高数(下)综合练习题

1、肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀

2、袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇

3、聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁

4、羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅

5、螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀

6、羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄

7、袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈

8、肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅

9、羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿

10、螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄

11、羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈

12、袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂

13、肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆

14、袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁

15、膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈

16、羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂

17、螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆

18、肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁

19、袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅

20、膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿

21、羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆

22、蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀

23、肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅

24、袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿

25、膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃

26、罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇

27、螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂

28、肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿

29、袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃

30、肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇

31、罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁

32、螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆

33、肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀

34、袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇

35、聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁

36、羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅

37、螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀

38、羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄

39、袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈

40、肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅

41、羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿

42、螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄

43、羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈

44、袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁蒆螄羆莀蕿薆袂荿芈螂螈莈蒁薅膇莇薃袀肃莆蚅蚃罿莆莅衿袅羂蒇蚁螁肁薀袇聿肀艿蚀羅聿莂袅羁聿薄蚈袇肈蚆薁膆肇莆螆肂肆蒈蕿羈肅薀螅袄膄芀薇螀膃莂螃肈膃蒅薆肄膂蚇螁羀膁莇蚄袆膀葿衿螂腿薁蚂肁膈芁袈羇芈莃蚁袃芇蒆袆蝿芆薈虿膇芅莈蒂肃芄蒀螇罿芃薂薀袅节节螅螁节莄薈肀莁 软件学院高数(下)综合练习题参考答案周世国：软件学院高等数学（下）综合练习参考答案高等数学(下)综合练习(一)一、计算下列各题：(每小题5分,共30分)1.设z求xzxyzy.

45、解：z11xxy.xyxxy.12x；由轮换对称性知：z11yxy.2y.所以xzz11x yy2xy.xyxy112xy.xy12.2.设由方程 xzlnzy 可以确定函数zz(x,解一：（公式法）（这里x,y,z令Fx,y,zxzlnzyxzlnzlny.则，F111xz,Fyy,z.故有1 zFyz；zyz2,zxzyFzx1xyyzz2zz2z所以 dzzxzdxz2xyyzdy.解二：（一）方程两边同时关于x求导（视z为zzx,y，并视y常数），有：11zzx11z1xz1z2.xzy.xzz2.xz，y1周世国：软件学院高等数学（下）综合练习参考答案 故zz； 1xxxz2zz1（

46、二）方程两边同时关于x求导（视z为zzx,y，并视y常数），有：x1z2.zy1z1y2.z1z1xz1y.yzz2.yy，y故有1zyx1z2.zxyzxyz2所以 dzzxzdxz2xyyzdy.解三：方程两边取全微分，得：dxzzdlny111zzdxxz2dzzy2dyy1zxz2dz1所以，dzydxzdxz2dy.1xxzxyyzzz23. (yx,x2y2),其中f(u,v)可微, 求zzx,y.解：zyxfxfx2y2y12x f12xxf2.2x；zyfyxf2.y12x2yy f1f2.2y.yx； 2周世国：软件学院高等数学（下）综合练习参考答案4. 求曲面zx2y21在

47、点2,1,4 处的切平面与法线方程.解：设 Fx,y,zx2y2z1，.则，FxM0,FyM0,FzM02x,2y,1|2,1,44,2,1.所以，切平面的方程为：4x22y1z40切平面的法线方程为：x2y412z41.n!sin5. 判定级数 n12n 的敛散性.解： 记un因为n n6. 求函数z解：（一）解方程组fxx,y3x23yx0,x1,fy2yx33x0.y0.或者y1.P10,0,P21,1.Afxxx,y6x,Bfxyx,y3,Cfyyx,y6y.（1）.在P10,0处，因为A0,B3,C0,ACB290, ，所以P10,0非极值点.（2）.在P21,1.处，因为A60,B

