2010年江苏省普通高校“专转本”统一考试试题高等
数学
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高等数学 试题卷 注意事项： 1．本试卷分为试题卷和答题卡两部分，试题卷共3页，全卷满分150分，考试时间120分钟． 2．必须在答题卡上作答，作答在试卷上无效．作答前务必将自己的姓名和准考证号准确清晰地填写在试题卷和答题卡上的指定位置． 3．本试卷共8页，五大题24小题，满分150分，考试时间120分钟． 一、 单项选择题（本大题共6小题，每小题4分，满分24分.在下列每小题中，选出一个 正确答案，请在答题卡上将所选项的字母标号涂黑） 1．若是1x =函数224()32 x x a f x x x -+=-+的可去间断点，则常数a = ( ) A. 1 B. 2 C. 3 D. 4 2．曲线4 3 2y x x =-的凹凸区间为( ) A. (,0],[1,)-∞+∞ B. [0,1] C. 3(,]2-∞ D. 3[,)2 +∞ 3．若函数)(x f 的一个原函数为sin x x ，则 ()f x dx ''=?( ) A. sin x x C + B. 2cos sin x x x C -+ C. sin cos x x x C -+ D. sin cos x x x C ++ 4．已知函数(,)z z x y =由方程3 3 320z xyz x -+-=所确定，则 10 x y z x ==?=?( ) A. 1- B. 0 C. 1 D. 2 5．二次积分2 21 (,)x dx f x y dy -? ? 交换积分次序后得( ) A. 2 21 (,)y dy f x y dx -? ? B. 1 20 0(,)y dy f x y dx -?? C. 12 02(,)y dy f x y dx -?? D. 2 201 (,)y dy f x y dx -?? 6．下列级数发散的是( ) A. ∑∞ =-1)1(n n n B. 21sin n n n ∞=∑ C. 2111()2 n n n ∞ =+∑ D. 212n n n ∞=∑ 二、填空题（本大题共6小题，每小题4分，共24分） 7．曲线21x y x ?? =- ??? 的水平渐近线的方程为______________________． 8．设函数3 2 ()912f x ax x x =-+在2x =处取得极小值，则()f x 的极大值为__________．
1．关于比特的叙述，错误的是____d______。 A．存储(记忆)1个比特需要使用具有两种稳定状态的器件 B．比特的取值只有“0”和“1” C．比特既可以表示数值、文字、也可以表示图像、声音 D．比特既没有颜色也没有重量，但有大小 2．下列关于信息系统的叙述，错误的是____c______。 A．电话是一种双向的、点对点的、以信息交互为主要目的的系统 B．网络聊天室一种双向的、以信息交互为主要目的的系统 C．广播是一种点到面的、双向信息交互系统 D．因特网是一种跨越全球的多功能信息系统 3．下列关于IC卡的叙述，错误的是_____c_____。 A．IC卡按卡中镶嵌的集成电路芯片不同可分为存储器卡和CPU卡 B．现在许多城市中使用的公交IC卡属于非接触式IC卡 C．只有CPU卡才具有数据加密的能力 D．手机中使用的SIM卡是一种特殊的CPU卡 4．对两个8位二进制数01001101与00101011分别进行算术加、逻辑加运算，其结果用八进制形式表示分别为__________。 A．120、111 B．157、157 C．170、146 D．170、157 5．内存容量是影响PC机性能的要素之一，通常容量越大越好，但其容量受到多种因素的制约。下列因素中，不影响内存容量的因素是__________。 A．CPU数据线的宽度B．主板芯片组的型号 C．主板存储器插座类型与数目D．CPU地址线的宽度 6．下列存储器按读写速度由高到低排列，正确的是__________。 A．RAM、cache、硬盘、光盘B．cache、RAM、硬盘、光盘 C．RAM、硬盘、cache、光盘D．cache、RAM、光盘、硬盘 7．下列因素中，对微型计算机工作影响最小的是__________。 A．磁场B．噪声C．温度D．湿度 8．下列关于CPU的叙述，错位的是__________。 A．CPU中指令计数器的作用是统计已经执行过的指令数目 B．CPU所能执行的全部指令的集合称为该CPU的指令系统 C．CPU中含有若干寄存器 D．时钟频率决定着CPU芯片内部数据传输与操作速度的快慢 9．下列关于USB接口的叙述，错误的是__________。 A．主机可以通过USB接口向外设提供+5V电源 B．USB接口使用6线接线器 C．一个USB接口通过USB集线器可以连接最多127个设备 D．USB接口符合即插即用规范，即不需要关机或者重启计算机，就可以插拔设备 10．I/O操作是算机中最常见的操作之一，下列关于I/O操作的叙述，错误的是__________。A．I/O设备的种类多，性能相差很大，与计算机主机的连接方法也各不相同 B．为了提高系统的效率，I/O操作与CPU的数据处理操作通常是并行进行的 C．I/O设备的操作由I/O控制器负责完成的
江苏省2012 年普通高校专转本统一英 语考试 第一卷（共100 分） Part I Reading Comprehension(共20 题，每题 2 分，共40 分) Passage One Questions 1 to 5 are based on the following passage. American researchers have developed a technique that may become an important tool in fighting AIDS. The technique stops the AIDS virus from attacking its target-cells in the body's defense system. When AIDS virus enters the blood, it searches for blood cells called T4 lymphocytes （淋巴细胞）. The virus connects to the outside of T4 lymphocytes, then forces its way inside. There it directs the cells' genetic （基因的）material to produce copies of the AIDS virus. This is how AIDS spreads.Researchers think they may be able to stop AIDS from spreading by preventing virus from connecting to T4 cells. When AIDS virus finds a T4 cell, it actually connects to a part of the cell called CD4 protein.Researchers want to fool the virus by putting copies or clones of the CD4 protein into the blood. This way the