2023年电大专科《微积分初步》期末复习题资料参考小抄

1、电大微积分初步期末复习题资料参考小抄1、填空题1函数的定义域是 答案：且.2函数的定义域是答案：3函数，那么 答案：4假设函数在处连续，那么 答案：5函数，那么 答案：6函数的间断点是 答案： 7 答案：18假设，那么 答案：9曲线在点的切斜率是答案：10曲线在点的切线方程是答案：11，那么=答案：=2712，那么=答案：，=13假设，那么答案：14函数的单调增加区间是答案：15函数在区间内单调增加，那么应满足答案：16假设的一个原函数为，那么.答案：17假设，那么答案：18假设答案：19答案：20答案：21假设，那么答案：22假设，那么答案：23答案：24.答案：025= 答案：(26)曲线

2、在任意点处切线的斜率为，且曲线过，那么该曲线的方程是.答案：(27)由定积分的几何意义知，= .答案： (28)微分方程的特解为. 答案：(29)微分方程的通解为.答案：(30)微分方程的阶数为答案：42单项选择题1设函数，那么该函数是A奇函数 B偶函数C非奇非偶函数 D既奇又偶函数答案：B2以下函数中为奇函数是A B CD答案：C3函数的定义域为A B C且D且答案：D4设，那么 ABCD答案：C5当 时，函数在处连续.A0 B1CD答案：D6当 时，函数，在处连续.A0 B1CD答案：B7函数的间断点是 A BC D无间断点答案：A8假设，那么= A. 2 B. 1 C. -1 D. -2

3、答案：C9设，那么 A B C D答案：B10设是可微函数，那么 AB C D答案：D 11假设，其中是常数，那么 AB CD答案：C1函数在区间是 A单调增加 B单调减少C先增后减 D先减后增答案：D12满足方程的点一定是函数的 .A极值点B最值点 C驻点D间断点答案：C13以下结论中 不正确 A在处连续，那么一定在处可微. B在处不连续，那么一定在处不可导. C可导函数的极值点一定发生在其驻点上.D函数的极值点可能发生在不可导点上.答案： 14以下函数在指定区间上单调增加的是 ABC D答案：B15以下等式成立的是ABCD答案：C16以下等式成立的是 A BCD答案：D17 A. B. C

4、. D. 答案：A18以下定积分中积分值为0的是 ABCD答案：A19设是连续的奇函数，那么定积分 A0BCD答案：A20以下无穷积分收敛的是ABCD答案：D (21)微分方程的通解为 A B C D答案：C(22)以下微分方程中为可别离变量方程的是A.；B. ；C. ；D. 答案：B计算题 1 解：2解：3解：4设，求 解：5设，求.解：6设，求.解： 7设，求.解：8解：9解：(10)解：=(11)解： (12)解：(13)解：应用题1欲做一个底为正方形，容积为108立方米的长方体开口容器，怎样做法用料最省？解：设底边的边长为，高为，用材料为，由令，解得是唯一驻点， 且，说明是函数的极小值

5、点，所以当，用料最省.2用钢板焊接一个容积为4的正方形的水箱，钢板每平方米10元，焊接费40元，问水箱的尺寸如何选择，可使总费最低？最低总费是多少？解：设水箱的底边长为，高为，外表积为，且有所以令，得， 因为本问题存在最小值，且函数的驻点唯一，所以，当时水箱的面积最小. 此时的费用为 元 请您删除一下内容，O(_)O谢谢！2023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Many people have the same mixed feelings when planning a trip during Golden Week. With heaps of tim

6、e, the seven-day Chinese请您删除一下内容，O(_)O谢谢！National Day holiday could be the best occasion to enjoy a destination. However, it can also be the easiest way to ruin how you feel about a place and you may become more fatigued after the holiday, due to battling the large crowds. During peak season, a drea

7、m about a place can turn to nightmare without careful planning, especially if you travel with children and older people. As most Chinese people will take the holiday to visit domestic tourist destinations, crowds and busy traffic are inevitable at most places. Also to be expected are increasing tran

8、sport and accommodation prices, with the possibility that there will be no rooms available. It is also common that youllwait in the line for one hour to get a ticket, and another two hours at the site, to only see a tiny bit of the place due to the crowds. Last year, 428 million tourists traveled in

