2

-; C. 1; D. 1-. 14.极限0

x →=( ).A A .

12

; B. 1

2

-; C. 2; D. 2-. 15.极限0

x →=( ).B

A. 32-

; B. 32 ; C. 12- ; D. 12

. 16

.极限1

x →=( ).C

A. -2 ;

B. 0 ;

C. 1 ;

D. 2 .

17

.极限4

x →=( ).B

A .43-

; B. 43; C. 34-; D. 34

. 18

.极限x →∞

= ( ).D

A .∞; B. 2; C. 1; D. 0.

19.极限2256

lim

2

x x x x →-+=- ( ).D A .∞; B. 0; C. 1; D. -1.

20.极限32

21

lim 53

x x x x →-=-+ ( ).A A .73-

; B. 73; C. 13; D. 13

-. 21.极限22

31

lim 254

x x x x →∞-=-+ ( ).C A .∞; B.

23; C. 32; D. 34

. 22.极限sin lim

x x

x

→∞=( ).B

A .1-; B. 0; C. 1; D. 2.

23.极限0

1

lim sin

x x x

→=( ).B A .1-; B. 0; C. 1; D. 2.

24.极限0

2

sin 1lim

x

x t

dt t x →-=?

( ).B

A .

12; B. 12-; C. 13; D. 13

-.

25.若232lim 43

x x x k

x →-+=-,则k =( ).A

A .3-; B. 3; C. 13-

; D. 1

3

. 26.极限2323

lim 31

x x x x →∞++=- ( ).B A .∞; B. 0; C. 1; D. -1.

1.2.3无穷小量与无穷大量

27.当0x →时,2

ln(12)x +与2

x 比较是( )。D

A .较高阶的无穷小; B. 较低阶的无穷小; C. 等价无穷小; D. 同阶无穷小。

28.

1

x

是( ).A A. 0x →时的无穷大; B. 0x →时的无穷小;

C. x →∞时的无穷大;

D. 1001

10

x →时的无穷大.

29.12

x -是( ).D

A. 0x →时的无穷大;

B. 0x →时的无穷小;

C. x →∞时的无穷大;

D. 2x →时的无穷大.

30.当0x →时,若2

kx 与2

sin 3

x 是等价无穷小,则k =( ).C

A .

12; B. 12-; C. 13; D. 13

-. 1.2.4两个重要极限 31.极限1

lim sin

x x x

→∞

=( )

.C A .1-; B. 0; C. 1; D. 2.

32.极限0sin 2lim

x x

x

→=( ).D

A .1-; B. 0; C. 1; D. 2.

33.极限0sin 3lim

4x x

x

→=( ).A

A.

34; B. 1;

C. 4

3; D. ∞. 34.极限0sin 2lim

sin 3x x

x

→=( )

.C A .32; B. 32-; C. 23; D. 23

-. 35.极限0tan lim

x x

x

→=( )

.C A .1-; B. 0; C. 1; D. 2.

36.极限201cos lim

x x

x

→-=( ).A A .

12; B. 12-; C. 13; D. 1

3

-. 37.下列极限计算正确的是( ).D

A. 0

1lim(1)x x e x

→+=; B. 0lim(1)x x x e →+=;

C. 1

lim(1)x

x x e →∞

+=; D. 1lim(1)x

x e x

→∞

+=.

38.极限21lim(1)

x

x x

→∞

-=( )

.B A .2

e ; B. 2e -; C. e ; D. 1e -.

39.极限1lim(1)3x

x x

→∞

-

=( )

.D A .3

e ; B. 3

e -; C. 13

e ; D. 13

e

-

.

40.极限1lim(

)1

x

x x x →∞

+=-( )

.A A .2

e ; B. 2e -; C. e ; D. 1e -.

41.极限2lim(

)2

x

x x x →∞

+=-( ).D A. 4e -; B. 2e -;

C. 1;

D. 4

e . 42.极限5

lim(1)x

x x

→∞

+( ).B

A .5e -; B. 5

e ; C. 15

e ; D. 15

e

-

.