AIDS virus will connect to the cloned protein instead of the real ones. Scientists use the genetic engineering methods to make the clones. Normally a CD4 protein remains on the T4 cell at all times. The AIDS virus must go to it.In a new technique, however, the cloned CD4 protein is not connected to a cell. It floats freely, so many more can be put into the blood to keep the AIDS virus away from real CD4 proteins on T4 cells. One report says the AIDS virus connects to the cloned proteins j ust as effectively as to real protein. That report was based on tests with blood cells grown in labs. The technique is just now beginning t o be tested in animals. If successful, it may be tested in humans within a year. 1. The new technique can ________. A. cure AIDS B. kill the AIDS virus C. prevent the AIDS virus from spreading D. produce new medicines for AIDS 2. When the AIDS virus enters the blood, it is reproduced by ________. A. the inside of the virus itself B. any blood cells in the body C. the CD4 protein D. the genetic material of T4 cells 3 The AIDS virus connects to cloned proteins instead of to the real ones because ________. A. the cloned proteins stay on the T4 cells B. the cloned proteins can float freely in the blood C. it connects to cloned proteins more effectively than to the real ones D. the cloned proteins are made by genetic engineering methods 4. Which of the following statements is NOT true? A. The new technique has been tested in labs. B. The new technique is being tested in animals. C. The new technique may be tested in humans. D. The new technique is now under clinical test. 5 Which of the following could be the best title of this passage? A. AIDS---a Fatal Disease. B. A New Technique in fighting AIDS. C. A Report on the Spread of AIDS Virus. D. The Technique of Cloned CD4 Protein. Passage TWO Questions 6 to 10 are based on the following passage. During the early ears of last century, wheat was seen as the very lifeblood of Western Canada.
江苏省2010年普通高校专转本选拔统一考试 数 学 试 题 一、单项选择题（本大题共6小题，每小题4分，满分24分） 1.设当0x →时，函数()sin f x x x =-与()n g x ax =是等价无穷小，则常数,a n 的值为( ) A. 1,36a n == B. 1,33a n == C. 1,412a n == D. 1,46 a n == 2.曲线223456 x x y x x -+=-+的渐近线共有( ) A. 1条 B. 2条 C. 3条 D. 4条 3.设函数22 ()cos t x x e tdt Φ=?，则函数()x Φ的导数()x 'Φ等于( ) A. 222cos x xe x B. 222cos x xe x - C. 2cos x xe x - D. 22cos x e x - 4.下列级数收敛的是( ) A. 11n n n ∞=+∑ B. 21 21n n n n ∞=++∑ C. 1n n ∞= D. 212n n n ∞=∑ 5.二次积分11 01(,)y dy f x y dx +? ?交换积分次序后得( ) A. 1101(,)x dx f x y dy +?? B. 2110(,)x dx f x y dy -?? C. 2111(,)x dx f x y dy -?? D. 2111 (,)x dx f x y dy -?? 6.设3()3f x x x =-，则在区间(0,1)内( ) A. 函数()f x 单调增加且其图形是凹的 B. 函数()f x 单调增加且其图形是凸的 C. 函数()f x 单调减少且其图形是凹的 D. 函数()f x 单调减少且其图形是凸的 二、填空题（本大题共6小题，每小题4分，满分24分） 7. 1lim()1 x x x x →∞+=- 8. 若(0)1f '=，则0()()lim x f x f x x →--= 9. 定积分31 2111x dx x -++?的值为 10. 设(1,2,3),(2,5,)a b k ==，若a 与b 垂直，则常数k = 绝密★启用前
江苏省 2017 年普通高校专转本选拔考试 高数试题卷 一、单项选择题（本大题共 6 小题，没小题 4 分，共 24 分。在下列每小题中选出一个正确答案，请在答题卡上将所选项的字母标号涂黑） 1.设 f (x) 为连续函数，则 f ( x 0 ) 0 是 f (x) 在点 x 0 处取得极值的 ( ) A.充分条件 B.必要条件 C.充分必要条件 D.非充分非必要条件 2.当 x 时，下列无穷小中与 x 等价的是 ( ) A. tan x sin x B. 1 x 1 x C. 1 x 1 D.1 cos x e x 1, x 0 2, x 0 x sin 1 , x 0 3. x 0 为函数 f ( x) = x 的（ ） A.可去间断点 B.跳跃间断点 C.无穷间断点 D.连续点 x 2 6x 8 y 4.曲线 x 2 4x 的渐近线共有（ ） A.1 条 B.2 条 C.3 条 D.4 条 5.设函数 f (x) 在 点 x 0 处可导，则有（ ） f ( x) f ( x) f ' (0) lim f (2x) f (3x) f ' (0) lim x x A. x B. x lim f ( x) f (0) f ' (0) lim f (2x) f ( x) f ' (0) C. x x D. x x
