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電大《微積分初步》（15春）期末復(fù)習(xí)考試試題及參考答案 填空題 ?、焙瘮?shù)，則 ． ⒉若，則 1 ?。?br>?、城€在處的切線斜率是 ?。?br>⒋若是的一個(gè)原函數(shù)，則 ?。?br>⒌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 ?。?br>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 ?。?nbsp; 19.若，則= ． 20.微分方程的階數(shù)為 ． 21.函數(shù)的定義域是 ?。?br>23.若函數(shù),在處連續(xù)，則 2 ． 24.曲線在點(diǎn)處的斜率是 ． 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(wú)窮小量. 29.若y = x (x – 1)(x – 2)(x – 3)，則(1) = ． 30. ． 31.微分方程的特解為 . 32.函數(shù)的定義域是 ?。?br>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. ?。?br>39.曲線在點(diǎn)處的切線方程是 ． 40.若，則 ?。?nbsp; 51.微分方程的階數(shù)為 5 ． 二、單項(xiàng)選擇題 ⒈函數(shù)的圖形關(guān)于（B?。?duì)稱． A。坐標(biāo)原點(diǎn) B。軸 C．軸 D。 ⒉當(dāng)（ C ）時(shí)，函數(shù)在處連續(xù). A．0 B．1 C． D． ⒊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 ⒋下列等式成立的是（A?。?br> A． B． C． D． ⒌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(wú)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?。?br>A. ； B. ； C. ； D. 11.設(shè)函數(shù)，則該函數(shù)是（A?。?br>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). A．0 B．1 C． D． 14.下列結(jié)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(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?。?br> A . B. C. D. 16.微分方程的階數(shù)為（B?。?br>A. 2； B. 3； C. 4； D. 5 ⒈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(wú)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2x的積分曲線族中，通過(guò)點(diǎn)（1, 4）的曲線為（ C ）． A． B． C．y = x2 + 3 D． y = x2 + 4 20.微分方程的通解是（A?。?br>A. ； B. ； C. ； D. 21.設(shè)，則（ D ） A． B． C． D． 22.若函數(shù)f (x)在點(diǎn)x0處可導(dǎo)，則( B )是錯(cuò)誤的． A．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 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?。?br>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(x0) = 0，則x0必是f (x)的極值點(diǎn) B．x0是f (x)的極值點(diǎn)，且(x0)存在，則必有(x0) = 0 C．x0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) 39.下列無(wú)窮積分收斂的是（ A?。?br> A． B． C． D． 40.微分方程的階數(shù)為（D?。?br>A. 1； B. 2； C. 3； D. 4 41.設(shè)，則（ C ） A． B． C． D． 42.若函數(shù)f (x)在點(diǎn)x0處可導(dǎo)，則( B)是錯(cuò)誤的． A．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 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) 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(wú)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 ⒈計(jì)算極限． ?、苍O(shè)，求. ⒊計(jì)算不定積分 ⒋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)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(wèn)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(kāi)口容器，怎樣做法用料最??？ 3.欲做一個(gè)底為正方形，容積為108立方米的長(zhǎng)方體開(kāi)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，解得是唯一駐點(diǎn)， 且， 說(shuō)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(kāi)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?。?br> 16分 5.用鋼板焊接一個(gè)容積為4的底為正方形的無(wú)蓋水箱，已知鋼板每平方米10元，焊接費(fèi)40元，問(wèn)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?wèn)題存在最小值，且函數(shù)的駐點(diǎn)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(wú)蓋水箱，已知鋼板每平方米10元，焊接費(fèi)40元，問(wèn)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?wèn)題存在最小值，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(kāi)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?。?br> 16分 8.欲做一個(gè)底為正方形，容積為108立方米的長(zhǎng)方體開(kāi)口容器，怎樣做法用料最省？ 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?wèn)題存在最小值，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） ?、焙瘮?shù)，則 ． ⒉當(dāng) 時(shí)，為無(wú)窮小量. ⒊若y = x (x – 1)(x – 2)(x – 3)，則(1) = ． ⒋ ?。?nbsp; ⒌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） ⒈函數(shù)的定義域是（?。?br>A． B． C． D． ⒉曲線在處切線的斜率是（ ）． A． B． C． D． ⒊下列結(jié)論正確的有（ ）． A．若(x0) = 0，則x0必是f (x)的極值點(diǎn) B．x0是f (x)的極值點(diǎn)，且(x0)存在，則必有(x0) = 0 C．x0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) ⒋下列無(wú)窮積分收斂的是（ ）． A． B． C． D． ⒌微分方程的階數(shù)為（?。?br>A. 1； B. 2； C. 3； D. 4 三、計(jì)算題（本題共44分，每小題11分） ⒈計(jì)算極限． ?、苍O(shè)，求. ⒊計(jì)算不定積分 ⒋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(wú)蓋水箱，已知鋼板每平方米10元，焊接費(fèi)40元，問(wèn)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） ?、?nbsp; ⒉0 ⒊ ⒋ ⒌ 二、單項(xiàng)選擇題（每小題4分，本題共20分） ?、盋 ⒉ D ?、矪 ⒋A ?、?nbsp;D 三、（本題共44分，每小題11分） ⒈解： ⒉解： ⒊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?wèn)題存在最小值，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)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(wú)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?。?！2015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(guò)小抄After earning his spurs in the kitchens of The Westin, The Sheraton, Sens on the Bund, and a sprinkling of other top-notch venues, Simpson Lu fi nally got the chance to become his own boss in November 2010. 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 this Sinan Mansions'stalwart. 'It’s 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 example, these jobs are strictly demarcated, so it’s a great opportunity to learn how a business operates 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 CPK’s China debut. 'For sure it was a big step, and unlike all their other Asia operations that are franchises, they decided to manage it directly to begin 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 hand to ensure the business adheres to its ethos of creating 'innovative, hearth-baked pizzas', a slice 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 change the toppings. Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the toppings perfectly.' The largely local customer base evidently agrees and on Saturday and Sunday, at least, the place is teeming. The kids-eat-for-free policy at weekends is undoubtedly a big draw, as well as is the spacious second-fl oor layout overlooked by a canopy of green from Fuxing 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 enough to admit that business could be better; as good, in fact, as in CPK’s 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 hasn’t been easy for any of the tenants here,' adds Simpson. 'We’re planning a third outlet in the city in 2015, and we will probably choose a shopping mall again because of the better foot traffic.' The tearooms once frequented by Coco Chanel and Marcel Proust are upping sticks and coming to Shanghai, Xu Junqian visits the Parisian outpost with 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 particular. One of the most popular tearooms in Paris, Angelina is famous for having once been frequented by celebrities such as Chanel and writer Marcel Proust. Now Angelina has packed up its French ambience, efficient service, and beautiful, comforting desserts and flown them to Shanghai. At the flagship dine-in and take-out space in Shanghai, everything mimics the original tearoom designed from the beginning of the 20th century, in Paris, the height of 'Belle Epoque'. The paintings on the wall, for example, are exactly the same as the one that depicts 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 afternoon for hot chocolate. The famous hot chocolate, known as L’Africain, is a luxurious mixture of four types of cocoa beans imported from Africa, blended in Paris and then shipped to Shanghai. It’s sinfully sweet, rich and thick as if putting a bar of melting chocolate directly on the tongue and the fresh whipped 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 top, the vanilla cream like stuffing, and the meringue as base. Get all three layers in one scoop, not only for the different textures but also various flavors of sweetness. The dessert has maintained its popularity for a century, even in a country like France, perhaps the world’s most competitive place for desserts. A much overlooked pairing, is the Paris-New York choux pastry and N226 chocolate flavored tea. The choux 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 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 mix of different styles of French cuisines', according to the management team. The semi-cooked foie gras terrine, is seductive and deceptive. It’s generously served at the size and shape of a toast, while the actual brioche toast is baked into a curved slice dipped with fig chutney. The flavor, however, is honest: strong, smooth and sublime. And you don’t actually need the toast for crunchiness. This is the season for high teas, with dainty cups of fine china and little pastries that appeal to both visual and physical appetites. But there is one high tea with a difference, and Pauline D. Loh finds out just exactly 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 for those who prefer savory to sweet, there is still the selection of classic 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 sufficiently robust to take the edge off the hunger that strikes hours after lunch. The afternoon tea special at Shang-Xi at the Four Seasons Hotel Pudong has just the right elements. It is a pampering meal, with touches of luxury that make the high tea session a treat in itself. Whole baby abalones are braised and then topped on a shortcrust pastry shell, 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-Xi, has scored a winner again. Sweet prawns and aromatic truffles — what’s not to love? His masterful craftsmanship is exhibited in yet another pastry — a sweet pastry that is shaped to look like a walnut, but which you can put straight into the mouth. It crumbles immediately, and the slightly sweet, nutty morsel is so easy to eat you’ll 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 bird’s nest – made with ingredients that resonate with every female soul. It does taste like ambrosia, with the sweet-sour fragrance of the mango forming the first layer of taste and sensation, and the pomelo sacs and sago pearls providing the tactile contrast. The bird’s nest — it’s the ingredient that gilds the lily, since it is supposed to nourish and nurture a perfect complexion. For those unfamiliar with this exotic ingredient, the bird’s nest is not a bundle of twigs, but is, instead, the dried secretion that cave swifts use to build their nest. Technically, it’s bird saliva, but the Chinese believe that it has collagen-boosting properties essential to beauty. To me, it just tastes good, adding a slight gelatinous crunch to the back of the teeth. There is also a baked mushroom puff pastry that includes the highly prized Matsutake or pine mushroom. You also get a choice of teas, but I strongly recommend the aged Pu’er from Yunnan province. It is a mellow tea that will go perfectly with the rich little nuggets, and will warm you up on a cold afternoon. Incidentally, the general guide is green tea such as Longjing or Dragonwell for the hot season, semi-fermented teas like Wu-long or Iron Buddha for autumn, and more warming teas like Pu’er for winter. The Shang-Xi afternoon tea costs 228 yuan ($37) per person, and 388 yuan for the more opule |
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