电大经济数学基础12复习资料参考小抄 一、单项选择题 1．下列函数中为偶函数的是（ ）． 　　(A) 　　　　　 　(B) 　　(C) 　　　　 　(D) 正确答案：A 2．下列函数中为奇函数的是（ ）． 　　(A) 　　　　　 　(B) 　　(C) 　　　　 　(D) 正确答案：B 3．下列各函数对中，（ ）中的两个函数相等． A. B. C. D. 正确答案：D 4．下列结论中正确的是（ ）． (A) 周期函数都是有界函数 (B) 基本初等函数都是单调函数 (C) 奇函数的图形关于坐标原点对称 (D) 偶函数的图形关于坐标原点对称 正确答案：C 5．下列极限存在的是（ ）． A． B． 　　 C．　　 D． 正确答案：A 6．已知，当（ ）时，为无穷小量． A. B. C. D. 正确答案：A 7．当时，下列变量为无穷小量的是（ ） A． B． C． D． 正确答案：
D 8．函数 在x = 0处连续，则k = ( )． A．-2 B．-1 C．1 D．2 正确答案：B 9.曲线在点处的切线斜率是（ ）． (A) 　　　(B) 　(C) 　 (D) 正确答案：D　 10．曲线在点（0, 1）处的切线斜率为（ ）。

A． B． C． D． 正确答案：B 11．若，则（ ）． A．0 B．1 C． 4 D．-4 正确答案：C 12．下列函数在区间上单调减少的是（ ）． (A) (B) (C) (D) 正确答案：B　 13．下列结论正确的是（ ）． (A) 若，则必是的极值点 (B) 使不存在的点，一定是的极值点 (C) 是的极值点，且存在，则必有 (D) 是的极值点，则必是的驻点 正确答案：C 14．设某商品的需求函数为，则当时，需求弹性为（ ）． A． B．－3 C．3 D． 正确答案：B 15．若函数，则 ( )． A．-2 B．-1 C．-1.5 D．1.5 正确答案：A 16．函数的连续区间是（ ）． A． B． C． D． 正确答案：A 17．设，则=（ ）． A． B． C． D． 正确答案：C 18．下列积分值为0的是（ ）． A． B． C． D． 正确答案：C 19．若是的一个原函数，则下列等式成立的是( )． A． B． C． D． 正确答案：B 20.设，，是单位矩阵，则＝（ ）． A． B． C． D． 正确答案：A 21.设为同阶方阵，则下列命题正确的是（ ）. 　　A.若，则必有或 B.若，则必有, 　　C.若秩,秩，则秩 D. 正确答案：B 22．当条件（ ）成立时，元线性方程组有解． A. B. C. D. 正确答案：D 23.设线性方程组有惟一解，则相应的齐次方程组（ ）． A．无解 B．只有0解 C．有非0解 D．解不能确定 正确答案：B 24. 设线性方程组的增广矩阵为 ，则此线性方程组的一般解中自由未知量的个数为（ ）． A．1 B．2 C．3 D．4 正确答案：B 25. 若线性方程组的增广矩阵为，则当＝（　）时线性方程组无解． (A) 　(B) 　 (C) (D) 正确答案：A 26. 设，则（　）． (A) 　(B) 　 (C) 　(D) 正确答案：D 27.设线性方程组有无穷多解的充分必要条件是（ ）． A． B． C． D． 正确答案：B 28．设线性方程组有唯一解，则相应的齐次方程组（ ）． A．只有零解 B．有非零解 C．无解 D．解不能确定 正确答案：A 29.设A为矩阵，B为矩阵，则下列运算中（ ）可以进行． A．AB B．ABT C．A+B D．BAT 正确答案：A 30. 设是可逆矩阵，且，则（ ）. A． B． C． D． 正确答案：C 31.设需求量q对价格p的函数为 ,则需求弹性为Ep=( )。

A． B. C. D. 正确答案：D 32.在无穷积分中收敛的是（ ） A. B. C. D. 正确答案：C 33. 设A为3×4矩阵,B为5×2矩阵,且乘积矩阵有意义,则C为( )矩阵. A.4×2 B. 2×4 C. 3×5 D. 5×3 正确答案：B 34. 线性方程组的解的情况是（ ） A.无解 B.只有0解 C.有唯一解 D.有无穷多解 正确答案：A 二、填空题 1．函数的定义域是　　　 　　． 正确答案：
2．函数的定义域是　　 　. 正确答案：
3．若函数，则 ． 正确答案：
4．设，则函数的图形关于　　对称． 正确答案：y轴 5．已知需求函数为，则收入函数= . 正确答案：
6．　 　　　　　． 正确答案：1 7．已知，若在内连续，则 ． 正确答案：2 8．曲线在处的切线斜率是　　． 正确答案：
9．过曲线上的一点（0，1）的切线方程为 . 正确答案：
10．函数的驻点是　　　 　　． 正确答案：
11．设，当 　 时，是对称矩阵． 正确答案：1 12．已知，当 时，为无穷小量． 正确答案：
13．齐次线性方程组（是）只有零解的充分必要条件是　　 　　　． 正确答案：
14．若，则 = . 正确答案：
15．=　　　 　． 正确答案：
16．设线性方程组，且 ，则时，方程组有唯一解． 正确答案：
17．设齐次线性方程组，且 = r < n，则其一般解中的自由未知量的个数等于 ． 正确答案：n – r 18．线性方程组的增广矩阵化成阶梯形矩阵后为 则当=　 　时，方程组有无穷多解. 正确答案：-1 19. 已知齐次线性方程组中为矩阵，则 ． 正确答案：3 20.函数的间断点是　　 　　． 正确答案：
21.若，则 　 　　． 正确答案：
三、微积分计算题 1．已知，求． 解：由导数运算法则和复合函数求导法则得 2．设，求． 解；

