高数(上)A-09B - 2008-2009 1 AB 3 15 1 lim n 2 n 1 2n...

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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) : : 2008-2009 1 等数学 A (上) B 数理学院 赵立宽 全校相关本科各专业 孙绍权 (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 、极限 n n n 2 n ) 1 ( lim ___________ . 2 、设函数 ( ) y y x 由方程 5 2 ln 2 y x xy 确定,且当 1 x 时, 1 y ,则 ) 1 ( y 3 、已知 C x dx x f cos ) ( ,则 dx x xf ) ( 4 2 0 ( ) x d x t dt dx - 5 、曲线 2 3 - x x y 上与直线 1 x y 平行的切线方程为 二、选择题:(每小题 3 分,共 15 分) 1 、当 0 x 时, x x arctan 2 x 是同阶无穷小,则 )。 ) A 1 ) B 2 ) C 3 ) D 4 2 、设 x x y ln ) 1 ( ,则 y  )。 ) A 2 1 x x - ) B 2 1 x x - ) C x x 1 - ) D x x 1 2 - 3 、设函数 ) 4 )( 1 ( ) ( 2 2 - - x x x f ,则 ( ) 0 f x  有( )个实数根。 ) 0 A ) 1 B ) 2 C ) 3 D 4 、定积分 dx x 3 0 1 = )。 ) A 3 8 ) B 3 14 ) C 1 ) D 2 5 、函数 x x x 12 9 2 y 2 3 - 的单调减区间是( )。 ) A [1 3] ) B [1,2] ) C [-1 3] ) D [0 2] 三、计算题:(每小题 7 分,共 28 分)
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1 、求极限 ) 1 ( 1 lim 0 x - - - x x e x x e . 2 , a b 取何值时,函数 0 , 0 , 1 2 ) ( 2 x b ax x x x x f 0 x 处可导,并在 b a , 确定后 求导函数 ( ) f x (注:在 0 x 处用定义求 ) 0 ( f 3 2 3 1 x t y t ,求 dy dx 2
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