1、高等數學基礎試題類型高等數學基礎試題類型分為單項選擇題、填空題、計算題和應用題。單項選擇題的形式為四選一，即在每題的四個備選答案中選出一個正確答案；填空題只要求直接填寫結果，不必寫出計算過程和推理過程；計算題或應用題要求寫出文字說明、演算步驟或推證過程。四種題型分數的百分比為：單項選擇題20%，填空題20%，計算題44%，應用題16%。 期末考試采用閉卷筆試形式，卷面滿分為100分，考試時間為90分鐘。高等數學基礎模擬題 一、單項選擇題1.函數的圖形關于（A）對稱(A) 坐標原點 (B) 軸(C) 軸 (D) 2.在下列指定的變化過程中，（C）是無窮小量(A) (B) (C) (D) 3.設在

2、可導，則（C）(A) (B) (C) (D) 4.若，則（B）(A) (B) (C) (D) 5.下列積分計算正確的是（D）(A) (B) (C) (D) 6.設函數的定義域為，則函數的圖形關于（A）對稱(A) (B) 軸 (C) 軸 (D) 坐標原點7.當時，變量（C）是無窮小量(A) (B) (C) (D) 8.設，則（B）(A) (B) (C) (D) 9.（A）(A) (B) (C) (D) 10.下列無窮限積分收斂的是（B）(A) (B) (C) (D) 二、填空題（每小題3分，共15分）1.函數的定義域是2.若函數，在處連續，則 3.曲線在處的切線斜率是3 4.函數的單調增加區間是

3、5.若，則 6.函數的定義域是7.函數的間斷點是8.曲線在處的切線斜率是 9.函數的單調減少區間是 10. 三、計算題（每小題11分，共44分）1.計算極限 解：2.設，求 解： 3.計算不定積分 解：由換元積分法得4.計算定積分解：由分部積分法得 5.計算極限解：6.設，求 解： 7.計算不定積分 解： 8.計算定積分 解： 四、應用題（本題16分）1、某制罐廠要生產一種體積為V的有蓋圓柱形容器，問容器的底半徑與高各為多少時用料最省？解：設容器的底半徑為，高為，則其表面積為由，得唯一駐點，由實際問題可知，當時可使用料最省，此時，即當容器的底半徑與高分別為與時，用料最省2、圓柱體上底的中心到下

4、底的邊沿的距離為l，問當底半徑與高分別為多少時，圓柱體的體積最大？解：如圖所示，圓柱體高h，與底半徑r滿足 圓柱體的體積公式為 將代入得求導得令得，并由此解得，即當底半徑為，高時，圓柱體得體積最大。典型例題例1 計算極限解 利用重要極限，及極限的運算法則得 例2 計算極限解：利用極限的運算法則得例3 設，求解：利用導數的運算法則得 例4 設，求解：設，得 利用復合函數求導法則，得 例5 設是由方程確定的函數，求解：利用導數運算法則和復合函數求導法則，等式兩端分別對求導得 左： 右： 由此得 整理得由微分定義得例6 計算解：利用換元積分法得 例7 計算解：利用分部積分法得 例8 求曲線上的點，使

5、其到點的距離最短解：曲線上的點到點的距離公式為與在同一點取到最小值，為計算方便求的最小值點，將代入得令 令得可以驗證是的最小值點，并由此解出，即曲線上的點和點到點的距離最短高等數學基礎第一次作業單項選擇題下列各函數對中，（C）中的兩個函數相等 A. ， B. ， C. ， D. ，設函數的定義域為，則函數的圖形關于（C）對稱 A. 坐標原點 B. 軸 C. 軸 D. 下列函數中為奇函數是（B） A. B. C. D. 下列函數中為基本初等函數是（C） A. B. C. D. 下列極限存計算不正確的是（D） A. B. C. D. 當時，變量（C）是無窮小量 A. B. C. D. 若函數在點滿

6、足（A），則在點連續。 A. B. 在點的某個鄰域內有定義 C. D. （二）填空題函數的定義域是 已知函數，則 x2-x 若函數，在處連續，則e 函數的間斷點是 計算題設函數求：解：，求函數的定義域解：有意義，要求解得， 則定義域為在半徑為的半圓內內接一梯形，梯形的一個底邊與半圓的直徑重合，另一底邊的兩個端點在半圓上，試將梯形的面積表示成其高的函數解： A R O h E B C設梯形ABCD即為題中要求的梯形，設高為h，即OE=h，下底CD2R直角三角形AOE中，利用勾股定理得則上底故求解：求解：求解：求解： 求解：求解：設函數討論的連續性，并寫出其連續區間解：分別對分段點處討論連續性 （

