南昌大学03—04学年第二学期高等数学试题C02.docVIP

南昌大学2003~2004学年第二学期高等数学（双语）A卷期末考试答案 一、 0 14 0 二、 Solution 2. Solution and . Since the line is perpendicular to and . is parallel to the line. Thus, the parametric equations of the line is , , and . 3. Solution 4. Solution Since and is a convergent series, is also convergent. 5. Solution Since , 三、 1. Solution Thus, the series converges if , that is, if ; it diverges if . At , and converges by the Alternation Series Test. At , and is divergent. Therefore, the convergence set is . 2. Solution Let and . Then , , and . We want to solve the Lagrange equations: for and . This is equivalent to findint the solutions of the following five equations in the variables , and . (1) (2) (3) (4) (5) From (1), ; from (2) ; from (3) .Thus, from (4) , which implies that . The solution yield the critical point , and yields the critical point . 3. Solution Suppose the density . Then By symmestry, . 4. Solution 5. Solution Let and are solutions of and . Then and So