48、3,C6,ACB2270, 故f1,12为极小值.二、计算下列积分：(每题10分,共70分)3周世国：软件学院高等数学（下）综合练习参考答案 1.Ix2y2,其中D是由直线y1,x2及yx所围成的闭区域. D解：I22x122x3x21xdx1y2dy1x21xy|1dx1x2xdx232|516.2.I(x2y2)dv,其中为曲面zx2y2与平面z4所围成的闭区域.解：本题宜采用“切片法”计算x2y2dxdydz4dzx20y2dxdy Dz4dz2dzr2.4r4z3000rdr2040dz43223|03.如采用柱面坐标系：x2y2dxdydz2d2422300rdrr0r.4r2dr2

49、4.r44r66|2rdz23.IxyL3，其中L为圆周x2y2x2y2解：IxyLx2y2xy3L1yds000. 4. Ilx2ydxx2dy,其中l为圆周x上由点(0,0)到(0,2)的一段弧.解一：l可化为x2yx0. l:xcost,y1sint,t:22.ldxxy2dy22cost1sintsintcost1sint2.costdt 22cos2t.sintsint2sint.costdt2sin2tcos2tcostsin2tcostdt22 0220cos2tcostsin2tcostdt212sin2tsint1383sint203.4周世国：软件学院高等数学（下）综合练习

50、参考答案 解二：记A0,2，记D为l所围成的区域.由格林公式，得：xy2x2y IAOxyD又AOdxdy11dxdy0. Dx208ydxxy2dy0y2dy，故： 2388 I0. 33xy2x2y解三：由于1，故Ix2ydxxy2dy与路径无关， lxyIx2ydxxy2dylOA280y2dy. 035.Iz2dS,其中为锥面zz1解：由:zx2y2,zzdSyx222dxdy. dxdy故222zdS2xydxdyDxy6. I(8y1)xdydz2(14yzdxdy,其中为半球面z.解：若取10（下侧）.则与1一起构成一个封闭曲面.记它们所围成的半球型闭区域为.在8y1x21y24

51、yzdxdyd zxyz18y14y4ydxdydz21dxdydz. 3所以，2220dxdy. 313Dxy35周世国：软件学院高等数学（下）综合练习参考答案8. 求函数f(x,y)x212xyy2在闭区域4x2y225上的最大值与最小值.解：（一） （1）上，问题转化为求f(x,y)x212xyy2 （2）在条件4x2y2250下的极值.5由（*）式，可设xcos,0,22y5sin,代入（2）得：2f52cos12.52cos.5sinin2 254cos275.sin225sin2 251cos24.275.sin25.1cos22 1258758cos275sin212582.75

52、865cos2. (tan18)所以f(x,yy2 在边界上的最大值是125875865；最小值是125875865.f0,00与125875865及125875865知f(x,y)x212xyy2在闭区域4x2y225上的最大值与最小值分别125875865和125875865.9求nxn的和函数,并求级数nn1n12n的和.解：（一）记 ann.n1,2,6周世国：软件学院高等数学（下）综合练习参考答案 因为liman1nalimn1nnn1,所以，R1.又在端点x11nn发散； 在端点x11n也发散. nn1总之，nxn的收敛区间为1,1.n1（二）设sxnxnxn1xgx，x1,1.n

53、1nxn1其中 gxnxn1n1对gx积分，有：xxn10gxdxnxdxxn10 xn1x. n1故 gxx11x1x2.所以 sxxgxx1x. （三）ns1n12n22.10. 把函数13x2展成. 解：1113x2x288.138x218.1n3x2n1.n3nnn0881n08n1x2,另由 138x21收敛域为23x143. 7周世国：软件学院高等数学（下）综合练习参考答案 高等数学(下)综合练习(二)一.计算下列各题1. 设zx3y23xy3lnx, 求2z2x2zy2; 解：z3x2y23y31zxx；y2yx39xy2.2zx26xy212zx2； y22x318xy.所以

54、2z2z1x2y26xy23x22x18xy.2. 设zf(x,x2y,yx),其中f可微,求dz解：dzf.dx2yfy1dxf23.dxff11dx2.d2xydxx2dyf3.xdyf2xyf112x2f2xf3dy.3. 设ez可以确定函数zz(x,y),求zx,zy.dezdxyz1ezdzyzdxxzdyxyd z所以ezxydzyzdxxzdydzyzezxydxxzezxydy.从而 zxyzzxzezxy；yezxy.8周世国：软件学院高等数学（下）综合练习参考答案514. 求曲面x22y2z2在点(1,1)处的切平面与法线方程. 225解：设 Fx,y,zx22y2z2.

