電大微積分初步形成性考核冊(cè)作業(yè)答案小抄最新打印版

1、微積分初步形成性考核作業(yè)（一）解答函數(shù)，極限和連續(xù)一、填空題（每小題2分，共20分）1函數(shù)的定義域是解：， 所以函數(shù)的定義域是2函數(shù)的定義域是 解：， 所以函數(shù)的定義域是3函數(shù)的定義域是解： ， 所以函數(shù)的定義域是4函數(shù)，則 解： 所以5函數(shù)，則 解：6函數(shù)，則 解：，7函數(shù)的間斷點(diǎn)是 解：因?yàn)楫?dāng)，即時(shí)函數(shù)無(wú)意義 所以函數(shù)的間斷點(diǎn)是8解：9若，則解： 因?yàn)?所以10若，則解：因?yàn)?所以二、單項(xiàng)選擇題（每小題2分，共24分）1設(shè)函數(shù)，則該函數(shù)是（）a奇函數(shù) b偶函數(shù)c非奇非偶函數(shù) d既奇又偶函數(shù)解：因?yàn)?所以函數(shù)是偶函數(shù)。故應(yīng)選b2設(shè)函數(shù)，則該函數(shù)是（）a奇函數(shù) b偶函數(shù)c非奇非偶函數(shù) d既奇又

2、偶函數(shù)解：因?yàn)?所以函數(shù)是奇函數(shù)。故應(yīng)選a3函數(shù)的圖形是關(guān)于（）對(duì)稱(chēng)a b軸c軸 d坐標(biāo)原點(diǎn)解：因?yàn)?所以函數(shù)是奇函數(shù) 從而函數(shù)的圖形是關(guān)于坐標(biāo)原點(diǎn)對(duì)稱(chēng)的 因此應(yīng)選d4下列函數(shù)中為奇函數(shù)是（）a b c d解：應(yīng)選c5函數(shù)的定義域?yàn)椋ǎ゛ b c且 d且解：，所以應(yīng)選d 6函數(shù)的定義域是（）a bc d解：，函數(shù)的定義域是，故應(yīng)選d 7設(shè)，則（ ）a b c d 解： ，故應(yīng)選c8下列各函數(shù)對(duì)中，（）中的兩個(gè)函數(shù)相等 a， b， c， d， 解：兩個(gè)函數(shù)相等必須滿(mǎn)足定義域相同函數(shù)表達(dá)式相同，所以應(yīng)選d9當(dāng)時(shí)，下列變量中為無(wú)窮小量的是（ ）.a b c d解：因?yàn)?，所以?dāng)時(shí)，為無(wú)窮小量，所以應(yīng)選

3、c10當(dāng)（ ）時(shí)，函數(shù)，在處連續(xù).a0 b1 c d 解：因?yàn)椋?若函數(shù)，在處連續(xù)，則，因此。故應(yīng)選b11當(dāng)（ ）時(shí)，函數(shù)在處連續(xù).a0 b1 c d 解：，所以應(yīng)選d12函數(shù)的間斷點(diǎn)是（ ）ab c d無(wú)間斷點(diǎn)解：當(dāng)時(shí)分母為零，因此是間斷點(diǎn)，故應(yīng)選a三、解答題（每小題7分，共56分）計(jì)算極限 解：2計(jì)算極限解：3 解： 4計(jì)算極限 解：5計(jì)算極限解：6計(jì)算極限 解： 7計(jì)算極限解： 8計(jì)算極限 解： 微積分初步形成性考核作業(yè)（二）解答（除選擇題）導(dǎo)數(shù)、微分及應(yīng)用一、填空題（每小題2分，共20分）1曲線(xiàn)在點(diǎn)的斜率是 解：，斜率2曲線(xiàn)在點(diǎn)的切線(xiàn)方程是 解： ，斜率 所以曲線(xiàn)在點(diǎn)的切線(xiàn)方程是：3曲

