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高等数学基础试题类型高等数学基础试题类型分为单项选择题、填空题、计算题和应用题。单项选择题的形式为四选一，即在每题的四个备选答案中选出一个正确答案；填空题只要求直接填写结果，不必写出计算过程和推理过程；计算题或应用题要求写出文字说明、演算步骤或推证过程。四种题型分数的百分比为：单项选择题20%，填空题20%，计算题44%，应用题16%。 期末考试采用闭卷笔试形式，卷面满分为100分，考试时间为90分钟。高等数学基础模拟题 一、单项选择题1.函数的图形关于（A）对称(A) 坐标原点 (B) 轴(C) 轴 (D) 2.在下列指定的变化过程中，（C）是无穷小量(A) (B) (C) (D) 3.设在可导，则（C）(A) (B) (C) (D) 4.若，则（B）(A) (B) (C) (D) 5.下列积分计算正确的是（D）(A) (B) (C) (D) 6.设函数的定义域为，则函数的图形关于（A）对称(A) (B) 轴 (C) 轴 (D) 坐标原点7.当时，变量（C）是无穷小量(A) (B) (C) (D) 8.设，则（B）(A) (B) (C) (D) 9.（A）(A) (B) (C) (D) 10.下列无穷限积分收敛的是（B）(A) (B) (C) (D) 二、填空题（每小题3分，共15分）1.函数的定义域是2.若函数，在处连续，则 3.曲线在处的切线斜率是3 4.函数的单调增加区间是5.若，则 6.函数的定义域是7.函数的间断点是8.曲线在处的切线斜率是 9.函数的单调减少区间是 10. 三、计算题（每小题11分，共44分）1.计算极限 解：2.设，求 解： 3.计算不定积分 解：由换元积分法得4.计算定积分解：由分部积分法得 5.计算极限解：6.设，求 解： 7.计算不定积分 解： 8.计算定积分 解： 四、应用题（本题16分）1、某制罐厂要生产一种体积为V的有盖圆柱形容器，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，则其表面积为由，得唯一驻点，由实际问题可知，当时可使用料最省，此时，即当容器的底半径与高分别为与时，用料最省2、圆柱体上底的中心到下底的边沿的距离为l，问当底半径与高分别为多少时，圆柱体的体积最大？解：如图所示，圆柱体高h，与底半径r满足 圆柱体的体积公式为 将代入得求导得令得，并由此解得，即当底半径为，高时，圆柱体得体积最大。典型例题例1 计算极限解 利用重要极限，及极限的运算法则得 例2 计算极限解：利用极限的运算法则得例3 设，求解：利用导数的运算法则得 例4 设，求解：设，得 利用复合函数求导法则，得 例5 设是由方程确定的函数，求解：利用导数运算法则和复合函数求导法则，等式两端分别对求导得 左： 右： 由此得 整理得由微分定义得例6 计算解：利用换元积分法得 例7 计算解：利用分部积分法得 例8 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高等数学基础第一次作业（一） 单项选择题下列各函数对中，（C）中的两个函数相等 A. ， B. ， C. ， D. ，设函数的定义域为，则函数的图形关于（C）对称 A. 坐标原点 B. 轴 C. 轴 D. 下列函数中为奇函数是（B） A. B. C. D. 下列函数中为基本初等函数是（C） A. B. C. D. 下列极限存计算不正确的是（D） A. B. C. D. 当时，变量（C）是无穷小量 A. B. C. D. 若函数在点满足（A），则在点连续。 A. B. 在点的某个邻域内有定义 C. D. （二）填空题函数的定义域是 已知函数，则 x2-x 若函数，在处连续，则e 函数的间断点是 （二） 计算题设函数求：解：，求函数的定义域解：有意义，要求解得， 则定义域为在半径为的半圆内内接一梯形，梯形的一个底边与半圆的直径重合，另一底边的两个端点在半圆上，试将梯形的面积表示成其高的函数解： A R O h E B C设梯形ABCD即为题中要求的梯形，设高为h，即OE=h，下底CD2R直角三角形AOE中，利用勾股定理得则上底故求解：求解：求解：求解： 求解：求解：设函数讨论的连续性，并写出其连续区间解：分别对分段点处讨论连续性 （1）所以，即在处不连续（2）所以即在处连续由（1）（2）得在除点外均连续故的连续区间为高等数学基础第四次作业（一）单项选择题 若的一个原函数是，则（D） A. B. C. D. 下列等式成立的是（D） A B. C. D. 若，则（B） A. B. C. D. （B） A. B. C. D. 若，则（B） A. B. C. D. 由区间上的两条光滑曲线和以及两条直线和所围成的平面区域的面积是（C）A. B. C. D. （二）填空题 函数的不定积分是 若函数与是同一函数的原函数，则与之间有关系式 若，则 3 若无穷积分收敛，则（三）计算题 （四）证明题证明：若在上可积并为奇函数，则证: 证毕证明：若在上可积并为偶函数，则证：证明：证：= 高等数学基础第二次作业（一）单项选择题 设且极限存在，则（C） A. B. C. D. cvx 设在可导，则（D） A. B. C. D. 设，则（A） A. B. C. D. 设，则（D） A. B. C. D. 下列结论中正确的是（ C ） A. 若在点有极限，则在点可导 B. 若在点连续，则在点可导 C. 若在点可导，则在点有极限 D. 若在点有极限，则在点连续 （二）填空题 设函数，则0 设，则 曲线在处的切线斜率是 曲线在处的切线方程是 设，则 设，则（三）计算题 求下列函数的导数： 求下列函数的导数： 在下列方程中，是由方程确定的函数，求： 求下列函数的微分： 两边对数得： 求下列函数的二阶导数： （四）证明题 设是可导的奇函数，试证是偶函数证：因为f(x)是奇函数 所以两边导数得：所以是偶函数。高等数学基础第三次作业（一）单项选择题 若函数满足条件（D），则存在，使得 A. 在内连续 B. 在内可导 C. 在内连续且可导 D. 在内连续，在内可导 函数的单调增加区间是（D） A. B. C. D. 函数在区间内满足（A） A. 先单调下降再单调上升 B. 单调下降 C. 先单调上升再单调下降 D. 单调上升 函数满足的点，一定是的（C） A. 间断点 B. 极值点 C. 驻点 D. 拐点设在内有连续的二阶导数，若满足（ C ），则在取到极小值 A. B. C. D. 设在内有连续的二阶导数，且，则在此区间内是（ A ） A. 单调减少且是凸的 B. 单调减少且是凹的 C. 单调增加且是凸的 D. 单调增加且是凹的 （二）填空题 设在内可导，且当时，当时，则是的 极小值 点 若函数在点可导，且是的极值点，则 0 函数的单调减少区间是 函数的单调增加区间是 若函数在内恒有，则在上的最大值是 函数的拐点是 x=0 （三）计算题 求函数的单调区间和极值令X2(2,5)5+极大-极小+y上升27下降0上升列表：极大值：极小值： 求函数在区间内的极值点，并求最大值和最小值令： 试确定函数中的，使函数图形过点和点，且是驻点，是拐点解： 求曲线上的点，使其到点的距离最短解：，d为p到A点的距离，则：圆柱体上底的中心到下底的边沿的距离为，问当底半径与高分别为多少时，圆柱体的体积最大？设园柱体半径为R，高为h，则体积一体积为V的圆柱体，问底半径与高各为多少时表面积最小？设园柱体半径为R，高为h，则体积答：当 时表面积最大。欲做一个底为正方形，容积为62.5立方米的长方体开口容器，怎样做法用料最省？解：设底连长为x，高为h。则：侧面积为：令 答：当底连长为5米，高为2.5米时用料最省。（四）证明题当时，证明不等式证：由中值定理得： 当时，证明不等式请您务必删除一下内容，O(_)O万分谢谢！