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Who has the answer to the urgent question of self-taught advanced mathematics (exercise book)? Please help us 1 1. Let the generalized integral converge, and then
a . q = 1b . q & lt； 1
c . q≥ 1d . q & gt； 1
12. The included angle between plane x-y- 1 1=0 and plane 3x+8=0 is
13. The equation z=x2+y2 is represented by a graph in a spatial rectangular coordinate system.
A. paraboloid of revolution B. Upper hemisphere
C. Cylindrical surface D. Conical surface
14. restrictions
A. equals 0b. Equal to 1.
C equals-1d. It doesn't exist.
15. known function z = xy(x >；; 0), then =
A.yxyB.y(y- 1)xy-2
xy- 1(ylnx+ 1)d . xy- 1(ylnx- 1)
16. let c be an ellipse: x=acost, y=bsint(0≤t≤2π), then the line integral.
A.0B.2π
2πab
17. Which of the following functions is not the solution of the differential equation y÷-4y '+3y = 0?
e2x
C.e3xD.ex+ 1
18. The general solution of differential equation xy "= y' is
A.y=C 1x+C2B.y=x2+C
C.y=C 1x2+C2D.y=
19. Among the following infinite series, the absolutely convergent infinite series is
20. When | x |
Second, fill in the blanks
Please fill in the correct answers in the blanks of each question. You don't score if you fill it wrong or not.
The domain of 2 1. function f(x, y)= is _ _ _ _.
22. Limit = _ _ _ _.
23. Let the function y=cos2x, then _ _ _ _.
24. Set indefinite integral, then f (x) = _ _ _ _.
25. Definite integral _ _ _ _.
26. The equation of a straight line passing through this point and perpendicular to the yoz coordinate plane is _ _ _ _ _ _.
27. Let the function z=e, then the total differential Dz = _ _ _ _ _.
28. After accumulating points, redeem points in the order of _ _ _ _ _.
29. Let the integral area b: x2+y2 ≤ 1, then the double integral = _ _ _ _ _.
30. The differential equation y "= x satisfies the condition y'(0)= y(0)= 0, and the special solution is _ _ _ _ _.
Third, the calculation problem
3 1. Find the limit
32. Let the equation ex+y-3x+2y2-5=0 determine the function y=y(x), and find
33. The known parameter equation determines the function y=y(x), and finds
34. Calculate definite integral
35. Expand the function f(x)=ln(x2+ 1) into a power series of X. 。
Fourth, the application and proof problems
It is proved that the equation 5×4+4x-2=0 has at least one real root between 0 and 1.
37. Prove inequality 38. Find the volume of the rotating body formed by the plane figure surrounded by parabola y=x2, straight line x=2 and X axis rotating once around X axis.
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