電大《經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ)》形成性考核冊(cè)及參考答案.doc

電大經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ)形成性考核冊(cè)及參考答案（一）填空題1.答案：02.設(shè)，在處連續(xù)，則.答案：13.曲線在的切線方程是 .答案：4.設(shè)函數(shù)，則.答案：5.設(shè)，則.答案：（二）單項(xiàng)選擇題1. 函數(shù)的連續(xù)區(qū)間是（ D ）A B C D或 2. 下列極限計(jì)算正確的是（ B ）A. B.C. D.3. 設(shè)，則（B ） A B C D4. 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 5.當(dāng)時(shí)，下列變量是無(wú)窮小量的是（ C ）. A B C D(三)解答題1計(jì)算極限（1） （2）原式=（3） 原式= = =（4）原式=（5） 原式= =（6）原式= = = 42設(shè)函數(shù)，問(wèn)：（1）當(dāng)為何值時(shí)，在處有極限存在？（2）當(dāng)為何值時(shí)，在處連續(xù).解：(1)當(dāng) (2). 函數(shù)f(x)在x=0處連續(xù).3計(jì)算下列函數(shù)的導(dǎo)數(shù)或微分：（1），求答案：（2），求答案：（3），求答案：（4），求答案：=（5），求答案： （6），求答案： （7），求答案： = （8），求答案：（9），求答案： = = =（10），求答案：4.下列各方程中是的隱函數(shù)，試求或(1) 方程兩邊對(duì)x求導(dǎo)： 所以 (2) 方程兩邊對(duì)x求導(dǎo)： 所以 5求下列函數(shù)的二階導(dǎo)數(shù)：（1），求答案： (1) (2) 作業(yè)（二）（一）填空題1.若，則.答案：2. .答案：3. 若，則 .答案：4.設(shè)函數(shù).答案：05. 若，則.答案：（二）單項(xiàng)選擇題1. 下列函數(shù)中，（ D ）是xsinx2的原函數(shù) Acosx2 B2cosx2 C-2cosx2 D-cosx2 2. 下列等式成立的是（ C ） A B C D3. 下列不定積分中，常用分部積分法計(jì)算的是（C ） A， B C D4. 下列定積分計(jì)算正確的是（ D ） A B C D 5. 下列無(wú)窮積分中收斂的是（ B ） A B C D (三)解答題1.計(jì)算下列不定積分（1）原式= = （2）答案：原式= =（3）答案：原式=（4）答案：原式=（5）答案：原式= =（6）答案：原式=（7）答案：(+) (-) 1 (+) 0 原式=（8）答案： (+) 1 (-) 原式= = =2.計(jì)算下列定積分（1）答案：原式=（2）答案：原式=（3）答案：原式=（4）答案： (+) (-)1 (+)0 原式= =（5）答案： (+) (-) 原式= =（6）答案：原式=又 (+) (-)1 - (+)0 =故：原式=作業(yè)三（一）填空題1.設(shè)矩陣，則的元素.答案：32.設(shè)均為3階矩陣，且，則=. 答案：3. 設(shè)均為階矩陣，則等式成立的充分必要條件是 .答案：4. 設(shè)均為階矩陣，可逆，則矩陣的解.答案：5. 設(shè)矩陣，則.答案：（二）單項(xiàng)選擇題1. 以下結(jié)論或等式正確的是（ C ） A若均為零矩陣，則有 B若，且，則 C對(duì)角矩陣是對(duì)稱矩陣 D若，則2. 設(shè)為矩陣，為矩陣，且乘積矩陣有意義，則為（ A ）矩陣 A B C D 3. 設(shè)均為階可逆矩陣，則下列等式成立的是（C ） A， B C D 4. 下列矩陣可逆的是（ A ） A B C D 5. 矩陣的秩是（ B ） A0 B1 C2 D3 三、解答題1計(jì)算（1）=（2）（3）=2計(jì)算解 =3設(shè)矩陣，求。解 因?yàn)樗?設(shè)矩陣，確定的值，使最小。解： 所以當(dāng)時(shí)，秩最小為2。5求矩陣的秩。答案：解：所以秩=2。6求下列矩陣的逆矩陣：（1）答案解：所以。 （2）A =答案解：所以。 7設(shè)矩陣，求解矩陣方程答案： 四、證明題1試證：若都與可交換，則，也與可交換。證明： ， 即 ，也與可交換。2試證：對(duì)于任意方陣，是對(duì)稱矩陣。證明： ，是對(duì)稱矩陣。3設(shè)均為階對(duì)稱矩陣，則對(duì)稱的充分必要條件是：。證明：充分性 ， 必要性 ， 即為對(duì)稱矩陣。4設(shè)為階對(duì)稱矩陣，為階可逆矩陣，且，證明是對(duì)稱矩陣。證明： ， 即 是對(duì)稱矩陣。作業(yè)（四）（一）填空題1.函數(shù)在區(qū)間內(nèi)是單調(diào)減少的.答案：2. 函數(shù)的駐點(diǎn)是，極值點(diǎn)是 ，它是極 值點(diǎn).答案：，小3.設(shè)某商品的需求函數(shù)為，則需求彈性 .答案：4.行列式.答案：45. 設(shè)線性方程組，且，則時(shí)，方程組有唯一解.答案：（二）單項(xiàng)選擇題1. 下列函數(shù)在指定區(qū)間上單調(diào)增加的是（ B ）Asinx Be x Cx 2 D3 x2. 已知需求函數(shù)，當(dāng)時(shí)，需求彈性為（ C ）A B C D3. 下列積分計(jì)算正確的是（ A） A BC D4. 設(shè)線性方程組有無(wú)窮多解的充分必要條件是（ D ）A B C D 5. 設(shè)線性方程組，則方程組有解的充分必要條件是（ C ）A B C D三、解答題1求解下列可分離變量的微分方程：(1) 答案：原方程變形為： 分離變量得： 兩邊積分得： 原方程的通解為：（2）答案：分離變量得：兩邊積分得：原方程的通解為：2. 求解下列一階線性微分方程：（1）答案：原方程的通解為： （2）答案：原方程的通解為： 3.求解下列微分方程的初值問(wèn)題：(1) ,答案：原方程變形為：分離變量得：兩邊積分得：原方程的通解為：將代入上式得：則原方程的特解為：(2),答案：原方程變形為：原方程的通解為： 將代入上式得：則原方程的特解為：4.求解下列線性方程組的一般解：（1）答案：原方程的系數(shù)矩陣變形過(guò)程為：由于秩()=2<n=4，所以原方程有無(wú)窮多解，其一般解為：（其中為自由未知量）。（2）答案：原方程的增廣矩陣變形過(guò)程為：由于秩()=2<n=4，所以原方程有無(wú)窮多解，其一般解為：（其中為自由未知量）。5.