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Indonesia has emerged as a top vacation destination for Chinese this summer, along with Thailands Phuket island and the Maldives archipelago. Encouraged by growth in Chinese travelers to Indonesia, the government in Jakarta has recently relaxed its visa policy. Since June 10, Chinese tourists can enter Indonesia through nine appointed locations, including the Soekarno Hatta International Airport in Jakarta, the Ngurah Rai International Airport in Bali and the Kuala Namu International Airport in Medan, by just getting their passports stamped on arrival. Officially, it is called the free-visa scheme. The new policy also means Chinese tourists can save $35 on visa fees, which will likely make trips to Indonesia more alluring. While such an arrangement allows Chinese visitors to stay up to 30 days for the purpose of traveling, those seeking extensions will need to get paid visas from that countrys missions inBeijing,Shanghai,GuangzhouorHong Kong, according to an official at the Indonesia embassy in Beijing. Santo Darmosumarto, head of the embassys information, social and cultural section, says the new policy is aimed at strengthening people-to-people contacts between the two countries. Dai Yu, marketing director of Ctrip, a major Chinese online travel agency, says: Weve seen a nearly 50 percent growth over the previous month in the number of Chinese tourists to Bali since the policy was announced. During his trip to China in March, Indonesian President Joko Widodo proposed that his country and China aim to increase two-way visits to a maximum of 10 million people in the next few years. The Indonesian government has set their sights on greeting 2 million Chinese tourists by the end of this year, according to the official. The Indonesian government hopes that Indonesian nationals would also be given preferential treatment while visiting China, says Darmosumarto. In 2013, the number of Chinese tourists who visited Indonesia stood around 807,000. Last year, it increased to 959,000, he adds. Bali remains the most popular site among Chinese tourists. In February, more than 92,200 Chinese tourists made trips to Bali, ranking first among overseas visitors, the Bali Times reported. Last year, the island witnessed more than 586,000 arrivals from China, an increase of 51 percent over 2013. Bali isnt just for sightseeing, but also for weddings, honeymoons, golf and many outdoor activities, says Fan Wenqing, a marketing executive at Garuda, Indonesias national airliner. Garuda offers three nonstop flights between Beijing and Bali, and four each week between Beijing and Jakarta. There are daily flights from Guangzhou, inGuangdongprovince, and Shanghai to Jakarta as well. It takes from six to eight hours on a nonstop flight to reach Indonesia from China. Indonesia is home to more than 17,000 islands. Tourists can tour Yogyakarta to see Prambanam and Borobudur, two historical and religious sites, and explore the local handicraft markets. The base of a volcano, Bandung, which is also known as the Paris of Java, is ideal for adventure-seekers. Many ecotourism destinations, such as Toba Lake in Sumatra, Tanjung Puting National Park in Kalimantan and Bunaken in Manado, are places the embassy official recommends for tourists. Indonesia boasts world-class surfing facilities along the shores of Sumatra down to Nusa Tenggara Islands. Recently, Lombok, a sister island east of Bali has gotten so much attention from Chinese travelers that some travel agencies are offering twin packages for Bali and Lombok. The best time to visit Bali is from May to October, when it doesntrainmuch and the weather is cool. At press