最新廣播電視大學（電大）期末考試《微積分初步》課程重點復習試題

1、2015年度最新廣播電視大學（電大）期末考試微積分初步課程重點復習試題一、填空題（每小題4分，本題共20分）函數(shù)的定義域是若，則2 曲線在點處的切線方程是0微分方程的特解為 二、單項選擇題（每小題4分，本題共20分）設函數(shù)，則該函數(shù)是（a）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（ c ）時，函數(shù)，在處連續(xù).a0 b1 c d下列結論中（ c ）正確 a在處連續(xù)，則一定在處可微. b函數(shù)的極值點一定發(fā)生在其駐點上. c在處不連續(xù)，則一定在處不可導. d函數(shù)的極值點一定發(fā)生在不可導點上.下列等式中正確的是（d）a . b. c. d. 微分方程的階數(shù)為（b）a. 2； b. 3； c.

2、4； d. 5三、計算題（本題共44分，每小題11分）計算極限原式設，求. 計算不定積分= 計算定積分四、應用題（本題16分） 欲做一個底為正方形，容積為108立方米的長方體開口容器，怎樣做法用料最??？解：設底邊的邊長為，高為，用材料為，由已知 令，解得是唯一駐點， 且，說明是函數(shù)的極小值點，所以當， 一、填空題（每小題4分，本題共20分）函數(shù)，則 當0時，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、單項選擇題（每小題4分，本題共20分）函數(shù)的定義域是（c）a bc d 曲線在處切線的斜率是（d ） a b c d下列結論正確的有（ b ）

3、 a若(x0) = 0，則x0必是f (x)的極值點 bx0是f (x)的極值點，且(x0)存在，則必有(x0) = 0 cx0是f (x)的極值點，則x0必是f (x)的駐點 d使不存在的點x0，一定是f (x)的極值點下列無窮積分收斂的是（a）a b c d 微分方程的階數(shù)為（d）a. 1；b. 2；c. 3； d. 4三、計算題（本題共44分，每小題11分）計算極限設，求. 計算不定積分= 計算定積分四、應用題（本題16分） 用鋼板焊接一個容積為4的底為正方形的無蓋水箱，已知鋼板每平方米10元，焊接費40元，問水箱的尺寸如何選擇，可使總費最低？最低總費是多少？解：設水箱的底邊長為，高為，

4、表面積為，且有所以 令，得， 因為本問題存在最小值，且函數(shù)的駐點唯一，所以，當時水箱的表面積最小. 此時的費用為 （元） 一、填空題（每小題4分，本題共20分）函數(shù)，則 1曲線在點處的切線方程是若，則 微分方程的階數(shù)為 5 二、單項選擇題（每小題4分，本題共20分）設函數(shù)，則該函數(shù)是（d）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)當時，下列變量中為無窮小量的是（ c ）.a b c d下列函數(shù)在指定區(qū)間上單調(diào)減少的是（ b） a b c d 設，則（ c ） a. b. c. d. 下列微分方程中，（a ）是線性微分方程 a b c d 三、計算題（本題共44分，每小題11分）計算極限原式

5、 設，求. 計算不定積分= 計算定積分 四、應用題（本題16分） 欲做一個底為正方形，容積為108立方米的長方體開口容器，怎樣做法用料最省？解：設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， 因為問題存在最小值，且駐點唯一，所以是函數(shù)的極小值點，即當，時用料最省. 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2 函數(shù)的單調(diào)增加區(qū)間是 微分方程的階數(shù)為 4 二、單項選擇題（每小題4分，本題共20分）設函數(shù)，則該函數(shù)是（b）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)當時，下列變量為無窮小量的是（ a ）.a b c d 若函數(shù)f (x)在點x0處可導

6、，則( d )是錯誤的 a函數(shù)f (x)在點x0處有定義 b函數(shù)f (x)在點x0處連續(xù) c函數(shù)f (x)在點x0處可微 d，但 若，則（ c ）. a. b. c. d. 下列微分方程中為可分離變量方程的是（b）a. ； b. ； c. ； d. 三、計算題（本題共44分，每小題11分）計算極限原式設，求 . 計算不定積分解：= 計算定積分解：四、應用題（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可使用料最??？解：設容器的底半徑為，高為，則其表面積為，由已知，于是，則其表面積為 令，解得唯一駐點，由實際問題可知，當時可使用料最省，此時，即當容器的底

7、半徑與高分別為與時，用料最省戀愛運up一緒lets月亭方正！気持今flying get！dou都斗豆逗陡抖痘兜讀蚪竇篼蔸乧侸兠凟剅吺唗投斣枓梪橷毭氀浢瀆瀆瞗窬竇脰艔豆讀逾郖酘酡鈄鋀鈄閗闘阧餖饾斗鬦鬪鬬鬭du讀度毒渡堵獨肚鍍賭睹杜督都犢妒頓蠹篤嘟瀆櫝牘黷髑芏儥凟剢剫匵厾噣土涂妬嬻剬塅媏彖斷毈瑖碫篅籪緞專腶葮褍踹躖鍛鍴mr najib met search crews at pearce raaf base near perth on thursday morning, before their planes left for the day, and then later held talks

8、with mr abbott.the disappearance of mh370 has tested our collective resolve, he told a news conference.faced with so little evidence, and such a herculean task, investigators from malaysia, the us, the uk, china, australia and france have worked without pausehe thanked both search teams and the aust

9、ralian government for their efforts in recent weeks, and said the search would go on.continue reading the main storymh370 - facts at a glance 8 march:malaysia airlines kuala lumpur-beijing flight carrying 239 people disappears planes transponder, which communicates with ground radar, was switched of

