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华东师范大学期中物理试卷

2019-2020年八年级英语期中试卷及答案

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华东师范大学2004数学分析试题

华东师范大学2004数学分析一、（30分）计算题。 1、求 2 1 20)2 (cos lim x x x x -→ 2、若)), sin(arctan 2ln x x e y x +=-求' y . 3、求 ?--dx x xe x 2)1(. 4、求幂级数∑∞ =1 n n nx 的和函数)(x f . 5、 L 为过 ) 0,0(O 和 )0,2 (π A 的曲线 ) 0(sin >=a x a y ,求 ?+++L dy y dx y x . )2()(3 xdx a x da dy x a y cos sin ,sin === 6、求曲面积分??++S zdxdy dydz z x )2(,其中) 10(,22 ≤≤+=z y x z , 取上侧. . 二、（30分）判断题（正确的证明，错误的举出反例） 1、若},,2,1,{ =n x n 是互不相等的非无穷大数列，则} {n x 至少存在一个聚点). ,(0 +∞-∞∈x 2、若)(x f 在),(b a 上连续有界，则)(x f 在),(b a 上一致连续. 3、若 ) (x f , ) (x g 在] 1,0[上可积，则 ∑?=∞→=-n i n dx x g x f n i g n i f n 1 10)()()1()(1lim .

4、若∑∞=1n n a 收敛，则∑∞ =1 2n n a 收敛. 5、若在 2 R 上定义的函数 ) ,(y x f 存在偏导数 ),(y x f x ,) ,(y x f y 且),(y x f x , ) ,(y x f y 在(0,0)上连续，则),(y x f 在 (0,0)上可微. 6、),(y x f 在2 R 上连续,} ) ()(|),{(),(22 2 r y y x x y x y x D r ≤-+-= 若??=>??r D dxdy y x f r y x ,0),(,0),,(0 0 则.),(,0),(2 R y x y x f ∈= 三、（15分）函数)(x f 在).,(+∞-∞上连续，且,)(lim A x f x =∞ → 求证：)(x f 在).,(+∞-∞上有最大值或最小值。四、（15分）求证不等式:]. 1,0[,122∈+≥x x x 五、设) (x f n , ,2,1=n 在],[b a 上连续,且) (x f n 在],[b a 上一致收敛于 ) (x f .若 ] ,[b a x ∈?, )(>x f .求证: , 0,>?δN 使 ],[b a x ∈?, N n >,. )(δ>x f n 六、（15分）设}{n a 满足（1）; ,2,1,1000 ++=≤≤k k n a a n k （2）级数∑∞ =1 n n a 收敛. 求证:0 lim =∞ →n n na . 七、（15分）若函数)(x f 在),1[+∞上一致连续，求证： x x f )(在),1[+∞上有界. 八、（15分）设),,(),,,(),,,(z y x R z y x Q z y x P 在3 R 有连续偏导数，而且对以任意点) ,(00, 0z y x 为中心，以任意正数r 为半径的上半球面, ,)()()(:02202020z z r z z y y x x S r ≥=-+-+-

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④两个数相互比较绝对值大的反而小．其中正确的是（） A ．①② B ．①③ C ．①②③ D ．②③④ 9．一根1米长的绳子，第一次剪去一半，第二次剪去剩下的一半，如此下去，第六次后剩下的绳子长度为（） A ．312?? ???米 B ．512?? ???米 C ．612?? ???米 D ．12 12?? ???米 10．下列说法中，正确的个数是（） ①a -表示负数； ②多项式2223721a b a b ab -+-+的次数是3； ③单项式2 29 xy -的次数为3； ④若x x =-，则0x <； ⑤若()2 3220m n -++=，则3,2m n ==． A ．0 B ．1 C ．2 D ．3 11．下列各数中，最大的数是（） A ．|﹣3| B ．﹣2 C ．0 D ．1 12．“比a 的4倍大3的数”用代数式表示为（） A ．43a + B ．()43a - C ．()43a + D ．43a - 13．若25-m x y 与n x y 是同类项，则m n +的值为 A ．1 B ．2 C ．3 D ．4 14．已知23x y -=-，则()()32526x y x y ---+的值是（） A ．6- B ．12 C ．36- D ．18 15．若代数式()()43235153x m x n x x -++--+不含3x 和2x ，则m.n 值为（） A ．m=-5,n=-1 B ．m=5,n=1 C ．m=-5,n=1 D ．m=5,n=-1 二、填空题

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