time, a weeklong package from Shanghai or Guangzhou to Bali was a little more than 3,000 yuan ($480) on Ctrips website. Chinese tourists have taken a shine to rafting in Ubud, sightseeing in Tanah Lot, and surfing and diving in Nusa Lembongan, says Dai. Civet coffee, essential oil and woodcarvings are among the most popular products for Chinese tourists in Indonesia, she says. Indonesian food is also something that visitors shouldnt miss. Local cuisines feature many spices, including peppers and cloves, and coconut pulp. Fried rice, dirty duck and roast suckling pig are recommended. Childrens illustration books first appeared in the 1600s in Europe. Their passage to China, however, took much longer, roughly 300 years. In China, childrens illustration books have a history of just 100 years and their development can be divided into four stages. From early 1900s to mid 1900s, a large number of books and magazines with illustrations appeared with the fast development of the modern publishing industry. The illustrationarts at that time were a mixed genre of Chinese traditionalpaintings and the westernstyle, and most of the stories originate from the fundamental changes that China experienced after the collapse of Qing Dynasty (1644-1911), the warlord struggles and the war against the Japanese invasion. The second stage was from mid 1900s to late 1970s, when the cultural revolution (1966-76) ended. The fast development of some special publishing houses for children gave birth to a large number of illustration-story books, which made a good use of folk art techniques, such as wood board carving, frescoes, and ink and wash painting, etc. Many of the popular stories are from Chinese history and wars after 1900s. The third stage is from early 1980s to late 1990s, a golden period for the development of childrens illustration books. The reform and opening-up brought in new concepts and ideas from the West to China, a country that had been closed to the West for nearly three decades. Fast development of economy, society and culture provided the writers and painters with a lot of inspiration to create new literature works and draw illustrations. China also imported large amounts of childrens illustration books from the West and Japan. Many young parents in China have a strong nostalgia about childrens illustration books they read in the 1980s and 1990s. This is also the last era in Chinas artistic innovation before the advent of the Internet period. The fourth stage is featured with the spread of the Internet and the other computerized means of art innovation. The hand-drawn childrens illustration books are gradually replaced by cartoons drawn and copied by software and machines, and shown on tablets, computers, television and smart phones, instead of books. Hainan Tropical Wildlife Park and Botanical Garden is natures haven, with no less than 4,000 rare birds and animals representing 200 species. With tropical forest covering over 90 percent of its area, the garden offers beautiful views of a wide range of tropical plants, flowers and fruit trees. The scenic spot about 25 kilometers from the center of Haikou offers a drive-thru safari tour where you can get up close with elephants, lions and bears. The Safari on Foot area features walking trails where visitors can see the rest of the animals, including hippos and monkeys, and feed them for a small fee. Visitors also can see what happens when you breed a lion and a tiger. Two unique attractions are rare hybrids: a