高数(上)B-07A - 2006-2007 1 BA 3 15 1 2 lim(1 3x sin...

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课程考试试题 学期 学年 拟题人 : 校对人 : 拟题学院(系) : : 2006-2007 1 等数学 B (上) A 数理学院 孙绍权 全校本、专科 赵立宽 (答案写在答题纸上,写在试题纸上无效) 一、填空题:(每小题 3 分,共 15 分) 1 2 sin 0 lim(1 3 ) x x x 2 .设 ( ) y y x 由方程 2 xy x y 确定,则 dy 3 .已知 2 ( ) f x dx x C ,则 2 (1 ) xf x dx 4 .若 ( ) f t 连续,则 0 ( ) x d xf t dt dx 5 .已知向量 (3, 1, 2), (1,2, 1) a b r r ,单位向量 e 同时垂直于 a b ,则 e = 二、选择题:(每小题 3 分,共 15 分) 1 .当 0 x 时,与 x 等价的无穷小量是( sin ) x A x 2 ) ( 1) B x x ) 1 1 C x x ) D x 2 .设 ( ) f x 是可导函数,则 3 3 0 0 0 ( ) ( ) lim h f x h f x h 等于( ) A 0 ) B 0 3 ( ) f x ) C ' 0 3 ( ) f x ) D 2 0 0 3 ( ) ( ) f x f x 3 .设常数 0 k ,函数 x 0 ( 内零点的个数为( ) 2 A ) 3 B ) 0 C ) 1 D 4 .若 ( ) F x ) ( x f 的一个原函数,则 ( ) xf x dx ) A ( ) ( ) xf x F x C ) B ( ) ( ) xf x F x C ) C ( ) ( ) xf x f x C ) D ( ) ( ) f x F x C 5 .向量 (4, 3,4) a - r 在向量 (2,2,1) b r 上的投影为( ) A 6 ) B 6 41 41 ) C 2 ) D 2 3 三、计算题:(共 50 分)
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1 0 1 1 lim( ) ln(1 ) sin x x x 6 分) 2 .函数 0 ( ) 0 x e x f x a bx x 0 x 处可导,求 , a b 的值 7 分) 3 .求参数方程 2 3 1 x t y t t 所确定的函数 ( ) y y x 的二阶导数 7
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