43.极限1

lim(13)x

x x →+( ).A

A .3e ; B. 3

e -; C. 13

e ; D. 13

e

-

.

44.极限5lim(

)1x

x x x

→∞

=+( )

.A A .5e -; B. 5

e ; C. e ; D. 1e -.

45.极限0ln(12)

lim

x x x

→+=( )

.D A .1-; B. 0; C. 1; D. 2.

函数的连续性(8题) 1.3.1函数连续的概念

46.如果函数sin 3(1)

,1()1

4, 1

x x f x x x k x -?≤?

=-??+>?处处连续,则k = ( ).B A .1;B. -1;C. 2;D. -2.

47.如果函数sin (1)

,1()1

arcsin , 1

x x f x x x k x π-?

=-??+≥?处处连续,则k = ( ).D A .2

π

-

;B.

2π;C. 2π-;D. 2

π.

48.如果函数1sin

1,1()2

3,1

x x

x f x e k x π-?+≤?=??+>?处处连续,则k = ( ).A A .-1;B. 1;C. -2;D. 2.

49.如果函数sin 1,12

()5ln ,11

x x f x x k x x π?+≤??=??+>?-?处处连续,则k = ( ).B

A .3;B. -3;C. 2;D. -2.

50.如果函数1 , 02

()ln(1),03x e x f x x k x x

?+≤??=?+?+>??处处连续,则k = ( ).C

A .

67;B. 67-;C. 76;D. 76

-. 51.如果sin 2,0()1,0ln(1),0ax

x x f x x x b x x

?+

==??+?+>?在0=x 处连续,则常数a ,b 分别为( ).D

A .0,1; B. 1,0; C. 0,-1; D. -1,0.

1.3.2函数的间断点及分类 52.设2,0

()2,0x x f x x x -≤?=?

+>?

,则0=x 是)(x f 的( ).D

A. 连续点;

B. 可去间断点;

C. 无穷间断点;

D. 跳跃间断点 .

53.设ln ,0

() 1, 0

x x x f x x >?=?

≤?,则0=x 是)(x f 的( ).B

A. 连续点;

B. 可去间断点;

C. 无穷间断点;

D. 跳跃间断点 .

2.一元函数微分学(39题)

导数与微分(27题) 2.1.1导数的概念及几何意义

54.如果函数)(x f y =在点0x 连续,则在点0x 函数)(x f y =( ).B

A. 一定可导;

B. 不一定可导;

C.一定不可导;

D. 前三种说法都不对.

55.如果函数)(x f y =在点0x 可导,则在点0x 函数)(x f y =( ).C

A. 一定不连续;

B. 不一定连续;

C.一定连续;

D. 前三种说法都不正确.

56.若000

(2)()

lim

1x f x x f x x ?→+?-=?,则=')(0x f ( )

.A A .

12; B. 1

2

-; C. 2; D. 2-. 57.如果2

(2)3

f '=,则0(23)(2)lim x f x f x →--=( )

.B A. -3 ; B. -2 ; C. 2 ; D. 3 .

58.如果(2)3f '=,则0

(2)(2)

lim

x f x f x x

→+--=( )。D

A. -6 ;

B. -3 ;

C. 3 ;

D. 6 . 59.如果函数)(x f 在0x =可导,且(0)2f '=,则0

(2)(0)

lim

x f x f x

→--=( )

.C A .-2; B. 2; C. -4; D. 4.

