最新電大《經(jīng)濟數(shù)學基礎(chǔ)》形成性考核冊及參考答案【精編完整版】

1、電大經(jīng)濟數(shù)學基礎(chǔ)形成性考核冊及參考答案（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x0處可導，則( b )是錯誤的 a函數(shù)f (x)在點x0處有定義 b，但 c函數(shù)f (x)在點x0處連續(xù) d函數(shù)f (x)在點x0處可微 5.當時，下列變量是無窮小量的是（ c ）. a b c d(三)解答題1計算極限（1） （2）原式=（3） 原

2、式= = =（4）原式=（5） 原式= =（6）原式= = = 42設(shè)函數(shù)，問：（1）當為何值時，在處有極限存在？（2）當為何值時，在處連續(xù).解：(1)當 (2). 函數(shù)f(x)在x=0處連續(xù).3計算下列函數(shù)的導數(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x求導： 所以 (2) 方程兩邊對x求導： 所以 5求下列函數(shù)的二階導數(shù)：（1），求答案： (1) (2) 作業(yè)（二）（一）填空題1.若，則

3、.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，常用分部積分法計算的是（c ） a， b c d4. 下列定積分計算正確的是（ d ） a b c d 5. 下列無窮積分中收斂的是（ b ） a b c d (三)解答題1.計算下列不定積分（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）

4、答案：(+) (-) 1 (+) 0 原式=（8）答案： (+) 1 (-) 原式= = =2.計算下列定積分（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）單項選擇題1. 以下結(jié)論或等式正確的是（ c ） a若均為零矩

5、陣，則有 b若，且，則 c對角矩陣是對稱矩陣 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計算（1）=（2）（3）=2計算解 =3設(shè)矩陣，求。解 因為所以4設(shè)矩陣，確定的值，使最小。解： 所以當時，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

6、交換，則，也與可交換。證明： ， 即 ，也與可交換。2試證：對于任意方陣，是對稱矩陣。證明： ，是對稱矩陣。3設(shè)均為階對稱矩陣，則對稱的充分必要條件是：。證明：充分性 ， 必要性 ， 即為對稱矩陣。4設(shè)為階對稱矩陣，為階可逆矩陣，且，證明是對稱矩陣。證明： ， 即 是對稱矩陣。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)的駐點是，極值點是 ，它是極 值點.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，方程組有唯一解.答案：（二）單項選擇題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

7、 2 d3 x2. 已知需求函數(shù)，當時，需求彈性為（ c ）a b c d3. 下列積分計算正確的是（ a） a bc d4. 設(shè)線性方程組有無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題：(1) ,答案：原方程變形為：分離變量得：兩

8、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)矩陣變形過程為：由于秩()=2n=4，所以原方程有無窮多解，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程為：由于秩()=2n=4，所以原方程有無窮多解，其一般解為：（其中為自由未知量）。5.當為何值時，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程為：所以當時，秩()=2n=4，原方程有無窮多解，其一般解為：5為何值時，方程組答案：當且時，方程組無解；當時，方程組有唯

9、一解；當且時，方程組無窮多解。原方程的增廣矩陣變形過程為：討論：（1）當為實數(shù)時，秩()=3=n=3，方程組有唯一解； （2）當時，秩()=2n=3，方程組有無窮多解；（3）當時，秩()=3秩()=2，方程組無解；6求解下列經(jīng)濟應用問題：（1）設(shè)生產(chǎn)某種產(chǎn)品個單位時的成本函數(shù)為：（萬元）,求：當時的總成本、平均成本和邊際成本；當產(chǎn)量為多少時，平均成本最小？答案： 平均成本函數(shù)為：（萬元/單位） 邊際成本為： 當時的總成本、平均成本和邊際成本分別為： （萬元/單位） （萬元/單位）由平均成本函數(shù)求導得： 令得唯一駐點（個），（舍去）由實際問題可知，當產(chǎn)量為20個時，平均成本最小。（2）.某廠生產(chǎn)

10、某種產(chǎn)品件時的總成本函數(shù)為（元），單位銷售價格為（元/件），問產(chǎn)量為多少時可使利潤達到最大？最大利潤是多少答案：（2）解：由 得收入函數(shù) 得利潤函數(shù)： 令 解得： 唯一駐點所以，當產(chǎn)量為250件時，利潤最大，最大利潤：(元)（3）投產(chǎn)某產(chǎn)品的固定成本為36(萬元)，且邊際成本為(萬元/百臺)試求產(chǎn)量由4百臺增至6百臺時總成本的增量，及產(chǎn)量為多少時，可使平均成本達到最低解：當產(chǎn)量由4百臺增至6百臺時，總成本的增量為答案：產(chǎn)量由4百臺增至6百臺時總成本的增量為 (萬元)成本函數(shù)為：又固定成本為36萬元，所以(萬元)平均成本函數(shù)為：(萬元/百臺)求平均成本函數(shù)的導數(shù)得：令得駐點，（舍去）由實際問題可

11、知，當產(chǎn)量為6百臺時，可使平均成本達到最低。（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)量為多少時利潤最大？在最大利潤產(chǎn)量的基礎(chǔ)上再生產(chǎn)50件，利潤將會發(fā)生什么變化？答案：求邊際利潤： 令得：（件） 由實際問題可知，當產(chǎn)量為500件時利潤最大；在最大利潤產(chǎn)量的基礎(chǔ)上再生產(chǎn)50件，利潤的增量為：（元）即利潤將減少25元。 o(_)o謝謝！2015年中央電大期末復習考試小抄大全，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 westin, the sheraton, sens on

12、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 mansionsst

13、alwart. 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. i

14、t 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 the

15、ir 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 i

16、ts 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

17、 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

18、 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 g

19、ood, 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

20、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

21、 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 write

22、r 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,

23、 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. t

24、he 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

25、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 th

26、e 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. t

27、he 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 y

28、our 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 a

29、t 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

30、 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 s

31、hopping. 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

32、 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

33、 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 sh

34、ang-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,

35、 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