10、f as it left malaysian airspace satellite pings indicate plane was still flying seven hours after satellite contact was lost 24 march:based on new calculations, malaysian pm says beyond reasonable doubt that plane crashed in southern indian ocean with no survivors what we know the search for flight

11、mh370i know that until we find the plane, many families cannot start to grieve. i cannot imagine what they must be going through. but i can promise them that we will not give up, he said.malaysian authorities have come in for heavy criticism over their management of the search, especially from relat

12、ives of thweather conditions were fair, with visibility of approximately 10km (6 miles), the joint agency coordination centre (jacc) - which is overseeing the search - said.the british submarine hms tireless is also in the southern indian ocean and is due to be joined by royal navy ship hms echo.the

13、 australian navy ship ocean shield is heading to the region and has equipment for detecting the planes black-box flight recorder.experts say timing is critical as the flight recorder may only have enough battery power to send out a signal until 7 april.air chief marshall angus houston, head of the j

14、acc, warned that the search operation faced multiple difficulties.this is one of the most demanding and challenging search and rescue operations, or search and recovery operations, that i have ever seen and i think probably one of the most complex operations of this nature that the world has ever se

15、en, he told mr najib and mr abbott.on wednesday malaysian police chief khalid abu bakar said investigators had cleared all passengers of possible involvement in hijacking, sabotage or having personal or psychological problems that could have been connected to the disappearance.but he said that the c

16、riminal investigation could go on and on and on. we have to clear every little thing.at the end of the investigations, we may not even know the real cause. we may not even know the reason for this incident, he added.the police chief said that more than 170 interviews had been conducted with family m

17、embers of the pilots and crew members, and that even cargo and food served on the plane were being investigated in case ofdui對隊堆兌敦鐓碓懟憝兊兌垖埻塠奪奪対對嵟憞懟捶杸濧濻瀢瀩痽磓祋綐膭薱謉譈譵追鈗銳銳錞鎚鐓鐜銳陮隊頧鴭dul乧dun噸頓蹲墩敦鈍盾囤遁不躉沌盹鐓礅燉砘伅俊噸墪壿庉忳敦憞撉撴楯橔潡燉犜獤碷腞腯蜳豚踲蹾躉逇遯鈍鐓鐜頓驐duo多朵奪舵剁垛跺惰墮掇哆馱度躲踱沲咄鐸裰哚綞亸仛兊兌兌凙刴剟剫吋喥嚉嚲垜埵墮墯夛奪奲媠嫷尮崜嶞憜挅挆捶揣敓敚敠敪朶雜杕枤柁柂柮桗棰椯橢毲

18、沰沱澤痥硾綞茤袳詑誃貀趓跢跥跿躱軃鄲鄲鈬錞鍺鐸鍺陀陊隋隋隓飿饳馱駄鬌鮵鵽點e餓哦額鵝蛾扼俄訛阿遏峨娥惡厄鄂鋨諤堊鍔閼萼苊軛婀莪鱷顎腭愕呃噩鶚屙亞亜亞偽佮侉偔偽偽僫匎匼卾吪呝咢咹啞唖啈啊啐啞惡囐囮埡埡堊堨堮妸妿姶娾娿媕屵岋峉峩崿庵廅悪惡戹搕搤搹擜曷枙椏櫮唉歞歹歺洝涐湂玀珴琧痷皒睋砈砐砨砵硆硪磀礘胺蒍蕚蘁蚅蝁覨訛咯誐諤譌讍豟軛軶輵迗遌遻邑鈋鋨鍔鑩閜閼阨阸隘頞頟額顎餓餩騀鬲魤魥鱷鰪鱷鴳鵈鵝鵞鶚齃腭齾青年（）、技術（）、戀愛（）、翡翠（）、読書（）、人（，）、幸福（）、訓讀詞匯：青（）、術（）、戀（）、好（）、読（）、人（）、幸（）、漢字“?！笨梢宰x成“”也可以讀成“”?！啊笔撬囊糇x，“”是它的訓讀

19、?！笆窇椌蕖钡葷h字一般只使用它們的一種音讀，“貝又咲（）”一般只使用它們的一種訓讀，但這類漢字較少。日語里的漢字通常都有兩三種甚至更多的音訓讀發(fā)音。比如“生”，音讀可讀作“”，訓讀可讀作“”等。同上面所說的，漢字每個字都有與之對應的音讀、訓讀，但也有一些比較特殊。比如“梅雨”，它的發(fā)音為“”，不能把每個漢字分別讀什么區(qū)分開來。我們把這類發(fā)音叫做“熟字訓”。以下這些也是“熟字訓”：田舎（） 時雨（）相撲（寫作“相撲”，）土產(chǎn)（） 為替（）紅葉（）吹雪（） 足袋（）日和（）蒲公英（）en恩摁蒽嗯奀峎煾饐唔eng鞥eo仒eol乻eom欕eos旕er而二耳兒餌爾貳洱珥鮞鴯佴邇鉺侕児兒刵咡唲奶尒尓峏弍弐杒栭栮樲毦洏渪濡爾粫耏聏胹臑荋薾衈袻誀貮貳趰輀輭轜邇鉺陑陾隭餌駬髵髶鮞鴯fa發(fā)法罰伐乏筏閥琺垡砝佱傠姂廢彂拔撥撥栰橃泛沷泛灋琺疺発發(fā)瞂笩罰罸茷蕟藅貶貶醗發(fā)鍅閥髪發(fā)fan反飯翻番犯凡帆返泛繁煩販范樊藩礬釩燔蘩畈蕃蹯梵幡仮伋凢凣勫匥噃墦奿婏嬎嬏嬔忛憣払拚旙幡杋柉棥楓橎氾泛渢滼瀪瀿煩犿璠畨盕礬笲笵范籓籵緐翻羳膰舤舧舩薠蟠蠜袢