60.如果(6)10f '=,则0

(6)(6)

lim

5x f f x x

→--=( ).B

A. -2 ;

B. 2 ;

C. -10 ;

D. 10 .

61.如果(3)6f '=,则0

(3)(3)

lim

2x f x f x

→--=( ).B

A. -6 ;

B. -3 ;

C. 3 ;

D. 6 .

62.曲线3

1y x x =-+在点(1,1)处的切线方程为( ).C

A. 210x y ++=;

B. 210x y -+=;

C. 210x y --=;

D. 210x y +-=.

63.曲线21y x =

在点1

(2,)4

处的切线方程为( ).A A. 1144y x =-+; B. 11

44y x =-;

C. 1144y x =--;

D. 11

44y x =+.

64.曲线1y x =在点1

(3,)3

处的切线方程为( ).B

A. 1293y x =--;

B. 12

93y x =-+;

C. 1293y x =-;

D. 1293

y x =+.

65.过曲线2

2y x x =+-上的一点M 做切线,如果切线与直线41y x =-平行,则切点坐标为( ).C

A. (1,0);

B. (0,1);

C. 37(,)24;

D. 73

(,)42.

2.1.2函数的求导 66.如果sin 1cos x x

y x

=

+,则y '= ( ).B

A.

sin 1cos x x x -+; B. sin 1cos x x x ++; C. sin 1cos x x x -+; D. sin 1cos x x

x

+-.

67.如果x y cos ln =,则y '= ( ).A

A. tan x -;

B. tan x ;

C. cot x -;

D. cot x .

68.如果lnsin y x =,则y '= ( ).D

A. tan x -;

B. tan x ;

C. cot x -;

D. cot x .

69.如果1arctan 1x

y x

-=+,则y '= ( ).A

A. 211x -

+; B. 211x +;

C. 211x --;

D. 2

1

1x -. 70.如果)3sin(2

x y =,则y '= ( ).C

A. 2

cos(3)x ; B. 2

cos(3)x -;

C. 2

6cos(3)x x ; D. 2

6cos(3)x x -.

71.如果

(ln )d

f x x dx

=,则()f x '= ( ).D A. 2

x -; B. 2

x ;

C. 2x

e

-; D. 2x

e .

72.如果y

x

xy e e +=,则y '= ( ).D

A. y x e x e y +-;

B. y x e x e y -+;

C. x y e y e x +-;

D. x y e y e x

-+.

73.如果arctan

y

x

=,则y '= ( ).A A.

x y x y +-; B. x y x y -+; C. y x y x +-; D. y x

y x

-+. 74.如果y x x x

=+?? ?

?

?

1sin ,则y '= ( ). B

A. sin cos ln()1(1)x x x x x x +++;

B. sin sin [cos ln()]1(1)1x

x x x x x x x x ??+ ?+++??

C. sin sin [ln()]1(1)1x

x x x x x x x ??

+ ?

+++??

; D. sin 1[cos ln()]111x

x x x x x x ??

+ ?

+++??

.

75.如果y x x x =--arccos 12,则y ''= ( ).A

A.

B.

C. ;

D.

2.1.3微分

76.如果函数)(x f y =在点0x 处可微,则下列结论中正确的是( ).C

A. )(x f y =在点0x 处没有定义;

B. )(x f y =在点0x 处不连续;

C. 极限0

0lim ()()x x f x f x →=; D. )(x f y =在点0x 处不可导.

77.如果函数)(x f y =在点0x 处可微,则下列结论中不正确的是( ).A

A. 极限0

lim ()x x f x →不存在 . B. )(x f y =在点0x 处连续;

C. )(x f y =在点0x 处可导;

D. )(x f y =在点0x 处有定义.

78.如果2

ln(sin )y x =,则dy = ( ).C

A. 2tan xdx ;

B. tan xdx ;

C. 2cot xdx ;

D. cot xdx .

79.如果ln 50y

xe y -+=,则dy = ( ).B

A. 1y y ye dx xye -;

B. 1y y ye dx xye --;

C. 1y y ye dx xye +;

D. 1y

y

ye dx xye -+. 80.如果x

y x =,则dy = ( ). A

A. (ln 1)x

x x dx -; B. (ln 1)x

x x dx +; C. (ln 1)x dx -; D. (ln 1)x dx +.