4、線(xiàn)在點(diǎn)處的切線(xiàn)方程是解：，斜率 所以曲線(xiàn)在點(diǎn)處的切線(xiàn)方程是：，即：4 解：5若y = x (x 1)(x 2)(x 3)，則(0) = 解：6已知，則=解：，7已知，則=解：，8若，則 解：， 9函數(shù)的單調(diào)增加區(qū)間是 解：，所以函數(shù)的單調(diào)增加區(qū)間是10函數(shù)在區(qū)間內(nèi)單調(diào)增加，則a應(yīng)滿(mǎn)足 解：，而，所以二、單項(xiàng)選擇題（每小題2分，共24分）1函數(shù)在區(qū)間是（ d ）a單調(diào)增加 b單調(diào)減少c先增后減 d先減后增2滿(mǎn)足方程的點(diǎn)一定是函數(shù)的（ c ）.a極值點(diǎn)b最值點(diǎn) c駐點(diǎn)d 間斷點(diǎn)3若，則=（c ） a. 2 b. 1 c. -1 d. -24設(shè)，則（b ） a b c d5設(shè)是可微函數(shù)，則（ d ）

5、 a b c d 6曲線(xiàn)在處切線(xiàn)的斜率是（ c ） a b c d 7若，則（ c ） a b c d 8若，其中是常數(shù)，則（ c ） a b c d9下列結(jié)論中（ b ）不正確 a在處連續(xù)，則一定在處可微. b在處不連續(xù)，則一定在處不可導(dǎo). c可導(dǎo)函數(shù)的極值點(diǎn)一定發(fā)生在其駐點(diǎn)上. d若在a，b內(nèi)恒有，則在a，b內(nèi)函數(shù)是單調(diào)下降的.10若函數(shù)f (x)在點(diǎn)x0處可導(dǎo)，則( b )是錯(cuò)誤的 a函數(shù)f (x)在點(diǎn)x0處有定義 b，但 c函數(shù)f (x)在點(diǎn)x0處連續(xù) d函數(shù)f (x)在點(diǎn)x0處可微 11下列函數(shù)在指定區(qū)間上單調(diào)增加的是（ b） asinx be x cx 2 d3 - x12.下列結(jié)

6、論正確的有（ a ） ax0是f (x)的極值點(diǎn)，且(x0)存在，則必有(x0) = 0 bx0是f (x)的極值點(diǎn)，則x0必是f (x)的駐點(diǎn) c若(x0) = 0，則x0必是f (x)的極值點(diǎn) d使不存在的點(diǎn)x0，一定是f (x)的極值點(diǎn)三、解答題（每小題7分，共56分）設(shè)，求 解：2設(shè)，求.解：3設(shè)，求.解：4設(shè)，求. 解：5設(shè)是由方程確定的隱函數(shù)，求.解：兩邊微分： 6設(shè)是由方程確定的隱函數(shù)，求. 解：兩邊對(duì)求導(dǎo)，得： ， 7設(shè)是由方程確定的隱函數(shù)，求.解：兩邊微分，得： ，8設(shè)，求解：兩邊對(duì)求導(dǎo)，得： 微積分初步形成性考核作業(yè)（三）解答（填空題除外）不定積分，極值應(yīng)用問(wèn)題一、填空題（

7、每小題2分，共20分）1若的一個(gè)原函數(shù)為，則 。2若的一個(gè)原函數(shù)為，則 。3若，則4若，則 5若，則6若，則78 9若，則10若，則二、單項(xiàng)選擇題（每小題2分，共16分）1下列等式成立的是（）a b cd解：應(yīng)選a2若，則（ ）. a. b. c. d. 解：兩邊同時(shí)求導(dǎo)，得：，所以應(yīng)選a3若，則（ ）. a. b. c. d. 解：應(yīng)選a4以下計(jì)算正確的是（ ）abcd 解：應(yīng)選a5（ ）a. b. c. d. 解：，所以應(yīng)選a6=（ ） a b c d 解：應(yīng)選c7如果等式，則（ ）a. b. c. d. 解：兩邊求導(dǎo)，得：，所以，故應(yīng)選b三、計(jì)算題（每小題7分，共35分）1解： 2 解：

