浙江师范大学《高等数学》(二)期末试卷(A卷)
(2007—2008学年第二学期)
考试形式:闭卷 使用学生:初阳综合理科07级
考试时间:150 分钟 出卷时间:2008年5月25日
说明: 考生应将全部答案都写在答题纸上, 否则作无效处理.
Multiple Choices (2 questions, 5.0 points in total)
[1] (3 points)
If series and are diverse, then which of the following series must be diverse:
(A);(B)
(C) ; (D).

Answer ( )
[2] (2 points)
Assuming that C circles counterclockwisely along x2+y2=R2 for a whole circle,then use Green's formula to calculate,
Answer ( )
Questions and answers (3 questions, 14.0 points in total)
[1] (3 points)
Try to transfer the function into power series with regard to.
[2] (8 points)
If ,then try to calculate the power series of with regard to x, and get the value of .
[3] (3 points)
Is series convergent,is it absolute convergent
Evaluations (12 questions, 77.0 points in total)
[1] (8 points)
Evaluate the curvilinear integral,where L is the positive border of the region rounded by the curve |x|+|y|=1
[2] (5 points)
Transform appropriately,and try to find the general solution of the equation .
[3] (6 points)
Calculate the double integral

Where D is the region rounded by xy=2,y=1+x2 and line x=2.
[4] (9 points)
Calculate , whie L is
[5] (6 points)
Proof (2xcosy-y2sinx)dx+(2ycosx-x2siny)dy is the total differential of a function,and find one of its original function.
[6] (6 points)
Find the solution of the differential solution with regard to the initial conditions given:
[7] (7 points)
Find the general solution to the differential equation .
[8] (6 points)
Suppose L is the arch from through to along ,calculate the curvilinear integral .

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