當(dāng)為何值時(shí)，線性方程組有解，并求一般解。答案：原方程的增廣矩陣變形過(guò)程為：所以當(dāng)時(shí)，秩()=2<n=4，原方程有無(wú)窮多解，其一般解為：5為何值時(shí)，方程組答案：當(dāng)且時(shí)，方程組無(wú)解；當(dāng)時(shí)，方程組有唯一解；當(dāng)且時(shí)，方程組無(wú)窮多解。原方程的增廣矩陣變形過(guò)程為：討論：（1）當(dāng)為實(shí)數(shù)時(shí)，秩()=3=n=3，方程組有唯一解； （2）當(dāng)時(shí)，秩()=2<n=3，方程組有無(wú)窮多解；（3）當(dāng)時(shí)，秩()=3秩()=2，方程組無(wú)解；6求解下列經(jīng)濟(jì)應(yīng)用問(wèn)題：（1）設(shè)生產(chǎn)某種產(chǎn)品個(gè)單位時(shí)的成本函數(shù)為：（萬(wàn)元）,求：當(dāng)時(shí)的總成本、平均成本和邊際成本；當(dāng)產(chǎn)量為多少時(shí)，平均成本最小？答案： 平均成本函數(shù)為：（萬(wàn)元/單位） 邊際成本為： 當(dāng)時(shí)的總成本、平均成本和邊際成本分別為： （萬(wàn)元/單位） （萬(wàn)元/單位）由平均成本函數(shù)求導(dǎo)得： 令得唯一駐點(diǎn)（個(gè)），（舍去）由實(shí)際問(wèn)題可知，當(dāng)產(chǎn)量為20個(gè)時(shí)，平均成本最小。（2）.某廠生產(chǎn)某種產(chǎn)品件時(shí)的總成本函數(shù)為（元），單位銷售價(jià)格為（元/件），問(wèn)產(chǎn)量為多少時(shí)可使利潤(rùn)達(dá)到最大？最大利潤(rùn)是多少答案：（2）解：由 得收入函數(shù) 得利潤(rùn)函數(shù)： 令 解得： 唯一駐點(diǎn)所以，當(dāng)產(chǎn)量為250件時(shí)，利潤(rùn)最大，最大利潤(rùn)：(元)（3）投產(chǎn)某產(chǎn)品的固定成本為36(萬(wàn)元)，且邊際成本為(萬(wàn)元/百臺(tái))試求產(chǎn)量由4百臺(tái)增至6百臺(tái)時(shí)總成本的增量，及產(chǎn)量為多少時(shí)，可使平均成本達(dá)到最低解：當(dāng)產(chǎn)量由4百臺(tái)增至6百臺(tái)時(shí)，總成本的增量為答案：產(chǎn)量由4百臺(tái)增至6百臺(tái)時(shí)總成本的增量為 (萬(wàn)元)成本函數(shù)為：又固定成本為36萬(wàn)元，所以(萬(wàn)元)平均成本函數(shù)為：(萬(wàn)元/百臺(tái))求平均成本函數(shù)的導(dǎo)數(shù)得：令得駐點(diǎn)，（舍去）由實(shí)際問(wèn)題可知，當(dāng)產(chǎn)量為6百臺(tái)時(shí)，可使平均成本達(dá)到最低。（4）已知某產(chǎn)品的邊際成本=2（元/件），固定成本為0，邊際收益，求： 產(chǎn)量為多少時(shí)利潤(rùn)最大？在最大利潤(rùn)產(chǎn)量的基礎(chǔ)上再生產(chǎn)50件，利潤(rùn)將會(huì)發(fā)生什么變化？答案：求邊際利潤(rùn)： 令得：（件） 由實(shí)際問(wèn)題可知，當(dāng)產(chǎn)量為500件時(shí)利潤(rùn)最大；在最大利潤(rùn)產(chǎn)量的基礎(chǔ)上再生產(chǎn)50件，利潤(rùn)的增量為：（元）即利潤(rùn)將減少25元。 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 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 example, these jobs are strictly demarcated, so its 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 CPKs 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 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 tenants here," adds Simpson. "Were 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 LAfricain, is a luxurious mixture of four types of cocoa beans imported from Africa, blended in Paris and then shipped to Shanghai. Its 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 worlds 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. Its 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 dont 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 whats 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 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 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 birds nest its 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 birds nest is not a bundle of twigs, but is, instead, the dried secretion that cave swifts use to build their nest. Technically, its 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 Puer 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 Puer for winter. The Shang-Xi afternoon tea costs 228 yuan ($37) per person, and 388 yuan for the more opule