55、21,1,1. 则 nFxM0,FyM0,FzM02x,4y,2z|12,2,2|1,121所以，切平面的方程为： x1yz10； 21x1z1. 切平面的法线方程为： 111y5. 求f(x,y)x3y39xy27的极值.解：（一）解方程组2fxx,y3x9y0, 2fyx,y3y9x0.x0,x3,或者 y0.y3.得两个驻点：P. 10,0,P23,3x,y6x,Bfxyx,y9x,y6y. （二）Afxx（1）.在P10,0处，因为A0,B9,C0,B2810, ，所以P10,0非极值点.（2）.在P23,3.处，因为A180,B,C18,ACB23240, 故f3,30为极小值.6.

56、求函数fx,y,z8x16z600在椭球面4x2y24z216上的最大值.解：所求最值问题即为求fx,y,z在条件4x2y24z2160下的极值.令Lx,y,z,x24yz16z6004x2y24z216Lx,y,z,的驻点，即LxLy 求解方程组LzLx0,x0,16x8x0,y5,y5,4z2y0,z,，z,4y168z0,24x2y2250.55x0,x0,y5,y5,335 z,z,22335.55故得到四个可能的条件极值点：9周世国：软件学院高等数学（下）综合练习参考答案 P,510,52，P20,5,2，P3350,5,，P3.240,5,2因为fP16002;fP260025;f

57、P3600;fP46005.故fx,y,z在椭球面4x2y24z216上的最大值为600.二.计算下列积分1. 计算5dy511yylnxdx;解：交换积分次序，得I511lnxdxx11ydy511lnxlny|x5151dx1lnx.lnxdxx|14. 2.1d，其中DDx2y2解：1Dx2y22d0 110r2.d1r223.x2yd其中D由x轴，xD解： x2ydxdy12xDxdx001020202204.4. Ilx2y2ds,其中x2y21.解：Il1ds2a.5.z(x2是由曲面zz1围成区域. zxy2dxdydz1zdzx2y2dxdy0Dz12dzr2.rdr2100z

58、r44|z0dzz6110zdz026|012.如采用柱面坐标系：zx2y2dxdydz10周世国：软件学院高等数学（下）综合练习参考答案 2d1rdr1z.r2dz21r30r0.z22|11rdr32r4r62100r1rdr46|012.6. x2l2ydx3xydy,其中l为圆周y(0,0)到(2,0)的一段.解一：l可化为x12y21,y0.其的参数方程为：l:x1cost,ysint,t:0.2lx2ydx3xydy01cost22sintsint31costsint.costdt0sintcost.sintcos2t.sint3costdt02sin2t3cos2tdtcots1

59、2co2st13co3st001cos2t|2.23 830125815082cos2tdt32t4sin2t|2解二：记A2,0，记D为lI3xyAODxy32dxdy1D2.又AOx22ydx3x82dy3，故： I2837.x2y2z29被平面z1截出的部分的顶部. ，则x，zyx2y2y9x2y2所以，22dSzz3xydxdy9x2y2dxd. y因此 I1z1.3Dxy9x2y29x2y2xd y11周世国：软件学院高等数学（下）综合练习参考答案3d 222 1rdr3ln9r229r|2|06ln3.12xy2介于z0,z2之间部分8. 求Ixz2dydzzdxdy.其中为旋转抛

60、物面:z2的下侧.解法一：（直接计算）（一）.将分成12.其中21的方程为x2zy，取前侧；2的方程为x2zy2，取后侧.2y2,1,2在yoz平面上的投影区域均为Dyz:12y2z2.，所以xz2dydz2zy2z2dyd；z1Dyz xz2dydz2zy2z2dyd. z2Dyz所以xz2dydz22zy2dyd zDyz22dy2121y22zy22zy2d2zy222 222z2322323224ydy（令y2sint） 3ost.2cotsdt642co4stdt 3034!24. （二）:2y2（下侧）在xoy平面上的投影区域为Dxy:x2y24. 1x2212d2r2.rdr4.