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第一套数学试题

第一套数学试题
第一套数学试题

第一套 数学试题

一、选择题(本大题满分72分,共8小题,每小题9分,每题都给出四个结论,其中只有一个结论是正确的)

1.x

x

x x e sin 1023lim ???

?

?

?+-→等于( ) A .1

B .e

C .0

D .1-e

2.设)1(sin 22+=x y ,则y '等于(

) A .x 2

B .)1sin(22+x

C .)1(2sin 22+x x

D .)1cos(22+x 3.设???<≥=00,

)(2

x x

x x x f 则)0(f '( ) A .等于0

B .等于1

C .不存在

D .等于-1

4.?xdx x cos 等于(

) A .x x sin

B .x cos

C .x x x cos sin +

D .c x x ++cos sin

5.dx e x x 2

32ln 0

?

等于(

A .2

12ln -

B .2

1-

C .2ln

D .2ln

6.

?dt e dx d t x 2

21

等于( )

A .2

x e

B .4

2x xe

C .4

x e

D .12-x

7.?

∞+- 2

32dx x 等于(

A .

4

1 B .1

C .4

D .0

8.曲线2sin 2x x y +=上横坐标为0=x 的点处的法线方程为(

A .0=-y x

B .02=+y x

C .02=-y x

D .02=+y x

二、解答题(本大题满分28分,每小题14分) 9.求函数322)1()5(+?-=x x y 的极大值。

10.求抛物线342-+-=x x y 及其在点(0,-3)和(3,0)处的切线所围成的图形的面积。

第一套 答案

一、

1.(D ) 2.(C ) 3.(C ) 4.(D ) 5.(A ) 6.(B ) 7.(A ) 8.(D ) 二、 9.3

1

·3)5)(12(4+--=

'x x x y 驻点21

1=x ,52=x ,导数不存在点13-=x x

(-∞,-1)

-1 ??? ??

-21,1

21

??

? ??5,21 5 (5,+∞) y '

不存在

+ 0 -

+

y

3

188

81

极大值为3188

81

21=??? ??y

10.两条切线分别为34-=x y ,62+-=x y ,其交点为??

?

??3,23,所求面积为

[

]

[]

4

9 )34(62 )34(343

2

3 223

0 2

=

-+--+-+-+---=??dx x x x dx x x x A

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————————————————————————————————作者:————————————————————————————————日期: 2

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