n （ 1） 6.若级数 n-1 n p 条件收敛，则常数 P 的取值范围（ ） A. 1， B. 1， C. 0,1 D. 0,1 二、填空题（本大题共 6 小题，每小题 4 分，共 24 分） lim ( x 1) x a e x dx 7.设 x x ，则常数 a= . 8.设函数 y f (x) 的微分为 dy e 2 x dx ，则 f (x) . 9.设 y f (x) 是由参数方程 x t 3 3t 1 dy (1,1) y 1 sin t 确定的函数 ,则 dx . = 10.设 F(x) cos x 是函数 f (x) 的一个原函数，则 xf ( x)dx . = 11. 设 a 与 b 均为单位向量， a 与 b 的夹角为 3 ，则 a + b = . 12. n x n . 幂级数 n -1 4n 的收敛半径为 三、计算题（本大题共 8 小题，每小题 8 分，共 64 分） x t 2 1) dt lim (e x . 13.求极限 x 0 tan x 2 z 14.设 z z(x, y) 是由方程 z ln z xy 0 确定的二元函数，求 x 2 . x 2 dx x 3 15.求不定积分 .
2006 01-05 BCADB 06-10 CBACA 11-15 ADBCC (非英语类学生必做):16-20 ADDBB (非英语类学生必做) 61-65 BCBDD 66-70 BDCBA 71-75 CBBCA 76-80 BACDB 81、菜园种植者一直认为，许多自家种的蔬菜要比市场上买来的好。 82、菜园不应种的太大，使人无法照料。 83、有许多女秘书能像男人一样做好这项工作。 (非英语类学生必做) 84、在三月的某个时候或四月初第一批生物刚刚形成，但是在此之前海洋中一直没有生命。 85、求职者得学会如何把因特网作为工具使用，而不是仅仅靠它来提交电子简历。 86. It is said that the painting is a masterpiece by Picasso. 87. I remember seeing him on TV before, but I am not sure. 88. Our refrigerator is out order and we must have it repaired. 89. Faced with a complicated situation, he tried to hold back his emotions. 90. I’m looking forward to seeing him again, for it’s ten years to the day since we last met. 书面表达 (共15分) College life is very interesting, exciting and sometimes demanding. Everyday morning, we get up early and go to the playground to do exercises. After that, most of us like to have breakfast in the cafeteria and then go to the classrooms to read our books. At 8:00 a.m. when the bell rings for the first class, we have already sat in the classrooms. Usually, we do not have as many lessons as we had in the senior high school. In the afternoon, we do not have any classes, but we have to spend much more time in the lab in doing various experiments. In the evening, some of us go to reading rooms; some of us go to the labs to continue to do their experiments. We are often kept busy until 11:00 p.m. everybody. College life is also very interesting. In the weekends, we often have parties. We may dance and sing to relax ourselves. We also have some clubs, where we can share our interests with our friends or develop our hobbies. Sometimes, we organize the whole class to go climbing mountains or to have barbecues and sometimes we go to visit some poor areas and help the students there. College life is quite different form that of the senior high school. It is more interesting and challengeable. 2007年 1-5 CBDCC 6-10 BABBA 11-15 ACABD 16-20 DBABD 21-25 BDCDB 26-30 ACBAD 31-35 CDABD 36-40 BABCC 41-45 DDBAB 46-50 DBCDC 51-55 DBCAA 56-60 BCDAB 61-65 CABBD 66-70 ADCAC 71-75 BDACD 76-80 BBADC
