第二學(xué)期高等數(shù)學(xué)期中考試試卷答1

1、last week, our economic work conference held today, held the countys rural areas for work and five water treatment, three to split conference, which this year was a matter of thirteen-five important meeting of our countys economic and social development. the main task of the meeting was, on rural wo

2、rk and conscientiously implement the central, provincial and municipal five water treatment, three to split series of important conferences, learn from the past, study deployment priority tasks this year. just now, the xxx deputy head and deputy county magistrate, respectively, on the work of the xx

3、 was fully deployed, and put forward specific measures and requirements about is in place. county environmental protection bureau, the xx town, town of xx 3 units for a position statement, resounding, demonstrated determination and confidence. conference also recognition has advanced representative,

4、 this, i also representative county, and county government, to by recognition of advanced said warm of congratulated! to rural, and water and three modified a split front general cadres workers extend sincere of greeting! following, i again told five points views: a, and deepening awareness, further

5、 enhanced work of sense and urgency since party of 18 session v plenary proposed has innovation, and coordination, and green, and open, and shared five big development concept hou, rural and environment governance work can said was upgrade to has more high of strategy level, is thirteen-five build w

6、ell-off a top priority task. xx, county besides lingxi, longgang, jinxiang, the treasury, the hills, several industrial town outside the city centre, is basically belong to other rural areas, area, the vast rural population. same time, the current and coming period, is the county into a crucial peri

7、od of the south gate of xx beautiful, environmental regulation directly affects the effectiveness of the strategic objectives can not be achieved. therefore, the focus on rural work and five water treatment, three to split, the xx economic and social development has an important role. last year, thr

8、ough the joint efforts of the county, reform of the agricultural and rural development has made great progress in our county, environmental remediation and achieved initial results. three agriculture agricultural modernization level continues to increase, new 4-level modern agriculture park, release

9、d 20 agricultural leading enterprises above the county level, the county area of 200 acres of land more than eco-leisure, investments of more than 5 million yuan reached more than more than 100 agricultural projects. rural development has improved continuously, boutique line 1 completed the beautifu

10、l countryside, fine village 17, beautiful rural development conference was held in lingxi peach lake in the city. promote comprehensive rural reform, included in the provinces building three in one system of farmers cooperative economic organization first promoting the county. improvement of farmers

11、第二學(xué)期高等數(shù)學(xué)期中考試試卷答案第二學(xué)期高等數(shù)學(xué)期中考試試卷答案一填空題（本題滿(mǎn)分15分，共有5道小題，每道小題3分），請(qǐng)將合適的答案填在空中 1已知球面的一直徑的兩個(gè)端點(diǎn)為和，則該球面的方程為_(kāi) 2設(shè)，則 _ 3設(shè)二元函數(shù)，則_ 4若函數(shù)在矩形區(qū)域上連續(xù)，且 ，則_ 5設(shè)，則_ 答案： ； ； ； ； 二選擇填空題（本題滿(mǎn)分15分，共有5道小題，每道小題3分）。以下每道題有四個(gè)答案，其中只有一個(gè)答案是正確的，請(qǐng)選出合適的答案填在空中，多選無(wú)效 1下列直線(xiàn)中平行坐標(biāo)面的是_ （a） ； （b）； （c）； （d） 2旋轉(zhuǎn)曲面是_ （a）坐標(biāo)面上的雙曲線(xiàn)繞軸旋轉(zhuǎn)而成； （b）坐標(biāo)面上的雙曲線(xiàn)繞軸

12、旋轉(zhuǎn)而成； （c）坐標(biāo)面上的橢圓繞軸旋轉(zhuǎn)而成； （d）坐標(biāo)面上的橢圓繞軸旋轉(zhuǎn)而成 3與在點(diǎn)處連續(xù)是的_ （a）必要條件 ； （b）充分條件 ； （c）充分必要條件 ； （d）既非充分條件，又非必要條件 4設(shè)平面區(qū)域由直線(xiàn)，圍成，若 ，則，之間的關(guān)系是_ （a）； （b）； （c）； （d） 5設(shè)曲線(xiàn)是任意不經(jīng)過(guò)的區(qū)域內(nèi)的曲線(xiàn)，為使曲線(xiàn)積分與路徑無(wú)關(guān)，則 _ （a）； （b）； （c）； （d） 答案： （d）； （a）； （b）； （c）； （a）三（本題滿(mǎn)分6分） 已知直線(xiàn)，求過(guò)且平行于的平面方程 解： 直線(xiàn)與的方向向量分別為 ， ，作 ，取直線(xiàn)上的一點(diǎn)，則過(guò)點(diǎn)且以為法向量的平面 ，就是過(guò)且

