# 高等数学下期末试题(七套附答案) - 3 15 1 1 z x...

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3 、 设 2 2 {( , ) 4} D x y x y ，利用极坐标求 2 D x dxdy  4 、 求函数 2 2 ( , ) ( 2 ) x f x y e x y y 的极值 5 、计算曲线积分 2 (2 3sin ) ( ) y L xy x dx x e dy 其中 L 为摆线 sin 1 cos x t t y t 从点 (0,0) O ( ,2) A 的一段弧 6 、求微分方程 x xy y xe  满足 1 1 x y 的特解 . 解答题（共 22 分） 1 、利用高斯公式计算 2 2 xzdydz yzdzdx z dxdy  Ò ，其中 由圆锥面 2 2 z x y 上半球面 2 2 2 z x y 所围成的立体表面的外侧 (10 ) 2 、（ 1 ）判别级数 1 1 1 ( 1) 3 n n n n 的敛散性，若收敛，判别是绝对收敛还是条件收敛；（ 6 2 ）在 ( 1,1) x   求幂级数 1 n n nx 的和函数（ 6 高等数学（下）试卷二 一．填空题（每空 3 分，共 15 分） 1 ）函数 2 2 2 4 ln(1 ) x y z x y 的定义域为 2 ）已知函数 xy z e ，则在 (2,1) 处的全微分 dz 3 ）交换积分次序， ln 1 0 ( , ) e x dx f x y dy 4 ）已知 L 是抛物线 2 y x 上点 (0,0) O 与点 (1,1) B 之间的一段弧，则 L yds 5
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