電大《微積分初步》（15春）期末復(fù)習(xí)考試試題及參考答案.doc

1、電大微積分初步（15春）期末復(fù)習(xí)考試試題及參考答案電大微積分初步（15春）期末復(fù)習(xí)考試試題及參考答案 一、 填空題 函數(shù)，則 若，則1 曲線在處的切線斜率是 若是的一個(gè)原函數(shù)，則 為 4 階微分方程. 6.函數(shù)，則 7.若函數(shù),在處連續(xù)，則3 8.曲線在點(diǎn)處的切線方程是 1 9. 10.微分方程的階數(shù)為 3 11.函數(shù)的定義域是 12.若，則2 13.曲線在點(diǎn)處的切線方程是 14. 0 15.微分方程的特解為 16.函數(shù)的定義域是 17.函數(shù)的間斷點(diǎn)是= 18.函數(shù)的單調(diào)增加區(qū)間是 19.若，則= 20.微分方程的階數(shù)為 21.函數(shù)的定義域是 23.若函數(shù),在處連續(xù)，則2 24.曲線在點(diǎn)處的斜

2、率是 25. 26.微分方程滿足初始條件的特解為 27.函數(shù)，則 28.當(dāng)0時(shí)，為無窮小量.29.若y = ( 1)( 2)( 3)，則(1) = 30. 31.微分方程的特解為 . 32.函數(shù)的定義域是 33.若函數(shù),在處連續(xù)，則1 34.曲線在點(diǎn)處的切線方程是 35. 36.微分方程的階數(shù)為 37函數(shù)，則 38. 39.曲線在點(diǎn)處的切線方程是 40.若，則 51.微分方程的階數(shù)為 5 二、單項(xiàng)選擇題 函數(shù)的圖形關(guān)于（B）對(duì)稱 A。坐標(biāo)原點(diǎn)B。軸 C軸D。 當(dāng)（ C ）時(shí)，函數(shù)在處連續(xù).A0 B1 CD 函數(shù)在區(qū)間是（ D ） A單調(diào)減少 B單調(diào)增加 C先減后增 D先增后減 下列等式成立的是

3、（A） AB C D 微分方程的通解為（B） A.； B.； C.； D. 6.設(shè)函數(shù)，則該函數(shù)是（A） 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) 7.已知，當(dāng)（ D ）時(shí)，為無窮小量.A B C D 8.函數(shù)在區(qū)間是（ C ） A單調(diào)增加 B單調(diào)減少 C先增后減 D先減后增 9.以下等式成立的是（ A ） A B C D 10.下列微分方程中為可分離變量方程的是（B） A.； B.； C.； D. 11.設(shè)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) 12.當(dāng)（ C ）時(shí)，函數(shù)，在處連續(xù).A0 B1 CD 14.下列結(jié)論中（ C ）正確 A在處連續(xù)，則一定在

4、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.15.下列等式中正確的是（D） A .B.C.D. 16.微分方程的階數(shù)為（B） A.2； B.3； C.4； D.5 設(shè)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) 17.當(dāng)時(shí)，下列變量中為無窮小量的是（C ）.A B C D 18.設(shè)，則（D ） A B C D 19.在切線斜率為2的積分曲線族中，通過點(diǎn)（1, 4）的曲線為（ C ） A B Cy = 2 + 3 D y = 2 + 4 20.微分方程的通解是（A） A.；B.；C.； D. 21.

5、設(shè)，則（ D ） A B CD 22.若函數(shù)f ()在點(diǎn)處可導(dǎo)，則( B )是錯(cuò)誤的 A函數(shù)f ()在點(diǎn)處有定義 B，但 C函數(shù)f ()在點(diǎn)處連續(xù) D函數(shù)f ()在點(diǎn)處可微 33.函數(shù)在區(qū)間是（ A ） A先減后增 B先增后減 C單調(diào)減少 D單調(diào)增加 34.若，則（ B ）. A. B.C.D. 35.微分方程的階數(shù)為（C） A.1 B.2 C.3 D.5 36.函數(shù)的定義域是（C） A B C D 37.曲線在處切線的斜率是（ D ） A B C D 38.下列結(jié)論正確的有（ B ） A若() = 0，則必是f ()的極值點(diǎn) B是f ()的極值點(diǎn)，且()存在，則必有() = 0 C是f ()

