1、電大微積分初步期末復習題資料參考小抄1、填空題（1）函數(shù)的定義域是 答案：且.（2）函數(shù)的定義域是答案：（3）函數(shù)，則 答案：（4）若函數(shù)在處連續(xù)，則 答案：（5）函數(shù)，則 答案：（6）函數(shù)的間斷點是 答案： （7） 答案：1（8）若，則 答案：（9）曲線在點的切斜率是答案： （10）曲線在點的切線方程是 答案： （11）已知，則=答案：=27（12）已知，則=答案：，=（13）若，則 答案：（14）函數(shù)的單調增加區(qū)間是 答案：（15）函數(shù)在區(qū)間內(nèi)單調增加，則應滿足 答案：（16）若的一個原函數(shù)為，則 .答案：（17）若，則答案： （18）若答案：（19）答案：（20） 答案：（21）若，則答

2、案：（22）若，則答案：（23） 答案：（24） .答案：0（25）= 答案：(26)已知曲線在任意點處切線的斜率為，且曲線過，則該曲線的方程是 .答案： (27)由定積分的幾何意義知，= .答案： (28)微分方程的特解為 . 答案： (29)微分方程的通解為 .答案：(30)微分方程的階數(shù)為 答案：42單項選擇題（1）設函數(shù)，則該函數(shù)是（）A奇函數(shù) B偶函數(shù)C非奇非偶函數(shù) D既奇又偶函數(shù)答案：B（2）下列函數(shù)中為奇函數(shù)是（）A B C D答案：C（3）函數(shù)的定義域為（）A B C且 D且答案：D（4）設，則（ ）A B C D答案：C （5）當（ ）時，函數(shù)在處連續(xù).A0 B1 C D 答

3、案：D（6）當（ ）時，函數(shù)，在處連續(xù).A0 B1 C D 答案：B（7）函數(shù)的間斷點是（ ）A B C D無間斷點答案：A（8）若，則=（ ） A. 2 B. 1 C. -1 D. -2答案：C（9）設，則（ ） A B C D答案：B（10）設是可微函數(shù)，則（ ） A B C D答案：D （11）若，其中是常數(shù)，則（ ） A B C D答案：C（1）函數(shù)在區(qū)間是（ ）A單調增加 B單調減少C先增后減 D先減后增答案：D（12）滿足方程的點一定是函數(shù)的（ ）.A極值點B最值點 C駐點D 間斷點答案：C（13）下列結論中（ ）不正確 A在處連續(xù)，則一定在處可微. B在處不連續(xù)，則一定在處不可導

4、. C可導函數(shù)的極值點一定發(fā)生在其駐點上.D函數(shù)的極值點可能發(fā)生在不可導點上.答案： （14）下列函數(shù)在指定區(qū)間上單調增加的是（ ） 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）下列定積分中積分值為0的是（ ） A B C D 答案：A（19）設是連續(xù)的奇函數(shù)，則定積分（ ）A0B CD 答案：A（20）下列無窮積分收斂的是（）A B C D答案：D (21)微分方程的通解為（ ） A B C D答案：C(22)下列微分方程中為可分離變量方程的是（）A. ； B

5、. ； C. ； D. 答案：B計算題 （1） 解：（2） 解： （3）解：（4）設，求 解： （5）設，求.解： （6）設，求.解： （7）設，求.解： （8） 解：（9）解：(10)解：=(11) 解： (12)解：(13)解：應用題（1）欲做一個底為正方形，容積為108立方米的長方體開口容器，怎樣做法用料最??？解：設底邊的邊長為，高為，用材料為，由已知 令，解得是唯一駐點， 且，說明是函數(shù)的極小值點，所以當，用料最省.（2）用鋼板焊接一個容積為4的正方形的水箱，已知鋼板每平方米10元，焊接費40元，問水箱的尺寸如何選擇，可使總費最低？最低總費是多少？解：設水箱的底邊長為，高為，表面積為，

6、且有所以 令，得， 因為本問題存在最小值，且函數(shù)的駐點唯一，所以，當時水箱的面積最小. 此時的費用為 （元） 請您刪除一下內(nèi)容，O(_)O謝謝！2015年中央電大期末復習考試小抄大全，電大期末考試必備小抄，電大考試必過小抄Many people have the same mixed feelings when planning a trip during Golden Week. With heaps of time, the seven-day Chinese請您刪除一下內(nèi)容，O(_)O謝謝！National Day holiday could be the best occasion t

7、o 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 travel w

8、ith 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 available

9、. 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 matter tha

10、t 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 regardles

11、s 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 Sino-Mo

12、ngolian 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 the year

13、 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 Inner Mong

14、olia 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 ecotour

15、ism 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 definitely

16、 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 themselv

17、es 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 red o

18、f 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 Saturday nig

19、ht, 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 the se

20、venth 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 leave

21、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 two f

22、ell 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 the he

23、aven 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 shoul

24、der 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 reunite

25、 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 a brig

26、ht 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 Festival

27、 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 good husb

28、and 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, particularly you

29、ngsters, 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 people

30、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 dotted

31、 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 public

32、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 world thi

33、s 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 dwellers fr

34、om 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 brothe

35、r 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. How

36、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 beautiful

37、 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 beautif

38、ul 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 there

39、. 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 you m

40、ore 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 actually

41、, 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 and ther

42、e 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 morni

43、ng. 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 abo