8、 3解：4解： 5解：四、極值應(yīng)用題（每小題12分，共24分）1 設(shè)矩形的周長(zhǎng)為120厘米，以矩形的一邊為軸旋轉(zhuǎn)一周得一圓柱體。試求矩形的邊長(zhǎng)為多少時(shí)，才能使圓柱體的體積最大。 解：設(shè)矩形的一邊長(zhǎng)為厘米，則另一邊長(zhǎng)為厘米，以厘米的邊為軸旋轉(zhuǎn)一周得一圓柱體，則體積為：，即：，令，得：（不合題意，舍去），這時(shí)由于根據(jù)實(shí)際問(wèn)題，有最大體積，故當(dāng)矩形的一邊長(zhǎng)為厘米、另一邊長(zhǎng)為厘米時(shí)，才能使圓柱體的體積最大。2 欲用圍墻圍成面積為216平方米的一成矩形的土地，并在正中用一堵墻將其隔成兩塊，問(wèn)這塊土地的長(zhǎng)和寬選取多大尺寸，才能使所用建筑材料最??？ 解：設(shè)矩形的長(zhǎng)為米，則矩形的寬為米，從而所用建筑材料為：，

9、即：，令得：（取正值），這時(shí)由于根據(jù)實(shí)際問(wèn)題，確實(shí)有最小值，故當(dāng)矩形的長(zhǎng)為米，寬為米時(shí)，才能使所用建筑材料最省五、證明題（本題5分）函數(shù)在（是單調(diào)增加的證明：因?yàn)?，?dāng)（時(shí)， 所以函數(shù)在（是單調(diào)增加的微積分初步形成性考核作業(yè)（四）解答（選擇題除外）定積分及應(yīng)用、微分方程一、填空題（每小題2分，共20分）1 解：2解：3已知曲線(xiàn)在任意點(diǎn)處切線(xiàn)的斜率為，且曲線(xiàn)過(guò)，則該曲線(xiàn)的方程是 。解：由得所求的曲線(xiàn)方程由確定 因?yàn)榍€(xiàn)過(guò)，所以，解得： 因此所求的曲線(xiàn)方程為4若 解：5由定積分的幾何意義知，= 。解：由定積分的幾何意義知，就等于圓在第象限的面積，即 圓面積的，因此6 .解：07= 解： 8微分方程的

10、特解為 . 解：由得，兩邊同時(shí)積分，得 因?yàn)?，所以，所?從而，因此微分方程的特解為9微分方程的通解為 .解：， ，即 所以微分方程的通解為10微分方程的階數(shù)為 解：微分方程的階數(shù)為階二、單項(xiàng)選擇題（每小題2分，共20分）1在切線(xiàn)斜率為2x的積分曲線(xiàn)族中，通過(guò)點(diǎn)（1, 4）的曲線(xiàn)為（ a ）ay = x2 + 3 by = x2 + 4 c d 2若= 2，則k =（ a ） a1 b-1 c0 d 3下列定積分中積分值為0的是（ a ） a b c d 4設(shè)是連續(xù)的奇函數(shù)，則定積分（ d ）ab cd 05（ d ）a0 b c d6下列無(wú)窮積分收斂的是（b ）abcd 7下列無(wú)窮積分收斂的

11、是（b ）ab cd8下列微分方程中，（ d ）是線(xiàn)性微分方程 a b c d9微分方程的通解為（ c ） a b c d10下列微分方程中為可分離變量方程的是（b ）a. ；b. ； c. ； d. 三、計(jì)算題（每小題7分，共56分）1解：2 解： 3解：4解： 5解： 6求微分方程滿(mǎn)足初始條件的特解解：微分方程的通解為 這里 ， 代入得微分方程的通解為 將初始條件代入上式，解得 所以微分方程的特解為7求微分方程的通解。解：微分方程的通解為 這里， 代入得微分方程的通解為四、證明題（本題4分）證明等式。證明： 考慮積分，令，則，從而 所以 ag an employment tribunal

12、clai emloyment tribunals sort out disagreements between employers and employees. you may need to make a claim to an employment tribunal if: you dont agree with the disciplinary action your employer has taken against you your employer dismisses you and you think that you have been dismissed unfairly.