7、1）所以，即在處不連續（2）所以即在處連續由（1）（2）得在除點外均連續故的連續區間為高等數學基礎第四次作業（一）單項選擇題 若的一個原函數是，則（D） A. B. C. D. 下列等式成立的是（D） A B. C. D. 若，則（B） A. B. C. D. （B） A. B. C. D. 若，則（B） A. B. C. D. 由區間上的兩條光滑曲線和以及兩條直線和所圍成的平面區域的面積是（C）A. B. C. D. （二）填空題 函數的不定積分是 若函數與是同一函數的原函數，則與之間有關系式 若，則 3 若無窮積分收斂，則（三）計算題 （四）證明題證明：若在上可積并為奇函數，則證: 證畢證

8、明：若在上可積并為偶函數，則證：證明：證：= 高等數學基礎第二次作業（一）單項選擇題 設且極限存在，則（C） A. B. C. D. cvx 設在可導，則（D） A. B. C. D. 設，則（A） A. B. C. D. 設，則（D） A. B. C. D. 下列結論中正確的是（ C ） A. 若在點有極限，則在點可導 B. 若在點連續，則在點可導 C. 若在點可導，則在點有極限 D. 若在點有極限，則在點連續 （二）填空題 設函數，則0 設，則 曲線在處的切線斜率是 曲線在處的切線方程是 設，則 設，則（三）計算題 求下列函數的導數： 求下列函數的導數： 在下列方程中，是由方程確定的函數，

9、求： 求下列函數的微分： 兩邊對數得： 求下列函數的二階導數： （四）證明題 設是可導的奇函數，試證是偶函數證：因為f(x)是奇函數 所以兩邊導數得：所以是偶函數。高等數學基礎第三次作業（一）單項選擇題 若函數滿足條件（D），則存在，使得 A. 在內連續 B. 在內可導 C. 在內連續且可導 D. 在內連續，在內可導 函數的單調增加區間是（D） A. B. C. D. 函數在區間內滿足（A） A. 先單調下降再單調上升 B. 單調下降 C. 先單調上升再單調下降 D. 單調上升 函數滿足的點，一定是的（C） A. 間斷點 B. 極值點 C. 駐點 D. 拐點設在內有連續的二階導數，若滿足（ C

10、 ），則在取到極小值 A. B. C. D. 設在內有連續的二階導數，且，則在此區間內是（ A ） A. 單調減少且是凸的 B. 單調減少且是凹的 C. 單調增加且是凸的 D. 單調增加且是凹的 （二）填空題 設在內可導，且當時，當時，則是的 極小值 點 若函數在點可導，且是的極值點，則 0 函數的單調減少區間是 函數的單調增加區間是 若函數在內恒有，則在上的最大值是 函數的拐點是 x=0 （三）計算題 求函數的單調區間和極值令X2(2,5)5+極大-極小+y上升27下降0上升列表：極大值：極小值： 求函數在區間內的極值點，并求最大值和最小值令： 試確定函數中的，使函數圖形過點和點，且是駐點，

11、是拐點解： 求曲線上的點，使其到點的距離最短解：，d為p到A點的距離，則：圓柱體上底的中心到下底的邊沿的距離為，問當底半徑與高分別為多少時，圓柱體的體積最大？設園柱體半徑為R，高為h，則體積一體積為V的圓柱體，問底半徑與高各為多少時表面積最小？設園柱體半徑為R，高為h，則體積答：當 時表面積最大。欲做一個底為正方形，容積為62.5立方米的長方體開口容器，怎樣做法用料最省？解：設底連長為x，高為h。則：側面積為：令 答：當底連長為5米，高為2.5米時用料最省。（四）證明題當時，證明不等式證：由中值定理得： 當時，證明不等式請您務必刪除一下內容，O(_)O萬分謝謝！2015年中央電大期末復習考試小

12、抄大全，電大期末考試必備小抄，電大考試必過小抄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,

13、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

14、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

15、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 bet

16、ween 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

17、 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 hope

18、s 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.

19、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, honeym

20、oons, 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 Shan

21、ghai 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 b

22、ase 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

23、 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

24、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

25、 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.

26、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 b

27、e 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 mos

28、t 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 de

29、velopment 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 1

30、900s. 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 e

31、conomy, 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 children

32、s 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 illustrat

33、ion 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

34、 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,

35、 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 o

36、ffspring 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 199

37、5, 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 i

38、ts 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 Gre

39、ece 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 eurozon

40、e 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 cu

41、rrency. 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 Commissi