9、 China over the week-long holiday in October. Traveling during this period is a matter that needs thorough preparation. If you are short on time to plan the upcoming Golden Week it may not be a bad idea to avoid some of the most crowded places for now. There is always a place so fascinating that eve

10、ryone yearns for. Arxan is a place like this. The beauty of Arxan is everlasting regardless of the changing of four seasons. Bestowed by nature, its spectacular seasonal landscape and mountains are just beyond word. Arxan is a crucial destination for the recommended travelling route, China Inner Mon

11、golia Arxan Hailar Manzhouli. It is also the joint of the four prairies across the Sino-Mongolian border, where people gravitate towards the exotic atmosphere mixed with Chinese, Russian, and Mongolia elements. As a historic site for the Yitian Battle, Arxan still embodies the spirit of Genghis Khan

12、. Walking into Arxan, you will be amazed by a kaleidoscope of gorgeous colors all the year round - the Spring azaleas blooming red in the snow, the Summer sea wavering blue in the breeze, the Autumn leaves painted in yellow covering volcanic traces, and the Winter woods shining white on the vast alp

13、ine snowscape. Hinggan League Arxan city is situated in the far eastern area of Inner Mongolia Autonomous Region. Its full name Haren Arxan means hot holy water in the Mongolian language. Arxan is a tourism city in the northern frontier with a blend of large forest, grand prairies, vast snowfield, h

14、eaven lake cluster, thermium, as well as volcanic cluster. It is a rare and unique ecotourism base filled with healthy sunshine, clean air and unspoiled green. Nestled close to the countrys largest virgin forest, and known for its spring and ecological environment, Arxan is marveled at by many touri

15、sts as the purest land on earth. You cannot miss out the Autumn of Arxan. It is definitely the best with brightly-colored scenery full of emotions. Autumn in the northern part of the country comes earlier than the South. A September rain followed by the footprints of Autumn brings more colors to the

16、 once emerald green mountain and blooming grassland. Shutterbugs flock to see for themselves the marvel of splendid colors around the mountains and waters, many of whom have travel a long distance and even camp here only to capture a moment of the nature wonder. The silver birch turns golden, while

17、the larch is still proudly green. You will find yourself drowned in the intoxicating red of the wild fruits as well as the glamour of flowers in full blown. And your heart will be lingering on the woods as its time for the wild fruits to ripe. The picturesque Arxan in Autumn is indeed a fairyland on

18、ly exists in a dream that satisfies all your fantasies. If itrains heavily on Saturday night, some elderly Chinese will say it is because Zhinu, or the Weaving Maid, is crying on the day she met her husband Niulang, or the Cowherd, on the Milky Way. Most Chinese remember being told this romantic tra

19、gedy when they were children on Qixi, or the Seventh Night Festival, which falls on the seventh day of the seventh lunar month, which is usually in early August. This year it falls on Saturday, August 2. Folklore Story As the story goes, once there was a cowherd, Niulang, who lived with his elder br

20、other and sister-in-law. But she disliked and abused him, and the boy was forced to leave home with only an old cow for company. The cow, however, was a former god who had violated imperial rules and was sent to earth in bovine form. One day the cow led Niulang to a lake where fairies took a bath on

21、 earth. Among them was Zhinu, the most beautiful fairy and a skilled seamstress. The two fell in love at first sight and were soon married. They had a son and daughter and their happy life was held up as an example for hundreds of years in China. Yet in the eyes of the Jade Emperor, the Supreme Deit

22、y in Taoism, marriage between a mortal and fairy was strictly forbidden. He ordered the heaven troop to catch Zhinu back. Niulang grew desperate when he discovered Zhinu had been taken back to heaven. Driven by Niulangs misery, the cow told him to turn its hide into a pair of shoes after it died. Th

23、e magic shoes whisked Niulang, who carried his two children in baskets strung from a shoulder pole, off on a chase after the empress. The pursuit enraged the empress, who took her hairpin and slashed it across the sky creating the Milky Way which separated husband from wife. But all was not lost as

24、magpies, moved by their love and devotion, formed a bridge across the Milky Way to reunite the family. Even the Jade Emperor was touched, and allowed Niulang and Zhinu to meet once a year on the seventh night of the seventh month. This is how Qixi came to be. The festival can be traced back to the H

