電大高數(shù)試題答案小抄參考

1、試題答案一、 單項(xiàng)選擇題1. a 2a 3. d 4. d 5. b 6. c 7. b 8. a 9. c 10. b 11. d 12. c二、填空題1. 2. -cos2x + c (c 是任意常數(shù)) 3. 4. 5. 0 6. 0 7. 收斂的 8. 2 + 9. 2 10. 三、計(jì)算題 解 = = 2解=3解 = xcos(1-x) - = xcos(1-x) + sin(1-x) + c 4解= = 5解 = = 6解 = = =12 7解 = 8解 =-=9解法一 = =1 解法二 令，則 = 10解 因?yàn)?， 用公式 由 ， 得 所以，特解為 11解 將原方程分離變量 兩端積分

2、得 lnlny = lnc sinx 通解為 y = ec sinx 12解：移項(xiàng)，分離變量，得 兩邊求積分，得 通解為： 由，得，c = 1 所以，滿足初始條件的特解為： 13解 將方程分離變量： 等式兩端積分得 將初始條件代入，得 ，c = 所以，特解為： 14. 解 將原方程化為：，它是一階線性微分方程， ，用公式 15解 在微分方程中，由通解公式 = = 16解：因?yàn)?，由通解公式?= = 四、應(yīng)用題1解 當(dāng)產(chǎn)量由4百臺增至6百臺時(shí)，總成本的增量為 = 10 （萬元） 又 = = 令 ， 解得. x = 6是惟一的駐點(diǎn)，而該問題確實(shí)存在使平均成本達(dá)到最小的值. 所以產(chǎn)量為6百臺時(shí)可使平

3、均成本達(dá)到最小. 2解 因?yàn)檫呺H利潤 =12-0.02x 2 = 10-0.02x 令= 0，得x = 500 x = 500是惟一駐點(diǎn)，而該問題確實(shí)存在最大值. 所以，當(dāng)產(chǎn)量為500件時(shí)，利潤最大. 當(dāng)產(chǎn)量由500件增加至550件時(shí)，利潤改變量為 =500 - 525 = - 25 （元）即利潤將減少25元. 3. 解 (x) =(x) -(x) = (100 2x) 8x =100 10x 令(x)=0, 得 x = 10（百臺）又x = 10是l(x)的唯一駐點(diǎn)，該問題確實(shí)存在最大值，故x = 10是l(x)的最大值點(diǎn)，即當(dāng)產(chǎn)量為10（百臺）時(shí)，利潤最大. 又 即從利潤最大時(shí)的產(chǎn)量再生產(chǎn)

4、2百臺，利潤將減少20萬元. 4解：因?yàn)榭偝杀竞瘮?shù)為 = 當(dāng)x = 0時(shí)，c(0) = 18，得 c =18即 c(x)= 又平均成本函數(shù)為 令 ， 解得x = 3 (百臺)該題確實(shí)存在使平均成本最低的產(chǎn)量. 所以當(dāng)x = 3時(shí)，平均成本最低. 最底平均成本為 (萬元/百臺) 5解：(1) 因?yàn)檫呺H成本為 ，邊際利潤 = 14 2x 令，得x = 7 由該題實(shí)際意義可知，x = 7為利潤函數(shù)l(x)的極大值點(diǎn)，也是最大值點(diǎn). 因此，當(dāng)產(chǎn)量為7百噸時(shí)利潤最大. 待添加的隱藏文字內(nèi)容1 (2) 當(dāng)產(chǎn)量由7百噸增加至8百噸時(shí)，利潤改變量為 =112 64 98 + 49 = - 1 （萬元）即利潤將

5、減少1萬元. winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the en

6、counter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league internati

7、onal federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blac

8、ks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.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 c

9、itys premier league match at chelsea 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

10、 the racist behaviour of their 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

11、found no racist insults from fans 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 precipita

12、tion 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 kilometers), drifting even higher than the cruisi

13、ng 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.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto

14、 something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conced

15、ed was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - s

16、trong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.th