2009-2013年江苏专转本英语历年真题 2009年江苏省普通高校“专转本”统一考试试卷大学英语 第Ⅰ卷（共100分） 注意事项： 1．答第Ⅰ卷前，考生务必按规定要求填涂答题卡上的姓名、准考证号等项目。 2．用铅笔把答题卡上相应题号中正确答案的标号涂黑。答案不涂写在答题卡上，成绩无效。 Part Ⅰ Reading Comprehension(共20小题，每小题2分，共40分) Directions: In this part there are four passages. Each passage is followed by four comprehension questions. Read the passage and answer the questions. Then mark your answer on the answer sheet. Passage One Questions 1～5 are besed on the following passage. Young Koreans are beginning to do it alone when it comes to finding a partner, though matchmaking is still the most common way for boys to meet girls. Professional matchmakers can make thousands of American dollars by introducing suitable marriage partners to each other, but partners also play a role in the process during which young Koreans meet. In Confucius Korea, where marriage is regarded as more of a business contract than a sacred thing, the scene of the first meeting is repeated hundreds of times a day in coffee shops in the main hotels around Seoul. The business of continuing the family lineage （血统）and keeping the blooding pure is often too important to be left to romance and chance encounters. Often, the girl will work out a system of secret signals with her mother, from which her parents can tell if she is interested. For example, if the girl orders a coffee it might mean that she wants her parents to leave her alone with the boy, while a milk shows that she wants them to stay. Sometimes the matchmaking is not always so formal, with the introduction being made by friends. But whether through friends or families, there is hardly a Korean man in the country who has not gone through this process --- sometimes six or seven times. 1. The word “matchmaking” in the passage means ____. A. a very formal ritual（仪式）attended by boys and girls B. introducing boys and girls to know each other for the purpose of marriage C. producing matches to make a fire or light a cigarette D. arranging games between men and women 2. The fact that the first meeting is repeated again and again in coffee shops in the main hotels suggests that ____. A. Koreans like drinking coffee in coffee shops very much B. men and women want to meet as many times as possible C. they are busy with communicating with different people D. marriage is seen as a business contract instead of something sacred
2006年江苏省普通高校“专转本”统一考试 高等数学 一、选择题（本大题共6小题，每小题4分，满分24分） 1、若 2 1 ) 2(lim 0=→x x f x ，则 =→)3 (lim x f x x （ ） A 、 2 1 B 、 2 C 、3 D 、 3 1 2 、 函 数 ?????=≠=0 01sin )(2 x x x x x f 在 =x 处 （ ） A 、连续但不可导 B 、连续且可导 C 、不连续也不可导 D 、可导但 不连续 3 、 下 列 函 数 在 [] 1,1-上满足罗尔定理条件的是 （ ） A 、x e y = B 、x y +=1 C 、2 1x y -= D 、x y 1 1- = 4、已知C e dx x f x +=?2)(， 则=-?dx x f )(' （ ） A 、C e x +-22 B 、 C e x +-221 C 、C e x +--22 D 、C e x +--22 1 5、设 ∑∞ =1 n n u 为正项级数，如下说法正确的是 （ ） A 、如果0lim 0 =→n n u ，则∑∞ =1n n u 必收敛 B 、如果l u u n n n =+∞→1 lim )0(∞≤≤l ，则∑∞ =1n n u 必收敛 C 、如果 ∑∞ =1 n n u 收敛，则 ∑∞ =1 2 n n u 必定收敛 D 、如果 ∑∞ =-1 ) 1(n n n u 收敛，则∑∞ =1 n n u 必定收敛 6、设对一切x 有),(),(y x f y x f -=-，}0,1|),{(2 2 ≥≤+=y y x y x D ，
江苏省2015年普通高校“专转本”选拔考试 一、选择题（本大题共6小题，每小题4分，满分24分） 1、当0x →时，函数sin ()1x f x e =-是函数 ()g x x =的 ( ) A. 高阶无穷小 B. 低阶无穷小 C. 同阶无穷小 D. 等价无穷小 2、函数(1) (1)x y x x =-<的微分dy 为 ( ) A. (1) [ln(1)]1x x x x dx x --+ - B. (1) [ln(1)]1x x x x dx x ---- C. 1(1)x x x dx -- D. 1(1)x x x dx --- 3、0x =是函数1 11, 0()1 1, 0 x x e x f x e x ?+?≠?=?-??=?的 ( ) A. 无穷间断点 B. 跳跃间断点 C.可去间断点 D. 连续点 4、设()F x 是函数()f x 的一个原函数，则 (32)f x dx -=? ( ) A. 1(32)2F x C --+ B. 1(32)2 F x C -+ C. 2(32)F x C --+ D. 2(32)F x C -+ 5、下列级数条件收敛的是 ( ) A. 21(1)n n n n ∞=--∑ B. 1 1(1)21n n n n ∞=+--∑ C. 1!(1)n n n n n ∞=-∑ D. 21 1(1)n n n n ∞=+-∑ 6、二次积分 11ln (,)e y dy f x y dx =?? ( ) A. 11ln (,)e x dx f x y dy ?? B. 1(,)x e dx f x y dy ?? 1 0 C. 0(,)x e dx f x y dy ?? 1 0 D. 1(,)x e dx f x y dy ?? 1 0 二、填空题（本大题共6小题，每小题4分，共24分） 7设()lim(1)n n x f x n →∞=-，则(ln 2)f =_________．