6、的極值點(diǎn)，則必是f ()的駐點(diǎn) D使不存在的點(diǎn)，一定是f ()的極值點(diǎn) 39.下列無窮積分收斂的是（A） AB C D 40.微分方程的階數(shù)為（D） A.1；B.2；C.3； D.4 41.設(shè)，則（ C ） A B CD 42.若函數(shù)f ()在點(diǎn)處可導(dǎo)，則( B)是錯(cuò)誤的 A函數(shù)f ()在點(diǎn)處有定義 B，但 C函數(shù)f ()在點(diǎn)處連續(xù) D函數(shù)f ()在點(diǎn)處可微 43.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 44.（ A ） A.B.C. D. 45.下列微分方程中為可分離變量方程的是（B） A.； B.； C.； D. 46.設(shè)函數(shù)，則該函數(shù)是（d） A非奇非偶函數(shù)

7、B既奇又偶函數(shù)C偶函數(shù) D奇函數(shù) 47.當(dāng)時(shí)，下列變量中為無窮小量的是（ c ）.A B C D 48.下列函數(shù)在指定區(qū)間上單調(diào)減少的是（ b ） A B C D 49.設(shè)，則（c ） A. B. C. D. 50.下列微分方程中，（a ）是線性微分方程 A B C D 三、計(jì)算題 計(jì)算極限 設(shè)，求. 計(jì)算不定積分 計(jì)算定積分 5.計(jì)算極限 6.設(shè)，求. 7.計(jì)算不定積分 8.計(jì)算定積分 9.計(jì)算極限 解：原式 10.設(shè)，求.解： 11.計(jì)算不定積分 解：= 12.計(jì)算定積分 解： 13.計(jì)算極限 解：原式 14.設(shè)，求.解： 9分 15.計(jì)算不定積分 解：= 16.計(jì)算定積分 解： 17.計(jì)

8、算極限 解：原式 18.設(shè)，求.解： 19.計(jì)算不定積分 解：= 20.計(jì)算定積分 解： 21.計(jì)算極限 解： 22.設(shè)，求.解： 23.計(jì)算不定積分 解：= 24.計(jì)算定積分 解： 25.計(jì)算極限 解：原式 26.設(shè)，求.解： 9分 27.計(jì)算不定積分 解：= 28.計(jì)算定積分 解： 29.計(jì)算極限 解：原式 30.設(shè)，求.解： 31.計(jì)算不定積分 解：= 32.計(jì)算定積分 解： 四、應(yīng)用題 1.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??？ 2.欲做一個(gè)底為正方形，容積為32立方米的長(zhǎng)方體開口容器，怎樣做法用料最??？ 3.欲做一個(gè)底為正方形，容積為1

9、08立方米的長(zhǎng)方體開口容器，怎樣做法用料最省？ 解：設(shè)底邊的邊長(zhǎng)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。 4.欲做一個(gè)底為正方形，容積為32立方米的長(zhǎng)方體開口容器，怎樣做法用料最??？ 解：設(shè)底邊的邊長(zhǎng)為，高為，用材料為，由已知 令，解得是惟一駐點(diǎn)，易知是函數(shù)的極小值點(diǎn)，此時(shí)有，所以當(dāng)，時(shí)用料最省 16分 5.用鋼板焊接一個(gè)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(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？ 解：設(shè)水箱的底邊長(zhǎng)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)

10、唯一，所以，當(dāng)時(shí)水箱的面積最小. 此時(shí)的費(fèi)用為 （元） 6.用鋼板焊接一個(gè)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(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？ 解：設(shè)水箱的底邊長(zhǎng)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） 7.欲做一個(gè)底為正方形，容積為32立方米的長(zhǎng)方體開口容器，怎樣做法用料最省？ 解：設(shè)底邊的邊長(zhǎng)為，高為，用材料為，由已知 令，解得是惟一駐點(diǎn)，易知是函數(shù)的極小值點(diǎn)，此時(shí)有，所以當(dāng)，時(shí)用料最省 16分 8.欲做一個(gè)底為正方形，容積為108立方米的長(zhǎng)方體

11、開口容器，怎樣做法用料最??？ 解：設(shè)長(zhǎng)方體底邊的邊長(zhǎng)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. 微積分初步考試仿真試題 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 = ( 1)( 2)( 3)，則(1) = 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） 函數(shù)的定義域是（） A B C 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() = 0，則必是f ()的極值點(diǎn) B是f ()的極值點(diǎn)，且()存在，則必有() = 0 C是f ()的極

12、值點(diǎn)，則必是f ()的駐點(diǎn) D使不存在的點(diǎn)，一定是f ()的極值點(diǎn) 下列無窮積分收斂的是（） AB 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？ 微積分初步模擬試題答案 （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：