13、平行于的平面方程四（本題滿(mǎn)分6分） 求球面與拋物面的交線(xiàn)在點(diǎn)處的切線(xiàn)方程 解： 由方程組兩端對(duì)求導(dǎo)，得 即 ，解得，所以， 因此，曲線(xiàn)在點(diǎn)處的切線(xiàn)方程為 五（本題滿(mǎn)分6分） 計(jì)算二重積分 ，其中為 解： 作極坐標(biāo)變換 則有 六（本題滿(mǎn)分7分） 證明：曲面，所圍立體的體積等于，其中是連續(xù)的正值函數(shù)，且， 解： 所求立體在面上的投影區(qū)域?yàn)?，因此?七（本題滿(mǎn)分7分） 求曲面積分 ，其中是曲面 的上側(cè) 解： 添加曲面 ，取下側(cè)，設(shè)閉曲面（取外側(cè)）所圍區(qū)域?yàn)椋蒰auss公式，得 （對(duì)稱(chēng)性） 八（本題滿(mǎn)分7分） 計(jì)算曲線(xiàn)積分，其中為圓周 解： 圓周的參數(shù)方程為 ，則 因此， 九（本題滿(mǎn)分7分） 設(shè)，其

14、中與分別具有二階連續(xù)的導(dǎo)數(shù)與偏導(dǎo)數(shù)，求 解： 令：，則 十（本題滿(mǎn)分8分） 設(shè)函數(shù)在平面上有連續(xù)的一階偏導(dǎo)數(shù)，且曲線(xiàn)積分與積分路徑無(wú)關(guān)，并且對(duì)任意的，恒有試求 解： 設(shè)，由曲線(xiàn)積分與路徑無(wú)關(guān)的條件，得 ，由此得 ，其中為待定函數(shù) 由題設(shè)：，得 上式兩端對(duì)求導(dǎo)，得 所以，因此，十一（本題滿(mǎn)分8分） 設(shè)曲線(xiàn)的方程為，函數(shù)有連續(xù)的一階偏導(dǎo)數(shù)，為曲線(xiàn)外一點(diǎn)，線(xiàn)段是點(diǎn)到曲線(xiàn)的最短距離，點(diǎn)在曲線(xiàn)上，證明：曲線(xiàn)上點(diǎn)處的法線(xiàn)必過(guò)點(diǎn) 解： 設(shè)，由題設(shè)知，必使函數(shù)在條件下取最小值 令：解方程組 ，解上面方程組中的前兩個(gè)方程，得這就是直線(xiàn)的方程，其斜率為 又曲線(xiàn)在點(diǎn)處的切線(xiàn)的斜率為所以， 因此，所以為曲線(xiàn)在點(diǎn)處的法

15、線(xiàn)十二（本題滿(mǎn)分8分） 計(jì)算曲線(xiàn)積分 ，其中球面與柱面 的交線(xiàn)，從軸的正向看，為逆時(shí)針?lè)较?解： 設(shè)上半球面被柱面所截下的部分為，則由stokes公式，得 而曲面的上側(cè)法線(xiàn)向量，故 ，因此， （因?yàn)椋┰儆汕骊P(guān)于坐標(biāo)面對(duì)稱(chēng)，故， 所以， living standards, poor farmers in less than complete elimination of 4600 yuan, 8949, 19008. five waters rule: the county invested 2.169 billion yuan, similar counties line the citys

16、 first complete the 42 km of sewage pipe network construction, completion rate ranked first in the city, won the provincial rural sewage treatment work better; key pollution sources such as electroplating, papermaking, chemical industry management through verification and acceptance of the municipal

17、 government, the county removed black and odorous river, river waste, beginning of river ecological restoration effects. three modified a split aspects: county total demolition illegal area up 2.759 million square meters, completed city issued annual task of 153%, split against area ranking city sec

18、ond; completed three modified area 4.846 million square meters, completed city issued annual task of 403%, ranking city third, which village in the a target completed total city ranking first; county government was named city level three modified a split work advanced. these achievements are hard wo

19、n and should be appreciated. however, we are fully aware, the new period, and work in the countryside and the environment facing higher standards and requirements, provincial party committee offered to high level build a comprehensive well-off society goal requires no filth, dirty environment illega

20、l buildings, into a well-off; municipal party committee also proposes to build into the well-off benchmark goals of the city. compared with the superior claim, south gate of xx beautiful goal, my county san nong and environment there are a number of weaknesses and gaps, highlighted in the following

21、five aspects: first, agriculture remained low pattern. low is reflected in the quality and low; short, value added of the industry chain is low; 123 fusion yield low employee age, low quality. small is reflected in smaller, specialized cooperatives throughout the county there were 3,396, but on the scale of too little. san is reflected in production, management, services, decentralized, centralized, standardized, brand, information and organizational level is not high. second, the countryside is still in dirty phase. dirty is dirty of rural sanitation situation has not