高等数学 英文试题A

西南大学课程考核

《高等数学IA 》课程试题 【A 】卷

(1) The function 4

14

)(-=

x x f at x = 4 is ( ). A. not continuous, f (4) does not exist and )(lim 4

x f x → does not exist. B. continuous.

C. not continuous, )(lim 4

x f x → exists but f (4) does not exist

D. not continuous, )(lim 4

x f x → and f (4) exist but )4()(lim 4

f x f x ≠→.

(2) For the function y = arcsin x , we have the assert ( ).

A ．'

y is undefined at x = -1 and x = 1, so its graph has not tangent lines at ⎪⎭⎫

⎝⎛2π,

1 and ⎪⎭⎫ ⎝

⎛

--2π,1.

B ．since its graph has not tangent lines at ⎪⎭⎫ ⎝⎛2π,

1 and ⎪⎭⎫ ⎝

⎛

--2π,1,'y is undefined at x = -1 and x = 1.

C ．'

y is defined at x = -1 and x = 1, and its graph has tangent lines at ⎪⎭⎫ ⎝⎛2π,

1 and ⎪⎭⎫ ⎝⎛

--2π,1.

D ．'

y is undefined at x = -1 and x = 1, and its graph has tangent lines at ⎪⎭⎫ ⎝⎛2π,

1 and ⎪⎭⎫ ⎝

⎛

--2π,1.

(3)

=⎰x x x d )(ln 1

5( ) .

A. C x x +-

4

)(ln 41 B.

C x +-6)(ln 61

. C. C x +-

4)(ln 41 D. C x x +-6

)

(ln 61

. (4) The definite integral

=+⎰-x x x

d 131

1

32

( ).

A.

334 B. 324. C. 423 D. 4

33 (5) Area of shaded region in the following figure is ( ).

西南大学课程考核(试题【A】卷) ——————————————

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封

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A.

3

32

B.

3

64

. C.

3

128

D. 32

3. Find the solutions for following problems by computing (8 points each，40 points in all)

(1) Find the limit

x

x

x2

ln

lim

+∞

→

(2) Evaluate )0('+f, )0('-f and )0('f for

⎩

⎨

⎧

≥

<

-

=

,

,

)

(

2x

x

x

x

x

f.

Figure 2

《高等数学IA 》课程试题 【A 】卷

(3) Use the implicit differentiation to find x

y d d for the equation xy y x 183

3=+.

(4) Find ⎪⎪⎭

⎫ ⎝⎛⎰2

23d )sin(d d x t t x x .

(5) Find the definite integral x x

d e

1

⎰.

西南大学课程考核(试题【A】卷)

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密————————————

封————————————

线——————————————4. Solve the following comprehensive problems (10 points each，30 points in all) (1) Evaluate the indefinite integral x

x d

ln

⎰.

(2) Sketch the graph of 10

4

)

(3

4+

-

=x

x

x

f usin

g the detailed steps of the graphing procedure.