13、 for more informu, take advice from one of the organisations listed underfur ther help. employment tribunals are less formal than some other courts, but it is still a legal process and you will need to give evidence under an oath or affirmation. most people find making a claim to an employment tribu

14、nal challenging. if you are thinking about making a claim to an employment tribunal, you should get help straight away from one of the organisations listed underfurther help. ation about dismissal and unfair dismissal, seedismissal. you can make a claim to an employment tribunal, even if you haventa

15、ppealedagainst the disciplinary action your employer has taken against you. however, if you win your case, the tribunal may reduce any compensation awarded to you as a result of your failure to appeal. remember that in most cases you must make an application to an employment tribunal within three mo

16、nths of the date when the event you are complaining about happened. if your application is received after this time limit, the tribunal will not usually accept i. if you are worried about how the time limits apply to you if you are being represented by a solicitor at the tribunal, they may ask you t

17、o sign an agreement where you pay their fee out of your compensation if you win the case. this is known as adamages-based agreement. in england and wales, your solicitor cant charge you more than 35% of your compensationif you win the case. you are clear about the terms of the agreement. it might be

18、 best to get advice from an experienced adviser, for example, at a citizens advice bureau. to find your nearest cab, including those that give advice by e-mail, click onnearest cab. for more information about making a claim to an employment tribunal, seeemployment tribunals. the (lack of) air up the

19、re watch m cay man islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday. i am going to be at the match tomorrow and i have asked to meet ya ya toure, he t

20、old bbc sport. for me its about how he felt and i would like to speak to him first to find out what his experience was. uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win. michel platini, president of european footballs governing body, has

21、also ordered an immediate investigation into the referees actions. cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. age has reached the end of the beginning of a word. may be guilty in his seems t

22、o passing a lot of different life became the appearance of the same day; may be back in the past, to oneself the paranoid weird belief disillusionment, these days, my mind has been very messy, in my mind constantly. always feel oneself should go to do something, or write something. twenty years of l

23、ife trajectory deeply shallow, suddenly feel something, do it.一字開(kāi)頭的年齡已經(jīng)到了尾聲?；蛟S是愧疚于自己似乎把轉(zhuǎn)瞬即逝的很多個(gè)不同的日子過(guò)成了同一天的樣子；或許是追溯過(guò)去，對(duì)自己那些近乎偏執(zhí)的怪異信念的醒悟，這些天以來(lái)，思緒一直很凌亂，在腦海中不斷糾纏。總覺(jué)得自己似乎應(yīng)該去做點(diǎn)什么，或者寫(xiě)點(diǎn)什么。二十年的人生軌跡深深淺淺，突然就感覺(jué)到有些事情，非做不可了。the end of our life, and can meet many things really do?而窮盡我們的一生，又能遇到多少事情是真正地非做不可？ during

24、 my childhood, think lucky money and new clothes are necessary for new year, but as the advance of the age, will be more and more found that those things are optional; junior high school, thought to have a crush on just means that the real growth, but over the past three years later, his writing of

25、alumni in peace, suddenly found that isnt really grow up, it seems is not so important; then in high school, think dont want to give vent to out your inner voice can be in the high school children of the feelings in a period, but was eventually infarction when graduation party in the throat, later a

26、gain stood on the pitch he has sweat profusely, looked at his thrown a basketball hoops, suddenly found himself has already cant remember his appearance. baumgartner the disappointing news: mission aborted. r plays an important role in this mission. starting at the ground, conditions have to be very

27、 calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 k

28、ilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence. we often close ourselves off when traumatic events happen in our lives

29、; instead of letting the world soften us, we let it drive us deeper into ourselves. we try to deflect the hurt and pain by pretending it doesnt exist, but although we can try this all we want, in the end, we cant hide from ourselves. we need to learn to open our hearts to the potentials of life and let the world soften us.生活發(fā)生不幸時(shí)，我們常常會(huì)關(guān)上心門(mén)；世界不僅沒(méi)能慰藉我們，反倒使我們更加消沉。我們假裝一切仿佛都不曾發(fā)生，以此試圖忘卻傷痛，可就算隱藏得再好，最終也還是騙不了自己。既然如此，何不嘗試打開(kāi)心門(mén)，擁抱生活中的各種可能