13、 解：= 4解： 四、應(yīng)用題（本題16分） 解：設(shè)水箱的底邊長(zhǎng)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） 微積分初步 期末復(fù)習(xí)指導(dǎo) 考試方式： 閉卷筆試，90分鐘。 考核形式與考核成績(jī)確定 考核形式：作業(yè)考核和期末考試相結(jié)合。 考核成績(jī)：滿分為100分，60分為及格，其中平時(shí)作業(yè)成績(jī)占考核成績(jī)的30，期末 考試成績(jī)占考核成績(jī)的70。 在考題試卷中為學(xué)生提供導(dǎo)數(shù)與積分的基本公式。 一、函數(shù)、極限與連續(xù)考核要求 1了解常量和變量的概念；理解函數(shù)的概念；了解初等函數(shù)和分段函數(shù)的概念.熟練掌握求函數(shù)的定義域、函數(shù)

14、值的方法；掌握將復(fù)合函數(shù)分解成較簡(jiǎn)單函數(shù)的方法。 2了解極限概念，會(huì)求簡(jiǎn)單極限。 3了解函數(shù)連續(xù)的概念，會(huì)判斷函數(shù)的連續(xù)性，并會(huì)求函數(shù)的間斷點(diǎn)。 二、 導(dǎo)數(shù)與微分部分考核要求 1了解導(dǎo)數(shù)概念，會(huì)求曲線的切線方程。 2熟練掌握求導(dǎo)數(shù)的方法(導(dǎo)數(shù)基本公式、導(dǎo)數(shù)的四則運(yùn)算法則、復(fù)合函數(shù)求導(dǎo)法則)，會(huì)求簡(jiǎn)單的隱函數(shù)的導(dǎo)數(shù)。 3了解微分的概念，掌握求微分的方法。 4了解高階導(dǎo)數(shù)的概念，掌握求顯函數(shù)的二階導(dǎo)數(shù)的方法。 三、導(dǎo)數(shù)應(yīng)用考核要求 1掌握函數(shù)單調(diào)性的判別方法。 2了解極值概念和極值存在的必要條件，掌握極值判別的方法。 3掌握求函數(shù)最大值和最小值的方法。 四、一元函數(shù)積分考核要求 1理解原函數(shù)與不定

15、積分的概念、性質(zhì)，掌握積分基本公式，掌握用直接積分法、第一換元積分法和分部積分法求不定積分的方法。 2了解定積分的概念、性質(zhì)，會(huì)計(jì)算一些簡(jiǎn)單的定積分。 3了解廣義積分的概念，會(huì)計(jì)算簡(jiǎn)單的無窮限積分。 五、積分應(yīng)用考核要求 1會(huì)用定積分計(jì)算簡(jiǎn)單的平面曲線圍成圖形的面積（直角坐標(biāo)系）和繞坐標(biāo)軸旋轉(zhuǎn)生成的旋轉(zhuǎn)體體積。 2了解微分方程的幾個(gè)概念，掌握變量可分離的微分方程和一階線性微分方程的解法。 請(qǐng)您刪除一下內(nèi)容，O()O謝謝！20年中央電大期末復(fù)習(xí)考試小抄大全，電大期末考試必備小抄，電大考試必過小抄After earning his spurs in the kitchens of The West

16、in, The Sheraton, Sens on the Bund, and a sprinkling of other -notch venues, Simpson Lu fi nally got the chance to become his own boss in November 2021.Sort of.The Shanghai-born chef might not actually own California Pizza Kitchen (CPK) but he is in sole charge of both kitchen and frontof- house at

17、this Sinan Mansionsstalwart.  “Its certainly a responsibility to be the head chef, and then to have to manage the rest of the restaurant as well,“ the 31-year-old tells Enjoy Shanghai.“In hotels, for ele, these jobs are strtly demarcated, so its a great opportunity to learn how a business opera

18、tes across the board.“  It was a task that management back in sunny California evidently felt he was ready for, and a vote of confi dence from a company that, to date, has opened 250 outlets in 11 countries.And for added pressure, the Shanghai branch was also CPKs China debut.  “For sure i

19、t was a big step, and unlike all their other Asia operations that are franchises, they decided to manage it directly to ben with,“ says Simpson.  Two years ago a private franchisee took over the lease, but the links to CPK headquarters are still strong, with a mainland-based brand ambassador on

20、 hand to ensure the business adheres to its ethos of creating “innovative, hearth-baked pizzas“, a sle of PR blurb that Simpson insists lives up to the hype.  “They are very innovative,“ he says.“The problem with most fast food places is that they use the same sauce on every pizza and just chan

21、ge the pings.Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the pings perfectly.“  The largely local customer base evidently agrees and on Saturday and Sunday, at least, the place is teeming.The kids-eat-for-free poly at weekends is undoubtedly a big

22、draw, as well as is the spacious second-fl oor layout overlooked by a canopy of green from Fuing Park over the road.  The company is also focusing on increasing brand recognition and in recent years has taken part in outside events such as the regular California Week.Still, the sta are honest e