导数的应用(12题) 2.2.1罗必塔法则

81.极限2

ln()

2lim tan x x x ππ

+

-= ( ).C A .1; B. -1; C. 0; D. ∞.

82.极限3

0lim

sin x x x x

→=- ( ).A A .6; B. -6; C. 0; D. 1.

83.极限1lim (1)x

x x e →+∞

-= ( ).B

A .-2; B. -1; C. 0; D. ∞.

84.极限0

11

lim(

)sin x x x

→-= ( ).C A .-2; B. -1; C. 0; D. ∞.

85.极限sin 0

lim x

x x +

→= ( ).B

A .0; B. 1; C. e ; D. ∞.

86.极限tan 0

lim x

x x +

→= ( ).A

A .1; B. 0; C. e ; D. 1

e -.

87.极限tan 01lim x

x x +→??

= ???

( ).B

A . 0; B. 1; C. e ; D. 1

e -.

2.2.2函数单调性的判定法

88.函数3

2

64y x x =-+的单调增加区间为( ).B

A .(,0]-∞和[4,)+∞; B. (,0)-∞和(4,)+∞; C. (0,4); D. [0,4].

89.函数3

2

31y x x =-+的单调减少区间为( ).C

A .(,0)-∞; B. (4,)+∞; C. )2,0(; D. [0,2].

90.函数y xe

x =-的单调增加区间为( ).A

A .(,1]-∞; B. (,0]-∞; C. [1,)+∞; D. [0,)+∞.

2.2.3函数的极值 91.函数2x

y xe

-=( ).A

A .在12x =

处取得极大值112e -; B. 在12x =处取得极小值1

12

e -; C. 在1x =处取得极大值2

e -; D. 在1x =处取得极小值2

e -.

92.函数3

2

()9153f x x x x =-++( ).B

A .在1x =处取得极小值10,在5x =处取得极大值22-;

B. 在1x =处取得极大值10,在5x =处取得极小值22-;

C. 在1x =处取得极大值22-,在5x =处取得极小值10;

D. 在1x =处取得极小值22-,在5x =处取得极大值10.

3.一元函数积分学(56题)

不定积分(38题)

3.1.1不定积分的概念及基本积分公式

93.如果x x f 2)(=,则)(x f 的一个原函数为( ).A

A. 2

x ; B.

212x ;

C. 2x x +;

D. 21

22x x +. 94.如果x x f sin )(=,则)(x f 的一个原函数为 ( ).C A. cot x -; B. tan x ;

C. cos x -;

D. cos x .

95.如果cos x 是)(x f 在区间I 的一个原函数,则()f x = ( ).B A. sin x ; B. sin x -;

C. sin x C +;

D. sin x C -+.

96.如果()2arctan(2)f x dx x c =+?

,则)(x f =( ).C

A.

2114x +; B. 2214x +; C. 2414x +; D. 2

8

14x +. 97.积分2sin 2x dx =? ( ).D A. 11sin 22x x C -++;B. 11

sin 22x x C --+;

C. 11sin 22x x C ++;

D. 11sin 22x x C -+.

98.积分cos 2cos sin x

dx x x

=-? ( ).A

A. sin cos x x C -+;

B. sin cos x x C -++;

C. sin cos x x C ++;

D. sin cos x x C --+.

99.积分

22cos 2sin cos x

dx x x =? ( ).B

A. cot tan x x C ++;

B. cot tan x x C --+;

C. cot tan x x C -+;

D. cot tan x x C -++.

100.积分2

tan xdx =?

( ).C

A. tan x x C ++;

B. tan x x C --+;

C. tan x x C -+;

D. tan x x C -++.

3.1.2换元积分法

101.如果)(x F 是)(x f 的一个原函数,则

()x x f e e dx --=?

