電大《高等數(shù)學(xué)基礎(chǔ)》必過(guò)考試精篇復(fù)習(xí)資料 必備小抄

1、高等數(shù)學(xué)基礎(chǔ)歸類復(fù)習(xí)考試小抄一、單項(xiàng)選擇題1-1下列各函數(shù)對(duì)中，（ c ）中的兩個(gè)函數(shù)相等 a. ， b. ， c.， d. ，1-設(shè)函數(shù)的定義域?yàn)?，則函數(shù)的圖形關(guān)于（c ）對(duì)稱a. 坐標(biāo)原點(diǎn) b. 軸 c. 軸 d. 設(shè)函數(shù)的定義域?yàn)?，則函數(shù)的圖形關(guān)于（d ）對(duì)稱a. b. 軸 c. 軸 d. 坐標(biāo)原點(diǎn).函數(shù)的圖形關(guān)于（ a ）對(duì)稱(a) 坐標(biāo)原點(diǎn) (b) 軸 (c) 軸 (d) 1-下列函數(shù)中為奇函數(shù)是（ b ）a. b. c. d. 下列函數(shù)中為奇函數(shù)是（a ）a. b. c. d. 下列函數(shù)中為偶函數(shù)的是（ d ）a b c d 2-1 下列極限存計(jì)算不正確的是（ d ） a. b.

2、c. d. 2-2當(dāng)時(shí)，變量（ c ）是無(wú)窮小量a. b. c. d. 當(dāng)時(shí)，變量（ c ）是無(wú)窮小量a b c d .當(dāng)時(shí)，變量（d ）是無(wú)窮小量a b c d 下列變量中，是無(wú)窮小量的為（ b ） a b c d.3-1設(shè)在點(diǎn)x=1處可導(dǎo)，則（ d ）a. b. c. d. 設(shè)在可導(dǎo)，則（ d ）a b c d 設(shè)在可導(dǎo)，則（ d ）a. b. c. d. 設(shè)，則（ a ） a b. c. d. 3-2. 下列等式不成立的是（d ）a. b c. d.下列等式中正確的是（b ）a. b. c. d.4-1函數(shù)的單調(diào)增加區(qū)間是（ d ） a. b. c. d. 函數(shù)在區(qū)間內(nèi)滿足（a ） a.

3、 先單調(diào)下降再單調(diào)上升 b. 單調(diào)下降 c. 先單調(diào)上升再單調(diào)下降 d. 單調(diào)上升.函數(shù)在區(qū)間（5，5）內(nèi)滿足（ a ）a 先單調(diào)下降再單調(diào)上升 b 單調(diào)下降 c先單調(diào)上升再單調(diào)下降 d 單調(diào)上升. 函數(shù)在區(qū)間內(nèi)滿足（d ）a. 先單調(diào)下降再單調(diào)上升 b. 單調(diào)下降 c. 先單調(diào)上升再單調(diào)下降 d. 單調(diào)上升5-1若的一個(gè)原函數(shù)是，則（d ） a. b. c. d. .若是 的一個(gè)原函數(shù)，則下列等式成立的是（ a ）。 a b c d5-2若，則（ b ） a. b. c. d. 下列等式成立的是（d ） a. b. c. d. （ b ） a. b. c. d. （ d ） a b c d

4、-3若，則（ b ） a. b. c. d. 補(bǔ)充： , 無(wú)窮積分收斂的是 函數(shù)的圖形關(guān)于 y 軸 對(duì)稱。二、填空題函數(shù)的定義域是（3，+） 函數(shù)的定義域是 （2，3） （3，4 函數(shù)的定義域是（5，2）若函數(shù)，則 1 2若函數(shù)，在處連續(xù)，則e .函數(shù)在處連續(xù)，則 2 函數(shù)的間斷點(diǎn)是x=0 函數(shù)的間斷點(diǎn)是 x=3 。函數(shù)的間斷點(diǎn)是 x=0 3-曲線在處的切線斜率是1/2 曲線在處的切線斜率是 1/4 曲線在（0，2）處的切線斜率是 1 .曲線在處的切線斜率是 3 3-2 曲線在處的切線方程是y = 1 切線斜率是 0 曲線y = sinx 在點(diǎn) (0,0)處的切線方程為 y = x 切線斜率是

5、 1 4.函數(shù)的單調(diào)減少區(qū)間是（，0 ） 函數(shù)的單調(diào)增加區(qū)間是（0，+） .函數(shù)的單調(diào)減少區(qū)間是 （，1 ） .函數(shù)的單調(diào)增加區(qū)間是 （0，+） 函數(shù)的單調(diào)減少區(qū)間是 （0，+） 5-1 . tan x +c 若，則9 sin 3x 5-2 3 0 0 下列積分計(jì)算正確的是（ b ）a b c d 三、計(jì)算題（一）、計(jì)算極限（1小題，11分）（1）利用極限的四則運(yùn)算法則，主要是因式分解，消去零因子。（2）利用連續(xù)函數(shù)性質(zhì)：有定義，則極限類型1： 利用重要極限 ， ， 計(jì)算1-1求 解： 1-2 求 解： 1-3 求 解：=類型2： 因式分解并利用重要極限 ， 化簡(jiǎn)計(jì)算。2-1求 解： =2-2

