电大高等数学期末考试复习试题资料

电大高等数学期末考试复习试题资料2、函数的对应规律 例：设求 解：由于中的表达式是x+1，可将等式右端表示为x+1的形式 或：令 3、判断两个函数是否相同：定义域相同及对应规律相同 例：1、下列各函数对中，（ B ）中的两个函数相同 A、 B、 C、 D、 4、判断函数的奇偶性：若，则为偶函数；若，则为奇函数， 也可以根据一些已知的函数的奇偶性，再利用“奇函数奇函数、奇函数偶函 数仍为奇函数；偶函数偶函数、偶函数偶函数、奇函数奇函数仍为偶函数”的性质来判断。 奇函数的图像关于原点对称，偶函数的图像关于y轴对称。 例：下列函数中，（ A ）是偶函数 A B C D 5、无穷小量：极限为零的变量。性质：无穷小量和有界变量的积仍是无穷小量 例1）: 当时，下列变量为无穷小量的是（ B ）A、cosx B、ln(1+x) C、x+1 D、 2）0 6、函数在一点处极限存在的充要条件是左右极限存在且相等 ( D ) A、1 B、1 C、1 D、不存在 7、极限的计算：对于“”形 例1）2）= 8、导数的几何意义：； 例：曲线在处的切线斜率是 解：= 9、导数的计算：复合函数求导原则：由外向内，犹如剥笋，层层求导 例1）设，求 解： 例2）设，求dy 解; 10、判断函数的单调性： 例：.函数的单调减少区间是11、应用题的解题步骤：1）根据题意建立函数关系式，2）求出驻点（一阶导数=0的点），3）根据题意直接回答 例1）求曲线上的点，使其到点的距离最短 解：曲线上的点到点的距离公式为 与在同一点取到最小值，为计算方便求的最小值点，将代入得 令 令得可以验证是的最小值点，并由此解出，即曲线上的点和点到点的距离最短 2）某制罐厂要生产一种体积为V的无盖圆柱形容器，问容器的底半径与高各为多少时用料最省？ 解：设容器的底半径为，高为，则其表面积为 因为 所以 由，得唯一驻点，此时，由实际问题可知，当底半径和高时可使用料最省 12、不定积分与原函数的关系: 设 ，则称函数是的原函数., 例1）若的一个原函数为，则（ B ）A、 B、 C、 D 、 解： 2）已知，则 （答案：C）A. B. C. D. 解： 13、性质： 例1）（B ） A. B. C. D. 例2）+C 14、不定积分的计算：1）凑微分；2）分部积分 1）常用凑微分： 例1）若，则（B ） A. B. C. D. 解： 例2）计算 解： 例3)计算 解; 2）分部积分的常见类型： ，再根据分部积分公式计算 例1）计算 解： 例2）计算不定积分 解： 例3）计算 = 15、定积分的牛顿莱布尼兹公式：设F（x）是f(x)的一个原函数，则 例：若是的一个原函数，则下列等式成立的是（ B ）A. B. C. D. 16、奇偶函数在对称区间上的积分： 若是奇函数，则有 若是偶函数，则有 例1)： 分析p ：为奇函数，所以0 例2）分析p ：为偶函数 故： 17、定积分的计算：1）凑微分，2）分部积分； 定积分的凑微分和不定积分的计算相同。 例1）计算 解：利用凑微分法，得 例2）计算定积分 解：利用凑微分法，得 定积分的分部积分与不定积分的计算基本相同： 定积分的分部积分公式： 例1）计算 解： = 例2）计算 解： 例3）计算 解： 请您删除一下内容，O(_)O谢谢！20XX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 bee his own boss in November 2022. 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 exle, 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 pany 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 plement 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 pany 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 20XX, 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 ing 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, forting 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 exle, 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 petitive 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 pering 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 plexion. 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 remend 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 第 13 页 共 13 页