( ).B

A .()x

F e C -+ B .()x

F e C --+ C .()x

F e C + D .()x

F e C -+

102.如果f x e

x

()=-,

(ln )

f x dx x '=?( ).C

A.1c x -+;

B.x c -+;

C.c x

+1

;D.x c +.

103.如果()x

f x e =,(ln )f x dx x

'=?( ).D

A.1c x -+;

B.x c -+;

C.c x

+1

;D.x c +.

104.如果()x

f x e -=,则

(2ln )

2f x dx x

'=?

( ).A

A.

214c x +;B. 2

1

c x

+;C.24x c +;D.2x c +. 105.如果()sin f x x =

'=( ).B

A. 2

x c +;B. x c +;C. sin x c +;D.cos x c +.

106.积分sin 3xdx =?

( ).D

A. 3cos3x C -+;

B.

1cos33x C +;C. cos3x C -+;D. 1

cos33

x C -+. 107.积分1

21x e dx x

=?( ).B

A. 1

x e C +;B. 1x

e C -+;C. 11x e C x +;D. 1

1

x e C x

-+.

108.积分tan xdx =?

( ).A

A. ln cos x C -+;

B. ln cos x C +;

C. ln sin x C -+;

D. ln sin x C +.

109.积分

2dx

x =-? ( ).D

A. 2

(2)x C -+; B. 2

(2)

x C --+;

C. ln 2x C --+;

D. ln 2x C -+.

110.积分

1

1cos dx x =+? ( ).C

A. cot csc x x C -+;

B. cot csc x x C ++;

C. cot csc x x C -++;

D. cot csc x x C --+.

111.积分

?-dx x cos 11

= ( ).D

A. cot csc x x C -+;

B. cot csc x x C ++;

C. cot csc x x C -++;

D. cot csc x x C --+.

112.积分

1

1sin dx x =+? ( ).B

A. tan sec x x C ++;

B. tan sec x x C -+;

C. tan sec x x C -++;

D. tan sec x x C --+.

113.积分

sin 1sin x

dx x =+? ( ).D

A. sec tan x x x c +++;

B. sec tan x x x c +-+;

C. sec tan x x x c --+;

D. sec tan x x x c -++.

114.积分

1

1sin dx x =-? ( ).A

A. tan sec x x C ++;

B. tan sec x x C -+;

C. tan sec x x C -++;

D. tan sec x x C --+.

115.积分

ln dx

x x =? ( ).A

A. ln ln x C +;

B. ln ln x C -+;

C. 2

ln x C +; D. 1

ln x x C --+.

116.积分

dx = ( ).C

A.

arctan C ; B.

C ;

C. 2arctan C ;

D. C .

117.积分1x

x

e dx e

=+? ( ).B A. ln(1)x

e C -++; B. ln(1)x

e C ++;

C. ln(1)x

x e C +++; D. ln(1)x

x e C -++.

118.积分2cos xdx =?

( ).C

A.

11

sin 224

x x C -+; B. 11sin 224x x C -++;

C. 11sin 224x x C ++;

D. 11sin 224

x x C --+.

119.积分3cos xdx =?

( ).A

A. 31sin sin 3x x C -+;

B. 3

1sin sin 3x x C -++;

C. 31sin sin 3x x C ++;

D. 3

1sin sin 3

x x C --+.

120.积分

=( ).A

A. C + ;

B. 2(arctan C + ;

C. C + ;

D. 2(arctan C + .

3.1.3分部积分法 121.如果

sin x

x

是()f x 的一个原函数,则()xf x dx '=?( ).D A. sin cos x x C x ++ ; B. sin cos x

x C x -+ ; C. 2sin cos x x C x +

+ ; D. 2sin cos x

x C x

-+ . 122.如果arccos x 是()f x 的一个原函数,则()xf x dx '=?

( ).B

A.

arcsin x c -+ ; B.

arccos x c -+ ;

C.

arcsin x c ++ ; D. arccos x c + .