6、 解： 2-3 解： 類型3：因式分解并消去零因子，再計(jì)算極限3-1 解： =3-2 3-3 解 其他： ， ， （0807考題）計(jì)算 解： =（0801考題. ）計(jì)算 解 （0707考題.）= （二） 求函數(shù)的導(dǎo)數(shù)和微分（1小題，11分）（1）利用導(dǎo)數(shù)的四則運(yùn)算法則 （2）利用導(dǎo)數(shù)基本公式和復(fù)合函數(shù)求導(dǎo)公式 類型1：加減法與乘法混合運(yùn)算的求導(dǎo)，先加減求導(dǎo)，后乘法求導(dǎo)；括號(hào)求導(dǎo)最后計(jì)算。1-1 解：1-2 解：1-3 設(shè)，求解： 類型2：加減法與復(fù)合函數(shù)混合運(yùn)算的求導(dǎo)，先加減求導(dǎo)，后復(fù)合求導(dǎo)2-1 ，求 解：2-2 ，求 解：2-3 ，求， 解：類型3： 乘積與復(fù)合函數(shù)混合運(yùn)算的求導(dǎo)，先乘積求

7、導(dǎo)，后復(fù)合求導(dǎo)，求 。 解：其他：，求。 解：0807.設(shè)，求 解：0801.設(shè)，求 解：0707.設(shè)，求 解：0701.設(shè)，求 解：（三）積分計(jì)算：（2小題，共22分）湊微分類型1： 計(jì)算 解：0707.計(jì)算 解： 0701計(jì)算 解： 湊微分類型2：.計(jì)算 解： 0807.計(jì)算 解：0801.計(jì)算 解： 湊微分類型3：， 計(jì)算 解：.計(jì)算 解： 5 定積分計(jì)算題，分部積分法類型1：計(jì)算 解： ， 計(jì)算 解： ， 計(jì)算 解：，=0807 0707 類型2 （0801考題） 類型3： 四、應(yīng)用題（1題，16分）類型1： 圓柱體上底的中心到下底的邊沿的距離為l，問(wèn)當(dāng)?shù)装霃脚c高分別為多少時(shí)，圓柱體的

8、體積最大？l解：如圖所示，圓柱體高與底半徑滿足 圓柱體的體積公式為 求導(dǎo)并令 得，并由此解出即當(dāng)?shù)装霃?，高時(shí)，圓柱體的體積最大類型2：已知體積或容積，求表面積最小時(shí)的尺寸。2-1（0801考題） 某制罐廠要生產(chǎn)一種體積為v的有蓋圓柱形容器，問(wèn)容器的底半徑與高各為多少時(shí)用料最??？解：設(shè)容器的底半徑為，高為，則其容積表面積為， 由得，此時(shí)。由實(shí)際問(wèn)題可知，當(dāng)?shù)装霃脚c高 時(shí)可使用料最省。一體積為v的圓柱體，問(wèn)底半徑與高各為多少時(shí)表面積最小？ 解： 本題的解法和結(jié)果與2-1完全相同。生產(chǎn)一種體積為v的無(wú)蓋圓柱形容器，問(wèn)容器的底半徑與高各為多少時(shí)用料最省？ 解：設(shè)容器的底半徑為，高為，則無(wú)蓋圓柱形容器表

9、面積為 ，令 ， 得 ，由實(shí)際問(wèn)題可知，當(dāng)?shù)装霃脚c高 時(shí)可使用料最省。2-2欲做一個(gè)底為正方形，容積為32立方米的長(zhǎng)方體開口容器，怎樣做法用料最??？（0707考題）解： 設(shè)底邊的邊長(zhǎng)為，高為，用材料為，由已知，表面積 ，令，得， 此時(shí)=2由實(shí)際問(wèn)題可知，是函數(shù)的極小值點(diǎn)，所以當(dāng)，時(shí)用料最省。欲做一個(gè)底為正方形，容積為62.5立方米的長(zhǎng)方體開口容器，怎樣做法用料最?。?解： 本題的解法與2-2同，只需把v=62.5 代入即可。類型3 求求曲線上的點(diǎn)，使其到點(diǎn)的距離最短曲線上的點(diǎn)到點(diǎn)的距離平方為 ， 3-1在拋物線上求一點(diǎn)，使其與軸上的點(diǎn)的距離最短 解：設(shè)所求點(diǎn)p（x，y），則滿足 ，點(diǎn)p 到點(diǎn)a