23、nough to admit that business could be better; as good, in fact, as in CPKs second outlet in the popular Kerry Parkside shopping mall in Pudong.  “Sinan Mansions has really struggled to get the number of visitors that were envisaged when it first opened, and it hasnt been easy for any of the ten

24、ants here,“ adds Simpson.“Were planning a third outlet in the city in 20, and we will probably choose a shopping mall again because of the better foot traff.“ The tearooms once frequented by Coco Chanel and Marcel Proust are upping stks and coming to Shanghai, u Junqian visits the Parisian outpost w

25、ith sweet treats.One thing the century-old Parisian tearoom Angelina has shown is that legendary fashion designer Coco Chanel not only had style and glamor but also boasted great taste in food, pastries in partular.One of the most popular tearooms in Paris, Angelina is famous for having once been fr

26、equented by celebrities such as Chanel and writer Marcel Proust.Now Angelina has packed up its French ambience, effient serve, and beautiful, comforting desserts and flown them to Shanghai. At the flagship dine-in and take-out space in Shanghai, everything mims the orinal tearoom designed from the b

27、enning of the 20th century, in Paris, the height of “Belle Epoque“.The paintings on the wall, for ele, are eactly the same as the one that depts the landscape of southern France, the hometown of the owner; and the small tables are intentional imitations of the ones that Coco Chanel once sat at every

28、 afternoon for hot chocolate.The famous hot chocolate, known as LAfrain, is a luurious miture of four types of cocoa beans imported from Afra, blended in Paris and then shipped to Shanghai.Its sinfully sweet, rh and thk as if putting a bar of melting chocolate directly on the tongue and the fresh wh

29、ipped cream on the side makes a light, but equally gratifying contrast.It is also sold in glass bottles as takeaway.The signature Mont-Blanc chestnut cake consists of three parts: the pureed chestnut on , the vanilla cream like stuffing, and the meringue as base.Get all three layers in one scoop, no

30、t only for the different tetures but also various flavors of sweetness.The dessert has maintained its popularity for a century, even in a country like France, perhaps the worlds most competitive place for desserts.A much overlooked pairing, is the Paris-New York chou pastry and N226 chocolate flavor

31、ed tea.The chou pastry is a mouthful of airy pecan-flavored whipped cream, while the tea, a blend of black teas from China and Ceylon, cocoa and rose petals, offers a more subtle fragrance of flowers and chocolate.Ordering these two items, featuring a muted sweetness, makes it easier for you to fit

32、into your little black dress.Breakfast, brunch, lunch and light supper are also served at the tearoom, “a hub of many cultures“ and takes in “a mi of different styles of French cuisines“, according to the management team.The semi-cooked foie gras terrine, is seductive and deceptive.Its generously se

33、rved at the size and shape of a toast, while the actual brioche toast is baked into a curved sle dipped with fig chutney.The flavor, however, is honest: strong, smooth and sublime.And you dont actually need the toast for crunchiness.This is the season for high teas, with dainty cups of fine china an

34、d little pastries that eal to both visual and physal etites.But there is one high tea with a difference, and Pauline D.Loh finds out just eactly why it is special.Earl Grey tea and macarons are all very well for the crucial recuperative break in-between intensive bouts of holiday season shopping.And

35、 for those who prefer savory to sweet, there is still the selection of class Chinese snacks called dim sum to satisfy and satiate.High tea is a meal to eat with eye and mouth, an in-between indulgence that should be light enough not to spoil dinner, but suffiently robust to take the edge off the hun

36、ger that strikes hours after lunch.The afternoon tea special at Shang-i at the Four Seasons Hotel Pudong has just the right elements.It is a pering meal, with touches of luury that make the high tea session a treat in itself.Whole baby abalones are braised and then ped on a shortcrust pastry shell,

37、a sort of Chinese version of the Western vol-au-vent, but classier.Even classier is the dim sum staple shrimp dumpling or hargow, upgraded with the addition of slivers of midnight dark truffles.This is a master touch, and chef Simon Choi, who presides unchallenged at Shang-i, has scored a ner again.

38、Sweet prawns and aromat truffles whats not to love? His masterful craftsmanship is ehibited in yet another pastry a sweet pastry that is shaped to look like a walnut, but whh you can put straight into the mouth.It crumbles immediately, and the slightly sweet, nutty morsel is so easy to eat youll probably reach straight for another.My favorite is the dessert that goes by the name yangzhi ganlu, or ambrosia from the gods.The hotel calls it chilled mango cream with sago, pomelo and birds nest made with ingredients that resonate wit