2011年江苏省普通高校“专转本”统一考试 高等数学参考答案 一、选择题（本大题共6小题，每小题4分，共24分） 1、C 2、B 3、A 4、B 5、D 6、D 二、填空题（本大题共6小题，每小题4分，共24分） 7、－１ 8、2ln 22+ 9、32 10、dx 41 11、 2 π 12、[)11，- 三、计算题（本大题共8小题，每小题8分，共64分） 13、原式=4lim 22) )((2lim ) (lim 22 =-=+-=--→--→-→x e e x e e e e x e e x x x x x x x x x x x 14、) 12)(1(2121 2++=++==t e t t e t dt dx dt dy dx dy y y 15、原式=??? + -=+= +x xd x dx x x x dx x x x x x sin cos 2)cos sin 2(cos sin 22 =C x x x ++-sin cos 16、令 t x =+1，则原式=? ? = -= +-2 1 2 2 1 2 3 5)22(211 dt t t tdt t t 17、设所求平面方程为0=+++D Cz By Ax . 因为该平面经过x 轴，所以0==D A ；又该平面经过已知直线，所以法向量互相垂直， 即03=+C B .综上，所求平面方程为03=-Bz By ，即03=-z y . 18、 '-=??? ????'+-?'?+?=??12210)(1f x y f f x y f x f x z " -"-'=?? ?????"+?"?+'??-?'+?'=???12112212111212 )11(11)11(f x y f x y f f x f y f x f x f y x z 19、原式=? ?= 2 2 4 32 3 2sin dr r d θθπ π 20、由已知可得x x x x e x e x e x e x f )13()1(2)1()(+=++++=，特征方程：
江苏专转本英语真题和答 案解析 It was last revised on January 2, 2021
江苏省2017年普通高校专转本选拔考试 英语试题卷 注意事项： 1.本试卷分为试题卷和答题卡两部分，试题卷共 10 页，全卷满分 150 分，考试时间 120 分钟。 2.必须在答疑卡上作答，作答在试题卷上无效。作答前务必将自己的姓名和准考正好准确 清晰的填写在试题卷和答题卡上的指定位置。 考试结束时，须将试题卷和答题卡一并交回。 Prat I Reading Comprehension （共 20 小题，每小题 2 分，共 40 分） Directions: There are 4 passage in this part . Each passage is followed by some questions or unfinished statements . For each of them there are 4 choices marked A,B,C and D. You should decide on the best choice and mark your answer by blackening the corresponding letter on the Answer Sheet . Passage One Questions 1 to 5 based on the following passage . We use both words and gestures to express our feelings ,but the problem is that these words and gestures can be understood in different ways . It is true that a smile means the same thing in any language . So does laughter or crying . There are also a number of striking similarities in the way different animals show the same feelings . Dogs , tigers and humans , for example , often show their teeth when they are angry . This is probably because they are born with those behavior patterns . Fear is another emotion that is shown in much the same way all over the world . In Chinese and English literature , a phrase like “he went pale and began to tremble”suggests that the man is either very afraid or deeply shocked . However , “he opened his eyes wide ” is used to suggest anger in Chinese whereas in English it means surprise . In Chinese surprise can be described in a phrase like “they stretched out their tongues ”. Sticking out your tongue in English is an insulting gesture or expresses strong dislike . Even in the same culture , people differ in the ability to understand and express feelings Experiments in America have shown that women are usually better than men at recognizing fear ,anger love and happiness on people’s faces . Other studies show that older people usually find it easier to recognize or understand body language than younger people do . to the passage , _________.
