2065438+03+00 June National Higher Education Self-taught Examination.

Advanced Mathematics (Exercise Book)

Course code: 00023

Candidates are required to scribble the answers to all questions on the answer sheet with pens as required.

Multiple choice problem section

Precautions:

1. Before answering the questions, candidates must fill in their examination course name, name and admission ticket number in the position specified in the answer sheet with a black pen or signature pen.

2. After selecting the answer to each question, black the answer label of the corresponding question on the answer sheet with 2B pencil. If you need to change it, clean it with an eraser, and then choose to apply other answer labels. I can't answer on the test paper.

First, multiple-choice questions (30 small questions in this big question, 65438+ 0 points for each small question, * * * 30 points)

Of the four options listed in each question, only one meets the requirements of the topic. Please select and black the code corresponding to "Answer Sheet". Wrong coating, too much coating or no coating do not score.

1. In the spatial rectangular coordinate system, the symmetry point of the point (-1, 4,2) about the axy coordinate plane is

A.(- 1，4，-2)B.( 1，-4，-2)

C.( 1，4，2)D.(- 1，-4，-2)

2. The point (0,0) is the function z= 1-xy.

A. Minimum point B. Maximum point

C. stagnation point D. discontinuous point

3. Let the integral curve L: x+y = 2 (0 ≤ x ≤ 2), and then integrate the curve with arc length.

A.B.

C.D.2

4. The following equations are differential equations with separable variables.

A.B.

C.D.

5. The following convergent infinite series is

A.B.

C.D.

Non-multiple choice part

Precautions:

Write the answers on the answer sheet with a black pen or signature pen, not on the test paper.

II. Fill in the blanks (5 small questions in this big question, 2 points for each small question, *** 10)

6. Given vector ={3, -5, 1}, ={-2, c, -6}, =0, then the constant c = _ _ _ _ _ _ _

7. Given the function z=ln, then = _ _ _ _ _ _.

8. Let the integration area be x2+y2≤ 1, and 0≤z≤, then the triple integration in cylindrical coordinates is _ _ _ _ _ _ _ _.

9. The general solution of differential equation is _ _ _ _ _ _ _.

10. Given infinite series …, the general term UN = _ _ _ _ _ _

Third, the calculation problem (this big question * * 12 small questions, each small question 5 points, ***60 points)

1 1. Find the plane equation passing through the point P(3,-1, 2) and the x axis.

12. let f be differentiable, z=f(3x+4y, xy2), and find the total differential d z.

13. Find the tangent equation of the curves x = 3cost, y = 3sint and z = 4t at the point corresponding to t=.

14. let the function f(x, y, z)=(x-y)2+(y-z)2+(z-x)2, and find the gradf(x, y, z).

15. Calculate the double integral, in which the integral region D: ≤ 4, x≥0 and y≥0.

16. Calculate the integral of three, where the integral area ω: ≤ 9 and z≥0.

17. Verify that the integral has nothing to do with the path and calculate I=.

18. Find the divergence divA of vector field A=.

19. Find the general solution of differential equation.

20. Find the general solution of differential equation.

2 1. Judge the convergence and divergence of infinite series.

22. It is known that f(x) is a periodic function with a period of 2, and its expression on the table is

Find the coefficient a5 in the Fourier series of f(x).

Four, comprehensive questions (this big question ***3 small questions, each small question 5 points, *** 15 points)

23. Find the extreme value of the function f(x, y)=(x2- 1)(2y-y2).

24. Find the solid volume surrounded by plane x= 1, y=0, y=x, z=0 and paraboloid z=x2+y2.

25. Expand the function into a power series of (x+ 1).