123.如果arcsin x 是()f x 的一个原函数,则='?

dx x f x )(( ).A

A.

arcsin x c -+ ; B.

arcsin x c + ;

C.

arcsin x c + ; D. arcsin x c + .

124.如果arctan x 是()f x 的一个原函数,则='?

dx x f x )(( ).B

A. 2arctan 1x x c x +++;

B. 2

arctan 1x

x c x -++ ;

C.

2arctan 1x x c x --++ ; D. 2

arcsin 1x

x c x -+++ .

125.如果()ln 3

x

f x =,(3)x x

f e dx e -'=?( ).C A. 3x C + ; B. 3x C -+ ;

C.

13x C + ; D. 1

3

x C -+ . 126.积分x xe dx =?

( ).B

A. x x xe e C -++ ;

B. x x

xe e C -+ ; C. x

x

xe e C --+ ; D. x

x

xe e C ++ .

3.1.4简单有理函数的积分 127.积分

221

(1)dx x x =+? ( ).C

A. 1arctan x C x -++ ;

B. 1

arctan x C x

-+ ; C. 1arctan x C x -

-+ ; D. 1

arctan x C x

++ . 128.积分4

2

1x dx x

=+?( ).A A. 31arctan 3x x x C -++ ; B. 31

arctan 3

x x x C +++ ; C.

31arctan 3x x x C --+ ; D. 31

arctan 3

x x x C +-+ . 129.积分2

1

25

dx x x =++?( ).B A. 1arctan

2x C ++ ; B. 11

arctan 22

x C ++ ; C. arctan(1)x C ++ ; D.

1

arctan(1)2

x C ++ .

130.积分

21

23dx x x =+-?( ).D

A.

11ln 43x C x ++- ; B. 13ln 41x C x -++ ; C.

13ln 41x C x ++- ; D. 11ln 43

x C x -++ . 定积分(18题) 3.2.1定积分的概念及性质 131.变上限积分

?

x

a

dt t f )(是( ).C

A. ()f x '的所有原函数;

B. ()f x '的一个原函数;

C. ()f x 的一个原函数;

D. ()f x 的所有原函数 .

132.如果0

()sin(2)x

x t dt Φ=

?

,则()x 'Φ=( ).C

A. cos(2)x ;

B. 2cos(2)x ;

C. sin(2)x ;

D. 2sin(2)x .

133.如果()x Φ=

,则()x 'Φ=( ).D

A.

B.

;C. ;D. . 134.设()sin x

a

F x tdt =

?

,则()F x '=( ).B

A. sin t ;

B. sin x ;

C. cos t ;

D. cos x .

135.如果

()ln cos x

f t dt x =?

,则()f x '=( ).B

A. 2

sec x ;B. 2

sec x -;C. 2

csc x ;D. 2

csc x -.

136.如果

30

()sin x

f t dt x x =+?

,则()f x '=( ).A

A. sin 6x x -+;

B. sin 6x x +;

C. 2

cos 3x x +;D. 2

cos 3x x -+.

137.积分

1

2

1

dx x

--=?

( ).B A. ln 2 ; B. ln 2- ;C. ln 3 ; D. ln 3- .

138.下列定积分为零的是( ).C

A .

1

2

1

cos x xdx -?

B .11

sin x xdx -? C .11

(sin )x x dx -+? D .1

1

(cos )x x dx -+?

139.若)(x f 在],[a a -上连续,则

[()()]cos a

a

f x f x xdx ---=?

( ).A

A. 0 ;

B. 1 ;

C. 2 ;

D. 3 .

140.下列定积分为零的是( ).C

A .

1

2

1

cos x xdx -?

B .11

sin x xdx -? C .11

(sin )x x dx -+? D .1

1

(cos )x x dx -+?

141.如果)(x f 在],[a a -上连续,则

[()()]cos a

a

f x f x xdx ---=?

( ).D

A.