3．设，求． 解：由导数运算法则和复合函数求导法则得 4．设，求． 解：由导数运算法则和复合函数求导法则得 5． 解：= == 6．计算 解 7．计算 解 8．计算 解 9．计算 解 = = 10．计算 解 = 11． 解 = == 12． 解：=- == 13． = =＝=1 四、代数计算题 1．设矩阵，求． 解：因为 　 即　 所以　 2．设矩阵，是3阶单位矩阵，求． 解：由矩阵减法运算得 利用初等行变换得 　　 即　　 3. 设矩阵 A =，B =，计算(AB)-1． 解 因为AB == (AB I ) = 所以 (AB)-1= 4.解矩阵方程。

解：由，得 所以， 5．求线性方程组的一般解． 解：因为系数矩阵 所以一般解为（其中，是自由元） 6．当取何值时，线性方程组 有解？并求一般解． 解 因为增广矩阵 所以，当=0时，线性方程组有无穷多解，且一般解为：
是自由未知量〕 五、应用题 1． 投产某产品的固定成本为36（万元），且边际成本为（万元/百台）。试求产量由4百台增至6百台时总成本的增量，及产量多少时，可使平均成本达到最低？ 当产量由4百台增至6百台时，总成本的增量为 （万元） 又 令，解得。

2．已知某产品的边际成本（万元/百台），为产量（百台），固定成本为18（万元），求最低平均成本． 解：总得成本函数为 平均成本函数为 ，令，解得（百台） 因为平均成本存在最小值，且驻点唯一，所以，当产量为300台时，可使平均成本达到最低。

最低平均成本为 （万元/百台） 3．生产某产品的边际成本为(万元/百台)，边际收入为（万元/百台），其中x为产量，问(1) 产量为多少时，利润最大？(2) 从利润最大时的产量再生产2百台，利润有什么变化？ 解 （1）边际利润函数为 令 得 （百台） 又是的唯一驻点，根据问题的实际意义可知存在最大值，故是的最大值点，即当产量为10（百台）时，利润最大． （2）利润函数 即从利润最大时的产量再生产2百台，利润将减少20万元． 4．已知某产品的边际成本（元/件），固定成本为0，边际收益。问产量为多少时利润最大？在最大利润产量的基础上再生产50件，利润将会发生什么变化？ 解：因为边际利润 令，得。是唯一驻点，而该问题确实存在最大值。所以，当产量为500件时，利润最大。

当产量由500件增加至550件时，利润改变量为 即利润将减少25元。

5.设生产某产品的总成本函数为 (万元)，其中x为产量，单位：百吨．销售x百吨时的边际收入为（万元/百吨），求：(1) 利润最大时的产量；
(2) 在利润最大时的产量的基础上再生产1百吨，利润会发生什么变化？ 解：(1) 因为边际成本为，边际利润 令，得 由该题实际意义可知，为利润函数的极大值点，也是最大值点. 因此，当产量为7百吨时利润最大. (2) 当产量由7百吨增加至8百吨时，利润改变量为 （万元） 即当产量由7百吨增加至8百吨时，利润将减少1万元。

6．设生产某种产品个单位时的成本函数为：（万元）,求：⑴当时的总成本和平均成本；

⑵当产量为多少时，平均成本最小？ 解：⑴因为总成本、平均成本和边际成本分别为：
， 所以， ， ⑵ 令 ，得（舍去），可以验证是的最小值点，所以当时，平均成本最小。

7.某厂每天生产某种产品件的成本函数为（元）.为使平均成本最低，每天产量应为多少？此时，每件产品平均成本为多少？ 解：因为 == （） == 令=0，即=0，得=140，= -140（舍去）。

=140是在其定义域内的唯一驻点，且该问题确实存在最小值。

所以=140是平均成本函数的最小值点，即为使平均成本最低，每天产量应为140件. 此时的平均成本为 ==176 （元/件） 8．已知某产品的销售价格（单位：元／件）是销量（单位：件）的函数，而总成本为（单位：元），假设生产的产品全部售出，求产量为多少时，利润最大？最大利润是多少？ 解：由已知条件可得收入函数 利润函数 求导得 令得，它是唯一的极大值点，因此是最大值点． 此时最大利润为 即产量为300件时利润最大．最大利润是43500元． 9. 设生产某种产品个单位时的成本函数为：（万元）,求：⑴当时的总成本和平均成本；
⑵当产量为多少时，平均成本最小？ 解：⑴因为总成本、平均成本和边际成本分别为：
；

， 所以，；

， ⑵ 令 ，得（舍去），可以验证是的最小值点，所以当时，平均成本最小． 10.设生产某产品的总成本函数为 (万元)，其中为产量，单位：百吨．销售百吨时的边际收入为（万元/百吨），求：⑴利润最大时的产量；
⑵在利润最大时的产量的基础上再生产百吨，利润会发生什么变化？ 解：⑴因为边际成本为 ，边际利润 令，得可以验证为利润函数的最大值点. 因此，当产量为百吨时利润最大. ⑵当产量由百吨增加至百吨时，利润改变量为 （万元） 即利润将减少1万元. 11.某厂生产某种产品q件时的总成本函数为 ，单位销售价格为，问产量为多少时可使利润最大？最大利润是多少？ 解：设产量为q，则收入函数为 因为边际利润时，利润最大。

则，得 产量为250时可使利润最大 最大利润为1230元 请您删除一下内容，O(∩_∩)O谢谢！！！2015年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄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