2015年电大专科《微积分初步》期末复习题资料参考小抄

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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，则 答案：（4）若函数在处连续，则 答案：（5）函数，则 答案：（6）函数的间断点是 答案： （7） 答案：1（8）若，则 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）已知，则=答案：=27（12）已知，则=答案：，=（13）若，则 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，则应满足 答案：（16）若的一个原函数为，则 .答案：（17）若，则答案： （18）若答案：（19）答案：（20） 答案：（21）若，则答

2、案：（22）若，则答案：（23） 答案：（24） .答案：0（25）= 答案：(26)已知曲线在任意点处切线的斜率为，且曲线过，则该曲线的方程是 .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，则该函数是（）A奇函数 B偶函数C非奇非偶函数 D既奇又偶函数答案：B（2）下列函数中为奇函数是（）A B C D答案：C（3）函数的定义域为（）A B C且 D且答案：D（4）设，则（ ）A B C D答案：C （5）当（ ）时，函数在处连续.A0 B1 C D 答

3、案：D（6）当（ ）时，函数，在处连续.A0 B1 C D 答案：B（7）函数的间断点是（ ）A B C D无间断点答案：A（8）若，则=（ ） A. 2 B. 1 C. -1 D. -2答案：C（9）设，则（ ） A B C D答案：B（10）设是可微函数，则（ ） A B C D答案：D （11）若，其中是常数，则（ ） A B C D答案：C（1）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：D（12）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：C（13）下列结论中（ ）不正确 A在处连续，则一定在处可微. B在处不连续，则一定在处不可导

4、. 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）下列函数在指定区间上单调增加的是（ ） A B C D答案：B（15）下列等式成立的是（）A BC D答案：C（16）以下等式成立的是（ ）A B C D 答案：D（17）（ ）A. B. C. D. 答案：A（18）下列定积分中积分值为0的是（ ） A B C D 答案：A（19）设是连续的奇函数，则定积分（ ）A0B CD 答案：A（20）下列无穷积分收敛的是（）A B C D答案：D (21)微分方程的通解为（ ） A B C D答案：C(22)下列微分方程中为可分离变量方程的是（）A. ； B

5、. ； C. ； D. 答案：B3、 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：4、 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，由已知 令，解得是唯一驻点， 且，说明是函数的极小值点，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，已知钢板每平方米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

6、，表面积为，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！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Many people have the same mixed feelings when planning a trip during Golden Week. With heaps of time, the seven-day Chinese请您删除一下内容，O(_)O谢谢！National Day holiday could be the best occa

7、sion 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 dream about a place can turn to nightmare without careful planning, especially if you tr

8、avel 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 transport and accommodation prices, with the possibility that there will be no rooms ava

9、ilable. 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 China over the week-long holiday in October. Traveling during this period is a matt

10、er 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 everyone yearns for. Arxan is a place like this. The beauty of Arxan is everlasting reg

11、ardless 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 Mongolia Arxan Hailar Manzhouli. It is also the joint of the four prairies across the S

12、ino-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. Walking into Arxan, you will be amazed by a kaleidoscope of gorgeous colors all th

13、e 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 alpine snowscape. Hinggan League Arxan city is situated in the far eastern area of Inne

14、r 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, heaven lake cluster, thermium, as well as volcanic cluster. It is a rare and unique e

15、cotourism 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 tourists as the purest land on earth. You cannot miss out the Autumn of Arxan. It is defi

16、nitely 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 once emerald green mountain and blooming grassland. Shutterbugs flock to see for th

17、emselves 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 the larch is still proudly green. You will find yourself drowned in the intoxicating

18、 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 only exists in a dream that satisfies all your fantasies. If itrains heavily on Saturd

19、ay 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 tragedy when they were children on Qixi, or the Seventh Night Festival, which falls on

20、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 brother and sister-in-law. But she disliked and abused him, and the boy was forced to

21、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 earth. Among them was Zhinu, the most beautiful fairy and a skilled seamstress. The

22、 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 Deity in Taoism, marriage between a mortal and fairy was strictly forbidden. He ordered

23、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. The magic shoes whisked Niulang, who carried his two children in baskets strung from a

24、 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 magpies, moved by their love and devotion, formed a bridge across the Milky Way to r

25、eunite 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 Han Dynasty (206 BC-AD 220). Traditionally, people would look up at the sky and find

26、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 special day for lovers, but also for girls. It is also known as the Begging for Skills Fe

27、stival 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, it proves the girl is a skilled embroiders. Single women also pray for finding a goo

28、d 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 ancient traditions and customs are slowly dying out. Many modern Chinese, particular

29、ly 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 is nowadays referred to as the Chinese Valentines Day. More and more young Chinese p

30、eople 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 Way, that is, if people even know on which day Qixi falls. There are ready reminders

31、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 to pray for cleverness. A large-scale of exhibition on the Silk Road opened to the p

32、ublic 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 Road in recent years. AsAPECis going on in Beijing, the exhibit aims to show the wor

33、ld 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 East by linking traders, merchants, pilgrims, monks, soldiers, nomads, and urban dwell

34、ers from China and India to the Mediterranean Sea during various periods of time. I met my dear hubby in 2009 the second year I was in my school and it was the first year when he came here. We became colleagues. And there was nothing special happening during that year. He was just a kind and humble

35、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 other when we both look up. But it is not the main reason that really draws us close

36、. 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 something really humorous. Then one day, to my great surprise, I found a pot of bea

37、utiful 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 me. He just simply said ,”well, I caught sight of this flower and thought that its b

38、eautiful 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 appreciate the beautiful flower and they noticed that something romance happened

39、 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 several pink diamond roses beside the flower with a piece of paper saying” I love

40、 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 grammar errors but I got what he meant. He meant so clear and so direct. And ac

41、tually, 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 change after getting hitched. You will find that love is no longer strong an

42、d 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 together and see each others face the moment you open your eyes in the early

43、 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 qualificati

44、on of a good husband? Once I was chatting with my colleague about this issue. And one of the qualifications I thought was that he must be a good cook. But to my surprise, my colleague said that a good husband must be someone who makes big money. What made her think so was quite beyond me. Maybe I am

45、 not sophisticated enough and what I want is just simple life style. The most enjoyable thing is that we go to the market to buy vegetables and other daily stuffs if we both have time. Maybe he is a housebound husband and I love housebound man. And there is another reason why We love going to the ma

46、rket. That is because we sometimes will get some surprises. The surprise is saving little fish which are disserted by the fish mongers. Because these fish are swellfish. Then we will collect them and set them free into the river. Swellfish are lovely creature. When they look like a little submarine

47、when they are swimming in the water and look like a meat ball when you hold them in your hand. And if they are scared, they will swell and look like a little ball. Every time we see them swim away and we feel their happiness of returning home and this also make us cherish life. Maybe some will consi

48、der these behavior as something childish. Well, that is fine with us. We love doing these together and feel happy that is what it is all about. My dear hubby is a kind hearted man and he love animals just as I do. I am lucky to have someone who can be both my intimated soul mate and my forever friend.