電大微積分初步答案小抄

1、專業(yè)好文檔微積分初步一、填空題（每小題2分，共20分）1函數(shù)的定義域是 答案：2函數(shù)的定義域是 答案：3函數(shù)的定義域是答案：4函數(shù)，則 答案：5函數(shù)，則 答案：6函數(shù)，則 答案： 7函數(shù)的間斷點(diǎn)是 答案： 8答案： 19若，則 答案： 210若，則答案： 1曲線在點(diǎn)的斜率是 2曲線在點(diǎn)的切線方程是 3曲線在點(diǎn)處的切線方程是4 5若y = x (x 1)(x 2)(x 3)，則(0) = 66已知，則=7已知，則=（07年1月考題(4分)即與此題相似）8若，則29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)滿足大于零1若的一個(gè)原函數(shù)為，則 。答案： （c為任意常數(shù)）2若的一個(gè)原函數(shù)為，則

2、 。答案：3若，則答案：4若，則 答案：5若，則答案：6若，則答案：7答案：8 答案：9若，則答案：10若，則答案：1 答案：2答案：23已知曲線在任意點(diǎn)處切線的斜率為，且曲線過，則該曲線的方程是 。答案：4若 答案：45由定積分的幾何意義知，= 。答案：，它是1/4半徑為a的圓的面積。6 .答案：07= 答案：8微分方程的特解為 . 答案：19微分方程的通解為 .答案：10微分方程的階數(shù)為 答案：2 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（）答案：ba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)2設(shè)函數(shù)，則該函數(shù)是（）答案：aa奇函數(shù) b偶函數(shù)c非奇非偶函數(shù) d既奇又偶

3、函數(shù)3函數(shù)的圖形是關(guān)于（）對(duì)稱答案：da b軸c軸 d坐標(biāo)原點(diǎn)4下列函數(shù)中為奇函數(shù)是（）答案：ca b c d5函數(shù)的定義域?yàn)椋ǎ┐鸢福篸a b c且 d且6函數(shù)的定義域是（）答案：da bc d7設(shè)，則（ ）答案：ca b c d 8下列各函數(shù)對(duì)中，（）中的兩個(gè)函數(shù)相等答案：d a， b， c， d，9當(dāng)時(shí)，下列變量中為無窮小量的是（ ）. 答案：ca b c d10當(dāng)（ ）時(shí)，函數(shù)，在處連續(xù). 答案：ba0 b1 c d 11當(dāng)（ ）時(shí)，函數(shù)在處連續(xù). 答案：da0 b1 c d 12函數(shù)的間斷點(diǎn)是（ ） 答案：aa b c d無間斷點(diǎn)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

4、后減 d先減后增2滿足方程的點(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 ） a b c d 6曲線在處切線的斜率是（ c ） a b c d7若，則（ c ） a bc d 8若，其中是常數(shù)，則（ c ） a b c d9下列結(jié)論中（ a ）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

5、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)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)1下列等式成立的是（）答案：aabc d3若，則（ ）. 答案：aa. b. c. d. 4若，則（ ）. 答案：a a. b. c. d. 5以下計(jì)算

6、正確的是（ ）答案：aa b c d 6（ ）答案：aa. b. c. d. 7=（ ）答案：ca b c d 8如果等式，則（ ）答案：ba. b. c. d. 1在切線斜率為2x的積分曲線族中，通過點(diǎn)（1, 4）的曲線為（ ）答案：aay = x2 + 3 by = x2 + 4 c d 2若= 2，則k =（ ） 答案：a a1 b-1 c0 d 3下列定積分中積分值為0的是（ ） 答案：a a b c d 4設(shè)是連續(xù)的奇函數(shù)，則定積分（ ）答案：dab cd 05（ ）答案：da0 b c d6下列無窮積分收斂的是（）答案：ba bc d 7下列無窮積分收斂的是（） 答案：ba bc

7、d8下列微分方程中，（ ）是線性微分方程 答案：d a b c d 9微分方程的通解為（ ） 答案：c a b c d 10下列微分方程中為可分離變量方程的是（）答案：ba. ； b. ； c. ； d. 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 設(shè)，求 （答案）2設(shè)，求.（答案）3設(shè)，求.（答案）4設(shè)，求. （答案，）5設(shè)，求.（答案）6設(shè)是由方程確定的隱函數(shù)，求. （答案）7設(shè)是由方程確定的隱函數(shù)，求.（答案）8設(shè)，求（答案）1解 2 解 3解 4 解 利用分步積分法： 設(shè)，則， 5

8、解 利用分步積分法： 設(shè)，則，1 解 2 解 3 解 利用分部積分法 設(shè)，則， 4 解 利用分部積分法 設(shè)，則， 5 解 利用分部積分法 設(shè)，則， 6求微分方程滿足初始條件的特解 解 與一階線性微分方程標(biāo)準(zhǔn)式比較，可知 ， 將代入上式，得，所以原微分方程滿足初始條件的特解為 7求微分方程的通解。 解 與一階線性微分方程標(biāo)準(zhǔn)式比較，可知 ， 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。60-x0xxy解 設(shè)矩形的一邊邊長(zhǎng)為x厘米，則另一邊邊長(zhǎng)為（60-x）厘米，邊長(zhǎng)為x厘米的邊繞軸旋轉(zhuǎn)得一

9、圓柱體，其底面積為(60-x)2，旋轉(zhuǎn)體的體積為 令，即 其中是極小值點(diǎn)，此時(shí)體積為0；是極大值點(diǎn)，也是最大值點(diǎn)，對(duì)應(yīng)的圓柱體最大體積值為 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)土地一邊長(zhǎng)為，另一邊長(zhǎng)為，共用材料為于是 =3令得唯一駐點(diǎn)（舍去） 10分 因?yàn)楸締栴}存在最小值，且函數(shù)的駐點(diǎn)唯一，所以，當(dāng)土地一邊長(zhǎng)為，另一邊長(zhǎng)為18時(shí)，所用材料最省.五、證明題（本題5分）1、函數(shù)在（是單調(diào)增加的證 只需證明當(dāng)時(shí)，有 因?yàn)?當(dāng)時(shí)，即有 所以，當(dāng)時(shí)，是單調(diào)增加的。1、證明等式。證明：顯然是偶函數(shù)，

10、是奇函數(shù)，if we dont do that it will go on and go on. we have to stop it; we need the courage to do it.his comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his complaint.cska general di

11、rector roman babaev says the matter has been exaggerated by the ivorian and the british media.blatter, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is a nonsense to have matches

12、 played without spectators because it is against the spirit of football and against the visiting team. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions that racism and discrimin

13、ation can be washed out of football.the (lack of) air up there watch mcayman 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

14、match tomorrow and i have asked to meet yaya toure, he told 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,

15、 president of european footballs governing body, has 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.baumgartner the disappointing

16、 news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule atta

17、ched, 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 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into

18、 the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.below, the earth become

19、s the concrete bottom of a swimming pool that he wants to land on, but not too hard. still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he is diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be enough to stop him completely.if he goes too fast or s