liger, the offspring of a mallion and a female tiger and a tigon, which is created by a female lion and a male tiger. As ateaching center of the National Popular Science Education program, the park also serves as a second classroom for students to learn about wildlife and plants. Since it was established in 1995, it has received more than one million student visitors. At a crucial moment when pessimism has brought the Greek crisis to such a head that the country is closer to a default on its debt repayments than ever, Li offered a spark of enthusiasm to restart the stalled talks by calling on Greece and its creditors to reach a last-minute deal that will allow Greece to remain in the eurozone. Given the escalation of the countrys crisis over the weekend sent a shock wave through the global stock markets on Monday, there are ample reasons to worry about the uncertainties surrounding the events in Greece and the effect a default would have on Europe, relations between China and the EU, global financial stability and the nascent global economic recovery. Greece has announced that it will hold a referendum on a bailout plan proposed last week by the countrys creditors. In response, Greeces eurozone partners have refused to extend the countrys bailout program and the European Central Bank capped its emergency support for the countrys banks. A real danger now looms of Greece exiting the euro, which might derail the global economic recovery and damage the long-term viability of the euro as a currency. However, such a tragedy is neither certain nor unavoidable. The EU should shoulder its responsibility to prevent the Greek crisis from overshadowing the fragile global recovery. As a major customer and supplier of the 28-nation EU, and a responsible long-term holder of Eurobonds, Chinas confidence in and commitment to a strong eurozone offers EU leaders the necessary support to look at the Greek crisis from a broader and longer perspective. When Li said that China will not only consider a China-EU investment platform to back European Commission President Jean-Claude Junckers plan to revive the European economy, but also buy more bonds issued by the European Investment Bank, EU leaders should be clear that China wants to see the EU maintain its integrity and a forward trajectory. Such a confidence-building effort is particularly valuable, especially from such a large country as China which already has a huge stake and seeks to further expand it in a strong eurozone. It will be a tragedy to allow inaction over the Greek crisis to stand in the way of growth-boosting Sino-EU cooperation. Like a shining pearl, West Lake is the symbol of Hangzhou city. From ancient times, many poems have praised the amazing scenery of the lake. At the very beginning, the West Lake was a part of the Qiantang River. In the year 822, Bai Juyi, a famous poet and an officer of the Tang Dynasty (AD 618-907), suggested to build a stronger causeway to store water so that the lake was doubled in size. And during the Song Dynasty (AD 960-1279), many temples and pagodas were built due to a Buddhist revival, and the look of West Lake was formed at that time.The West Lake is quite big and features different classic views from different locations. Technically, there are ten scenes which were marked by Emperor Qianlong with four-character inscriptions 200 years ago, such as the Melting Snow on the Broken Bridge and Sunset Glow over Leifeng Pagoda.
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