25、an Dynasty (206 BC-AD 220). Traditionally, people would look up at the sky and find a bright star in the constellation Aquila as well as the star Vega, which are identified as Niulang and Zhinu. The two stars shine on opposite sides of the Milky Way. Customs In bygone days, Qixi was not only a speci

26、al day for lovers, but also for girls. It is also known as the Begging for Skills Festival or Daughters Festival. In this day, girls will throw a sewing needle into a bowl full of water on the night of Qixi as a test of embroidery skills. If the needle floats on top of the water instead of sinking,

27、it proves the girl is a skilled embroiders. Single women also pray for finding a good husband in the future. And the newly married women pray to become pregnant quickly. Tradition transformed The love story of Niulang and Zhinu, and the Qixi Festival have been handed down for generations. Yet these

28、ancient traditions and customs are slowly dying out. Many modern Chinese, particularly youngsters, seem to know more about St Valentines Day on February 14, characterized by bouquets of roses, chocolates and romantic candlelight dinners, than they do about their home-grown day for lovers. Even Qixi

29、is nowadays referred to as the Chinese Valentines Day. More and more young Chinese people begin to celebrate this day in a very similar way as that in western countries. Fewer people than ever will gaze at the heavens on Saturday to pick out the two stars shining bright on either side of the Milky W

30、ay, that is, if people even know on which day Qixi falls. There are ready reminders dotted about, in the form of big ads saying Sales on Chinese Valentines Day! in shops, hotels and restaurants. But few young women will mark the festival with their boyfriends, or take part in traditional activities

31、to pray for cleverness. A large-scale of exhibition on the Silk Road opened to the public in the National Museum on Thursday. The exhibition displays more than 400 treasures from Shaanxi province, Gansu province and 14 other regions. It is largest scale exhibition that shows the history of the Silk

32、Road in recent years. AsAPECis going on in Beijing, the exhibit aims to show the world this brilliant section of history. The Silk Road is a series of trade and cultural transmission routes that were central to cultural interaction through regions of the Asian continent. It connected the West and Ea

33、st by linking traders, merchants, pilgrims, monks, soldiers, nomads, and urban dwellers from China and India to the Mediterranean Sea during various periods of time. I met my dear hubby in 2023 the second year I was in my school and it was the first year when he came here. We became colleagues. And

34、there was nothing special happening during that year. He was just a kind and humble brother graduated from the same college as me. But we did not know each other till he became my colleague and his office desk was just in front of me. There was only a glass between us. So actually we could see each

35、other when we both look up. But it is not the main reason that really draws us close. How we become close to each other was something seems quite natural. We went out to play badminton with other colleagues and we sometimes chatted for a while. He is a man of few words but somehow sometimes will say

36、 something really humorous. Then one day, to my great surprise, I found a pot of beautiful flower on my desk. It was just the flower I had talked about with my colleague the other day, and I thought it was her who put the flower there. But the truth is not. It was the humble guy sitting in front of

37、me. He just simply said ,well, I caught sight of this flower and thought that its beautiful and you may like it.I wonder why I was moved because of these simple words and present. Maybe it is the sincerity and the true self that impress me. I thanked him and some colleagues walked past my desk would

38、 appreciate the beautiful flower and they noticed that something romance happened there.Then later on, there were some little surprises once in a while. Once, there was something wrong with my drawer and I had complained about it unconsciously. And he fixed it for me. Then the other day, he placed s

39、everal pink diamond roses beside the flower with a piece of paper saying I love you more than I can say! Diamond stands for marriage, rose stand for love. I hope you are mine, become my wife. You are the only girl who I really want to spend the rest of my life to stand by.Although there were some gr

40、ammar errors but I got what he meant. He meant so clear and so direct. And actually, I accepted him some days earlier. I was just waiting for him to break the ice. So finally, the common interests and the common understanding brought us together. Some people say the relationship and the feeling will

41、 change after getting hitched. You will find that love is no longer strong and there is always lack of passion and whats worse you may find out many bad habits of your partner, which never appear when you are first in love before the marriage. It seems that many faults turn up after you truly living

42、 together and see each others face the moment you open your eyes in the early morning. But after almost 4 years from now, I do not feel any negative change in our relationship. During all these years, we know each other better and we become more tolerant about each other and I realize that if you really love a person you will accept his imperfect. And what is the qualification of a good husband? Once I was chatting with my colleague about this issue. And one