10、 的距離之平方為令，解得是唯一駐點(diǎn)，易知是函數(shù)的極小值點(diǎn)，當(dāng)時(shí)，或，所以滿足條件的有兩個(gè)點(diǎn)（1，2）和（1，2）3-2求曲線上的點(diǎn)，使其到點(diǎn)的距離最短解：曲線上的點(diǎn)到點(diǎn)a（2，0） 的距離之平方為令，得， 由此， 即曲線上的點(diǎn)（1，）和（1，）到點(diǎn)a（2，0）的距離最短。08074 求曲線上的點(diǎn)，使其到點(diǎn)a（0，2）的距離最短。解： 曲線上的點(diǎn)到點(diǎn)a（0，2）的距離公式為 與在同一點(diǎn)取到最大值，為計(jì)算方便求的最大值點(diǎn)， 令 得，并由此解出，即曲線上的點(diǎn)（）和點(diǎn)（）到點(diǎn)a（0，2）的距離最短emloyment tribunals sort out disagreements between em

11、ployers and employees. you may need to make a claim to an employment tribunal if: you dont agree with the disciplinary action your employer has taken against you your employer dismisses you and you think that you have been dismissed unfairly. for more informu, take advice from one of the organisatio

12、ns listed underfur ther help. employment tribunals are less formal than some other courts, but it is still a legal process and you will need to give evidence under an oath or affirmation. most people find making a claim to an employment tribunal challenging. if you are thinking about making a claim

13、to an employment tribunal, you should get help straight away from one of the organisations listed underfurther help. ation about dismissal and unfair dismissal, seedismissal. you can make a claim to an employment tribunal, even if you haventappealedagainst the disciplinary action your employer has t

14、aken against you. however, if you win your case, the tribunal may reduce any compensation awarded to you as a result of your failure to appeal. remember that in most cases you must make an application to an employment tribunal within three months of the date when the event you are complaining about

15、happened. if your application is received after this time limit, the tribunal will not usually accept i. if you are worried about how the time limits apply to you if you are being represented by a solicitor at the tribunal, they may ask you to sign an agreement where you pay their fee out of your co

16、mpensation if you win the case. this is known as adamages-based agreement. in england and wales, your solicitor cant charge you more than 35% of your compensationif you win the case. you are clear about the terms of the agreement. it might be best to get advice from an experienced adviser, for examp

17、le, at a citizens advice bureau. to find your nearest cab, including those that give advice by e-mail, click onnearest cab. for more information about making a claim to an employment tribunal, seeemployment tribunals. the (lack of) air up there watch m cay man islands-based webb, the head of fifas a

18、nti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday. i am going to be at the match tomorrow and i have asked to meet ya ya toure, he told bbc sport. for me its about how he felt and i would li

19、ke to speak to him first to find out what his experience was. uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win. michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees

20、actions. cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. age has reached the end of the beginning of a word. may be guilty in his seems to passing a lot of different life became the appearance of

21、 the same day; may be back in the past, to oneself the paranoid weird belief disillusionment, these days, my mind has been very messy, in my mind constantly. always feel oneself should go to do something, or write something. twenty years of life trajectory deeply shallow, suddenly feel something, do

22、 it.一字開頭的年齡已經(jīng)到了尾聲?；蛟S是愧疚于自己似乎把轉(zhuǎn)瞬即逝的很多個(gè)不同的日子過(guò)成了同一天的樣子；或許是追溯過(guò)去，對(duì)自己那些近乎偏執(zhí)的怪異信念的醒悟，這些天以來(lái)，思緒一直很凌亂，在腦海中不斷糾纏?？傆X得自己似乎應(yīng)該去做點(diǎn)什么，或者寫點(diǎn)什么。二十年的人生軌跡深深淺淺，突然就感覺到有些事情，非做不可了。the end of our life, and can meet many things really do?而窮盡我們的一生，又能遇到多少事情是真正地非做不可？ during my childhood, think lucky money and new clothes are neces

23、sary for new year, but as the advance of the age, will be more and more found that those things are optional; junior high school, thought to have a crush on just means that the real growth, but over the past three years later, his writing of alumni in peace, suddenly found that isnt really grow up,

24、it seems is not so important; then in high school, think dont want to give vent to out your inner voice can be in the high school children of the feelings in a period, but was eventually infarction when graduation party in the throat, later again stood on the pitch he has sweat profusely, looked at

25、his thrown a basketball hoops, suddenly found himself has already cant remember his appearance. baumgartner the disappointing news: mission aborted. r plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or hu

26、midity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitud

27、e of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence. we often close ourselves off when traumatic events happen in our lives; instead of letting the world soften us, we let it drive

28、us deeper into ourselves. we try to deflect the hurt and pain by pretending it doesnt exist, but although we can try this all we want, in the end, we cant hide from ourselves. we need to learn to open our hearts to the potentials of life and let the world soften us.生活發(fā)生不幸時(shí)，我們常常會(huì)關(guān)上心門；世界不僅沒(méi)能慰藉我們，反倒使我們更加消沉。我們假裝一切仿佛都不曾發(fā)生，以此試圖忘卻傷痛，可就算隱藏得再好，最終也還是騙不了自己。既然如此，何不嘗試打開心門，擁抱生活中的各種可能，讓世界感化我們呢？ whenever we start to le