2009 一、单项选择题（本大题共6小题，每小题4分，满分24分） 1、已知32 lim 22=-++→x b ax x x ，则常数b a ,的取值分别为 （ ） A 、2,1-=-=b a B 、0,2=-=b a C 、0,1=-=b a D 、1,2-=-=b a 2、已知函数4 23)(22-+-=x x x x f ，则2=x 为)(x f 的 A 、跳跃间断点 B 、可去间断点 C 、无穷间断点 D 、震荡间断点 3、设函数?? ???>≤=0,1sin 0,0)(x x x x x f α在点0=x 处可导，则常数α的取值范围为 （ ） A 、10<<α B 、10≤<α C 、1>α D 、1≥α 4、曲线2)1(1 2-+=x x y 的渐近线的条数为 （ ） A 、1 B 、2 C 、3 D 、4 5、设)13ln()(+=x x F 是函数 )(x f 的一个原函数，则=+?dx x f )12(' （ ） A 、C x ++461 B 、C x ++463 C 、C x ++8121 D 、C x ++8 123 6、设α为非零常数，则数项级数∑∞=+12n n n α （ ） A 、条件收敛 B 、绝对收敛 C 、发散 D 、敛散性与α有关 二、填空题（本大题共6小题，每小题4分，满分24分） 7、已知2)(lim =-∞→x x C x x ，则常数=C . 8、设函数dt te x x t ?= 20)(?，则)('x ?＝ . 9、已知向量)1,0,1(-=→a ，)1,2,1(-=→b ，则→→+b a 与→a 的夹角为 . 10、设函数),(y x z z =由方程12=+yz xz 所确定，则 x z ??＝ . 11、若幂函数)0(12>∑∞=a x n a n n n 的收敛半径为21，则常数=a .
2001年江苏省普通高校“专转本”统一考试 高等数学 一、选择题（本大题共5小题，每小题3分，共15分） 1、下列各极限正确的是 （ ） A 、e x x x =+→)11(lim 0 B 、e x x x =+∞→1 )1 1(lim C 、11sin lim =∞ →x x x D 、11 sin lim 0=→x x x 2、不定积分 =-? dx x 2 11 （ ） A 、 2 11x - B 、 c x +-2 11 C 、x arcsin D 、c x +arcsin 3、若)()(x f x f -=，且在[)+∞,0内0)(' >x f 、0)(' '>x f ，则在)0,(-∞内必有 （ ） A 、0)('
10、设)(x f 为连续函数，则 =+-+? -dx x x x f x f 31 1 ])()([ 三、计算题（本大题共10小题，每小题4分，共40分） 11、已知5 cos )21ln(arctan π +++=x x y ，求dy . 12、计算x x dt e x x t x sin lim 20 2 ?-→. 13、求) 1(sin )1()(2 --=x x x x x f 的间断点，并说明其类型. 14、已知x y x y ln 2 +=，求1 ,1==y x dx dy . 15、计算dx e e x x ?+12. 16、已知 ?∞-=+0 2 2 1 1dx x k ，求k 的值. 17、求x x y y sec tan ' =-满足00 ==x y 的特解. 18、计算 ??D dxdy y 2 sin ，D 是1=x 、2=y 、1-=x y 围成的区域. 19、已知)(x f y =过坐标原点，并且在原点处的切线平行于直线032=-+y x ，若 b ax x f +=2'3)(，且)(x f 在1=x 处取得极值，试确定a 、b 的值，并求出)(x f y =的表达式. 20、设),(2 y x x f z =，其中f 具有二阶连续偏导数，求x z ??、y x z ???2.