2

π

;B. 2()f a ;C. 2()cos f a a ;D. 0. 3.2.2定积分的计算

142.积分

211

1dx x -=+( ).D A. 12π;B. 6π;C. 3

π;D. 712π. 143.积分

cos x xdx π

=?

( ).A

A. -2;

B. 2;

C. -1;

D. 0.

144.积分

9

1

dx =?

( ).B

A. 2ln2- ;

B. 2ln 2 ;

C. ln 2- ;

D. ln 2 .

145.积分

01

x x dx e e -=+?( ).D

A. 3π ;

B. 4π ;

C. 6

π

; D. 12π .

146.积分

1

=?

( ).C

A.

; B. ;C.

; D. .

3.2.3无穷区间的广义积分

147.如果广义积分

20

110

k dx x π

+∞

=+?

,则k =( ).C A.

13;B. 14;C. 15;D. 1

6

.

148.广义积分

20

x xe dx +∞

-=?

( ).B

A.

13;B. 14;C. 15;D. 16

. 4.多元函数微分学(20题)

偏导数与全微分(18题) 4.1.1多元函数的概念

149.函数22

arcsin 4x y z +=( ).C A. 2

2

{(,)14}x y x y ≤+≤;B. 2

2

{(,)4}x y x y +≤; C. 2

2

{(,)14}x y x y <+≤;D. 2

2

{(,)1}x y x y +>.

150.如果(,)()y

f x y x y x x

+=+,则(,)f x y =( ).D

A. 2

1y

x +;B. 21y x +;C. 21x y +;D. 21x y +.

151.如果2

2

(,)f x y xy x y +=+,则(,)f x y =( ).A

A. 2

2x y -;B. 2

2x y +;C. 2

2y x -;D. 2

2y x +.

4.1.2偏导数与全微分

152.如果z =,则

2z

x y

?=??( ).A A. 2222()xy x y -+; B. 222

2()xy

x y +; C. 22222()y x x y -+; D. 22222()x y x y -+ .

153.设arctan y

z x

=,则

2z x y ?=??( ).C A. 2222()xy x y -+; B. 222

2()

xy

x y +; C. 22222()y x x y -+; D. 22222()x y x y -+ . 154.设22

,

y f x y y x x ?

?+=- ???,则(,)f x y x

?=?( ).A

A.

2(1)1x y y -+; B. 2(1)1x y y +-; C. 2(1)1y x x -+; D. 2(1)

1y x x

+- .

155.如果y

x z =,则2z

x y

?=??( ).A A. 1

(1ln )y x y x -+; B. 1(1ln )y x y x --; C. 1

(1ln )y x

x y -+; D. 1(1ln )y x x y -- .

156.如果arctan

x

z y

=,则dz =( ).D A.

2222x y dx dy x y x y -+++; B. 2222

x y

dx dy x y x y -+++; C.

2222y x dx dy x y x y -+++; D.

2222

y x

dx dy x y x y -+++ . 157.如果arctan

y

z x

=,则dz =( ).C A.

2222x y dx dy x y x y -+++; B. 2222

x y

dx dy x y x y -+++; C.

2222y x dx dy x y x y -+++; D.

2222

y x

dx dy x y x y -+++ . 158.如果2

ln(2)z x y =+,则dz =( ).C

A. 222222x dz dx dy x y x y =

+++; B.

2222

22x dz dx dy x y x y =+++; C. 22

2222y dz dx dy x y x y

=

+++; D. 2222

22y dz dx dy x y x y =+++ . 159.如果y

x z =,则dz =( ).B

A. 1

ln y

y x xdx yx dy -+; B. 1ln y y yx dx x xdy -+;

C. 1y y yx

dx x dy -+; D. 1y y x dx yx dy -+ .

160.如果x

z y =,则dz =( ).A

A. 1

ln x x xy

dx y ydy -+; B. 1ln x x y ydx xy dy -+;

2016年专升本试卷真题及答案(数学)

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