清華大學(xué)第二學(xué)期高等數(shù)學(xué)期末考試模擬試卷及答案

1、rapid development of the market economy environment to explore public servants duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier an

2、d approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants duty consumption further. Implementing an hone

3、st canteen, standardize official entertaining management; enhancing the telecommunication expense management; elimination of County travel and countryside subsidies; research village officials capitalization management of corporate spending, and so on. Finally, group .18 session to be held in Beijin

4、g from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretar

5、y pointed out that Chinas reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas

6、, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the five in one the General layout of socialist modernization requirements, 18 session of the decision was a five in one and the improvement of ov

7、erall scheme of reform, will promote an integrated and coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the partys construction in the area of institutional reform. The five in one programme is to achieve a comprehensive reform of ins

8、titutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 ple

9、nary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the partys Congress, on the theme person

10、nel, discussing election Centrals top leaders, such as the election of the Standing Committee of the political Bureau, through the Central Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election

11、, mainly to discuss a new State personnel issues. But by the third第二學(xué)期高等數(shù)學(xué)期末考試試卷答案清華大學(xué)第二學(xué)期期末考試模擬試卷一填空題（本題滿分30分，共有10道小題，每道小題3分），請將合適的答案填在空中 1. 設(shè)向量的終點(diǎn)坐標(biāo)為，它在軸、軸、軸上的投影依次為、和，則該向量的起點(diǎn)的坐標(biāo)為_ 2. 設(shè)、都是單位向量，且滿足，則_ 3. 設(shè)，則_ 4. 設(shè)，則_ 5. 某工廠的生產(chǎn)函數(shù)是，已知. 當(dāng)時，；（2）當(dāng)時，勞力的邊際生產(chǎn)率和投資的邊際生產(chǎn)率為，。如果工廠計劃擴(kuò)大投入到，則產(chǎn)量的近似增量為_ 6. 交換積分順序，有_

12、7. 設(shè)級數(shù)收斂，且，則級數(shù)_ 8. 級數(shù)在滿足_條件下收斂 9. 微分方程的通解為_ 10. 對于微分方程，利用待定系數(shù)法求其特解時，應(yīng)設(shè)其特解_ （只需列出特解形式，不必具體求出系數(shù)） 答案： 1. ； 2. ； 3. ； 4. ； 5. 單位； 6. ； 7. ； 8. ； 9. ； 10. 二（本題滿分8分） 求過點(diǎn)，且與兩平面和平行的直線方程 解： 所求直線過點(diǎn)，設(shè)其方向向量為， 由于平行于平面和，所以其方向向量同時垂直于向量與 因此，方向向量可取為 ， 從而所求直線方程為三（本題滿分8分） 設(shè)函數(shù)，其中是常數(shù)，函數(shù)具有連續(xù)的一階偏導(dǎo)數(shù)試求 解： 所以， 四（本題滿分8分） 計算二重

13、積分的值 解： 作極坐標(biāo)變換：，則有 五（本題滿分8分） 某工廠生產(chǎn)兩種型號的機(jī)床，其產(chǎn)量分別為臺和臺，成本函數(shù)為 （萬元）若市場調(diào)查分析，共需兩種機(jī)床8臺，求如何安排生產(chǎn)，總成本最少？最小成本為多少？ 解： 即求成本函數(shù)在條件下的最小值 構(gòu)造輔助函數(shù) 解方程組 解得 這唯一的一組解，即為所求，當(dāng)這兩種型號的機(jī)床分別生產(chǎn)臺和臺時，總成本最小，最小成本為： （萬）六（本題滿分10分） . 將展開為的冪級數(shù)； . 指出該冪級數(shù)的收斂域； . 求級數(shù)的和 解： . 因?yàn)?，且，所以， 而 所以， . 冪級數(shù)的收斂域?yàn)?. 令，則有 七（本題滿分10分） 求微分方程的通解 解： 該方程為一階線性微分方

14、程因此， 代入一階線性微分方程的求解公式，有 所以，原方程的通解為 八（本題滿分10分） 討論級數(shù)的絕對收斂性與條件收斂性 解： . 因?yàn)榧墧?shù)為交錯級數(shù)，由于， 所以數(shù)列單調(diào)減少而且 因此由Leibniz判別法知，級數(shù)收斂 . 討論級數(shù)其前項部分和為 所以，級數(shù)發(fā)散 綜上所述知，級數(shù)條件收斂九（本題滿分8分） 設(shè)函數(shù)具有二階連續(xù)的導(dǎo)函數(shù)，而且滿足方程，試求函數(shù) 解： 設(shè)，則有 ，所以， 代入方程 ，得，即，由此得微分方程 解此二階線性微分方程，得其通解為 （與為任意常數(shù)）此即為所求函數(shù)中國石油海外戰(zhàn)略的成功，既得益于黨和國家高度重視和能源外交的推動，也得益于經(jīng)濟(jì)全球化、改革開放和中國經(jīng)濟(jì)高速發(fā)

15、展的帶動plenary session, each session of the Central Committee of national institutions and personnel problems have been arranged, you can concentrate on national development and reforms. Previous plenary session is often branded with a central leading collective, often by looking at the third plenum of

16、 the initiative to found the current central leadership collective governance characteristics. From the analysis of the process of economic reform in China, plenary session, 12 session, 14, 16 plenary session have programmatic meaning, respectively, marking the four stages of Chinas economic reform,

17、 and that the start-up phase of reform, reform, construction phase and perfecting the Socialist market economy framework stage of socialist market economy. Previous plenary session topics proposed to the third plenary session of taking class struggle as the key link, shifted to socialist modernizati

18、on; 12 session marked the change from rural to urban, established with public ownership as the Foundation of a planned commodity economy; 13 session at a time when both the old and the new system change, governance and rectify the economic order; 14 . Fair and efficient and authoritative Socialist j

19、udicial system, safeguard the peoples interests. Legal authority to uphold the Constitution, deepening the reform of administrative law enforcement, ensure that the right to exercise judicial power independently and impartially according to law the prosecution, perfecting the running mechanism of ju

20、dicial power, improve the system of judicial protection of human rights. Plenary session, Affairs the right to adhere to the system, and let the people authority to let the power run in the Sun, is shut up in a cage of the system power policy. Decision Science, implementation should be constructed s

21、trong, supervise the running of powerful system, improve the system of punishing and preventing corruption, promoting political integrity, and strive to achieve cadres honest and Government integrity, clean politics. To form a scientific and effective coordination of power restriction and mechanisms to strengthen anti-corruption institutional innovation and institutional protection, sound improvement style normal system. Plenary session, building a socialist culture in China, enhancing national cultural soft power, must