高数(上)B-08A - 2007-2008 1 BA 3 15 1 a a lim(1 x 4...

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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) : : 2007-2008 1 等数学 B (上) A 数 理 学 院 全校本、专科 (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 lim(1 ) 4 x x a x  ,则 a 2 .设 ( ) y y x 由方程 2 xy x y 确定,则 0 d x y 3 .函数 ( ) sin x f x x 的间断点是 4 1 2 2 1 ( 4 ) x x dx 5. (1,1,1) A (2,2,1) B (2,1,2) C ,则 Pr j AB AC uuu r uuur 二、选择题:(每小题 3 分,共 15 分) 1 .下列极限存在的是 2 ( 1) .lim x x x A x  0 1 .lim 2 1 x x B 1 0 .lim x x C e 2 1 . lim x x D x  2 .设 ( ) ( ) ( ) f x x a x ,其中 lim ( ) 0, ( ) 2 x a x a ,则 ( ) f a . 2 A . B a . 0 C . D 不存在 3 .设 ( ) f x 0 x 的某邻域内连续,且 (0) 0, f ( ) f x ,则在 0 x 处, ( ) f x . A 不可导 . B 可导且 (0) 0 f . C 取极小值 . D 取极大值 4 .若 ( ) sin f x x ,则 ( ) f x 有一个原函数为 . A cos x x . B sin x x . C cos x x . D sin x x 5 .设 0 1 1 ( ) ( ) 2 2 x f t dt f x ,且 (0) 1, f ( ) f x = 2 . x A e 2 . x B e 1 . 2 x C e 2 1 . 2 x D e 三、 (本大题共 28 分)
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1. 7 分)求极限 2 0 2 0 lim ln(1 2 ) cos x t x x e dt x x x 2. 7 分)设 2 1 ( 1), 0 ( ) sin , 0 x e x f x x a bx x ,试确定 , a b 的值,使 ( ) f x 处处可导, 并求 ( ) f x 3. 7 分)设 1 sin sin cos t u x du u y t t t ,求 dy dx 2 2 d y dx 4. 7 分)求不定积分 2 2 3 1 ( ) 1 9 dx x x x 四、(本大题共 22 分) 1. 8 分)求定积分 6 4 0 (1) sin 2 xdx 2 0
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