電大《微積分初步》復(fù)習(xí)題及答案小抄

1、專業(yè)好文檔微積分初步模擬試題一、填空題（每小題4分，本題共20分）函數(shù)的定義域是若，則 曲線在點(diǎn)處的切線方程是微分方程的特解為 二、單項(xiàng)選擇題（每小題4分，本題共20分）設(shè)函數(shù)，則該函數(shù)是（）a偶函數(shù)b奇函數(shù)c非奇非偶函數(shù) d既奇又偶函數(shù)當(dāng)（ ）時(shí)，函數(shù)，在處連續(xù).a0 b1 c d下列結(jié)論中（ ）正確 a在處連續(xù)，則一定在處可微. b函數(shù)的極值點(diǎn)一定發(fā)生在其駐點(diǎn)上. c在處不連續(xù)，則一定在處不可導(dǎo). d函數(shù)的極值點(diǎn)一定發(fā)生在不可導(dǎo)點(diǎn)上.下列等式中正確的是（）a . b. c. d. 微分方程的階數(shù)為（）a. 2； b. 3； c. 4； d. 5三、計(jì)算題（本題共44分，每小題11分）計(jì)算極

2、限設(shè)，求. 計(jì)算不定積分計(jì)算定積分四、應(yīng)用題（本題16分） 欲做一個(gè)底為正方形，容積為108立方米的長方體開口容器，怎樣做法用料最??？參考答案一、填空題（每小題4分，本題共20分） 2 0 二、單項(xiàng)選擇題（每小題4分，本題共20分）accdb 三、（本題共44分，每小題11分）解：原式 解： 解：= 解： 四、應(yīng)用題（本題16分）解：設(shè)底邊的邊長為，高為，用材料為，由已知 令，解得是唯一駐點(diǎn)， 且，說明是函數(shù)的極小值點(diǎn)，所以當(dāng)，時(shí)用料最省。 一、填空題（每小題4分，本題共20分）函數(shù)，則 當(dāng)時(shí)，為無窮小量.若y = x (x 1)(x 2)(x 3)，則(1) = 微分方程的特解為 . 二、單

3、項(xiàng)選擇題（每小題4分，本題共20分）函數(shù)的定義域是（）a bc d 曲線在處切線的斜率是（ ） a b c d下列結(jié)論正確的有（ ） a若(x0) = 0，則x0必是f (x)的極值點(diǎn) bx0是f (x)的極值點(diǎn)，且(x0)存在，則必有(x0) = 0 cx0是f (x)的極值點(diǎn)，則x0必是f (x)的駐點(diǎn) d使不存在的點(diǎn)x0，一定是f (x)的極值點(diǎn)下列無窮積分收斂的是（）a b c d 微分方程的階數(shù)為（）a. 1；b. 2；c. 3； d. 4三、計(jì)算題（本題共44分，每小題11分）計(jì)算極限設(shè)，求. 計(jì)算不定積分計(jì)算定積分四、應(yīng)用題（本題16分） 用鋼板焊接一個(gè)容積為4的底為正方形的無蓋

4、水箱，已知鋼板每平方米10元，焊接費(fèi)40元，問水箱的尺寸如何選擇，可使總費(fèi)最低？最低總費(fèi)是多少？試題答案（供參考）一、填空題（每小題4分，本題共20分） 0 二、單項(xiàng)選擇題（每小題4分，本題共20分）cdba d三、（本題共44分，每小題11分）解： 解： 解：= 4解： 四、應(yīng)用題（本題16分）解：設(shè)水箱的底邊長為，高為，表面積為，且有所以 令，得， 因?yàn)楸締栴}存在最小值，且函數(shù)的駐點(diǎn)唯一，所以，當(dāng)時(shí)水箱的表面積最小. 此時(shí)的費(fèi)用為 （元） 一、填空題（每小題4分，本題共20分）函數(shù)，則 曲線在點(diǎn)處的切線方程是若，則 微分方程的階數(shù)為 二、單項(xiàng)選擇題（每小題4分，本題共20分）設(shè)函數(shù)，則該函

5、數(shù)是（）a非奇非偶函數(shù)b既奇又偶函數(shù)c偶函數(shù) d奇函數(shù)當(dāng)時(shí)，下列變量中為無窮小量的是（ ）.a b c d下列函數(shù)在指定區(qū)間上單調(diào)減少的是（ ） a b c d 設(shè)，則（ ） a. b. c. d. 下列微分方程中，（ ）是線性微分方程 a b c d 三、計(jì)算題（本題共44分，每小題11分）計(jì)算極限設(shè)，求. 計(jì)算不定積分計(jì)算定積分四、應(yīng)用題（本題16分） 欲做一個(gè)底為正方形，容積為108立方米的長方體開口容器，怎樣做法用料最?。繀⒖即鸢福ü﹨⒖迹┮?、填空題（每小題4分，本題共20分） 5二、單項(xiàng)選擇題（每小題4分，本題共20分）dcbca 三、（本題共44分，每小題11分）解：原式 解： 解

6、：= 4解： 四、應(yīng)用題（本題16分）解：設(shè)長方體底邊的邊長為，高為，用材料為，由已知 令，解得是唯一駐點(diǎn)， 因?yàn)閱栴}存在最小值，且駐點(diǎn)唯一，所以是函數(shù)的極小值點(diǎn)，即當(dāng)，時(shí)用料最省. 一、填空題（每小題4分，本題共20分）函數(shù)，則若函數(shù),在處連續(xù)，則 函數(shù)的單調(diào)增加區(qū)間是 微分方程的階數(shù)為 二、單項(xiàng)選擇題（每小題4分，本題共20分）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)當(dāng)時(shí)，下列變量為無窮小量的是（ ）.a b c d 若函數(shù)f (x)在點(diǎn)x0處可導(dǎo)，則( )是錯(cuò)誤的 a函數(shù)f (x)在點(diǎn)x0處有定義 b函數(shù)f (x)在點(diǎn)x0處連續(xù) c函數(shù)f (x)在點(diǎn)x0處可

7、微 d，但 若，則（ ）. a. b. c. d. 下列微分方程中為可分離變量方程的是（）a. ； b. ； c. ； d. 三、計(jì)算題（本題共44分，每小題11分）計(jì)算極限設(shè)，求. 計(jì)算不定積分計(jì)算定積分四、應(yīng)用題（本題16分） 某制罐廠要生產(chǎn)一種體積為v的有蓋圓柱形容器，問容器的底半徑與高各為多少時(shí)可使用料最??？參考答案一、填空題（每小題4分，本題共20分） 2 4二、單項(xiàng)選擇題（每小題4分，本題共20分）badcb 三、計(jì)算題（本題共44分，每小題11分）解：原式 解： 解：= 4解： 四、應(yīng)用題（本題16分）解：設(shè)容器的底半徑為，高為，則其表面積為，由已知，于是，則其表面積為 令，解得

8、唯一駐點(diǎn)，由實(shí)際問題可知，當(dāng)時(shí)可使用料最省，此時(shí)，即當(dāng)容器的底半徑與高分別為與時(shí)，用料最省 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

9、 to discuss his complaint.cska general director 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

10、pay them.it is a nonsense to have matches 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

11、harsh sanctions that racism and discrimination 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 c

12、helsea on sunday.i am going to be at the 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

13、 fans duringcitys 2-1 win.michel platini, 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 f

14、ans of cska.baumgartner the disappointing 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 cl

15、oud 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 kilometers), drifting even higher than the cruising altitude of commercial airli

16、ners (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.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 olympi

17、c diving platform.below, the earth becomes 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 pre

18、ps 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 spins out of control, he has a stabilization parachute