电大《高等数学基础》必过考试精篇复习资料必备小抄.doc
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1、Four short words sum up what has lifted most successful individuals above the crowd: a little bit more.-author-date电大高等数学基础必过考试精篇复习资料必备小抄计算机数学基础A作业高等数学基础归类复习考试小抄一、单项选择题1-1下列各函数对中,( C )中的两个函数相等 A. , B. , C., D. ,1-设函数的定义域为,则函数的图形关于(C )对称A. 坐标原点 B. 轴 C. 轴 D. 设函数的定义域为,则函数的图形关于(D )对称A. B. 轴 C. 轴 D. 坐标原点
2、.函数的图形关于( A )对称(A) 坐标原点 (B) 轴 (C) 轴 (D) 1-下列函数中为奇函数是( B )A. B. C. D. 下列函数中为奇函数是(A )A. B. C. D. 下列函数中为偶函数的是( D )A B C D 2-1 下列极限存计算不正确的是( D ) A. B. C. D. 2-2当时,变量( C )是无穷小量A. B. C. D. 当时,变量( C )是无穷小量A B C D .当时,变量(D )是无穷小量A B C D 下列变量中,是无穷小量的为( B ) A B C D.3-1设在点x=1处可导,则( D )A. B. C. D. 设在可导,则( D )A
3、B C D 设在可导,则( D )A. B. C. D. 设,则( A ) A B. C. D. 3-2. 下列等式不成立的是(D )A. B C. D.下列等式中正确的是(B )A. B. C. D.4-1函数的单调增加区间是( D ) A. B. C. D. 函数在区间内满足(A ) A. 先单调下降再单调上升 B. 单调下降 C. 先单调上升再单调下降 D. 单调上升.函数在区间(5,5)内满足( A )A 先单调下降再单调上升 B 单调下降 C先单调上升再单调下降 D 单调上升. 函数在区间内满足(D )A. 先单调下降再单调上升 B. 单调下降 C. 先单调上升再单调下降 D. 单调
4、上升5-1若的一个原函数是,则(D ) A. B. C. D. .若是 的一个原函数,则下列等式成立的是( A )。 A B C D5-2若,则( 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 -3若,则( B ) A. B. C. D. 补充: , 无穷积分收敛的是 函数的图形关于 y 轴 对称。二、填空题函数的定义域是(3,+) 函数的定义域是 (2,3) (3,4 函数的定义域是(5,2)若函数,则 1 2若函数,在处连续,则e .函数在处连续,则 2 函数的间断点是x=0 函数的间断点是
5、 x=3 。函数的间断点是 x=0 3-曲线在处的切线斜率是1/2 曲线在处的切线斜率是 1/4 曲线在(0,2)处的切线斜率是 1 .曲线在处的切线斜率是 3 3-2 曲线在处的切线方程是y = 1 切线斜率是 0 曲线y = sinx 在点 (0,0)处的切线方程为 y = x 切线斜率是 1 4.函数的单调减少区间是(,0 ) 函数的单调增加区间是(0,+) .函数的单调减少区间是 (,1 ) .函数的单调增加区间是 (0,+) 函数的单调减少区间是 (0,+) 5-1 . tan x +C 若,则9 sin 3x 5-2 3 0 0 下列积分计算正确的是( B )A B C D 三、计
6、算题(一)、计算极限(1小题,11分)(1)利用极限的四则运算法则,主要是因式分解,消去零因子。(2)利用连续函数性质:有定义,则极限类型1: 利用重要极限 , , 计算1-1求 解: 1-2 求 解: 1-3 求 解:=类型2: 因式分解并利用重要极限 , 化简计算。2-1求 解: =2-2 解: 2-3 解: 类型3:因式分解并消去零因子,再计算极限3-1 解: =3-2 3-3 解 其他: , , (0807考题)计算 解: =(0801考题. )计算 解 (0707考题.)= (二) 求函数的导数和微分(1小题,11分)(1)利用导数的四则运算法则 (2)利用导数基本公式和复合函数求导
7、公式 类型1:加减法与乘法混合运算的求导,先加减求导,后乘法求导;括号求导最后计算。1-1 解:1-2 解:1-3 设,求解: 类型2:加减法与复合函数混合运算的求导,先加减求导,后复合求导2-1 ,求 解:2-2 ,求 解:2-3 ,求, 解:类型3: 乘积与复合函数混合运算的求导,先乘积求导,后复合求导,求 。 解:其他:,求。 解:0807.设,求 解:0801.设,求 解:0707.设,求 解:0701.设,求 解:(三)积分计算:(2小题,共22分)凑微分类型1: 计算 解:0707.计算 解: 0701计算 解: 凑微分类型2:.计算 解: 0807.计算 解:0801.计算 解:
8、 凑微分类型3:, 计算 解:.计算 解: 5 定积分计算题,分部积分法类型1:计算 解: , 计算 解: , 计算 解:,=0807 0707 类型2 (0801考题) 类型3: 四、应用题(1题,16分)类型1: 圆柱体上底的中心到下底的边沿的距离为l,问当底半径与高分别为多少时,圆柱体的体积最大?l解:如图所示,圆柱体高与底半径满足 圆柱体的体积公式为 求导并令 得,并由此解出即当底半径,高时,圆柱体的体积最大类型2:已知体积或容积,求表面积最小时的尺寸。2-1(0801考题) 某制罐厂要生产一种体积为V的有盖圆柱形容器,问容器的底半径与高各为多少时用料最省?解:设容器的底半径为,高为,
9、则其容积表面积为, 由得,此时。由实际问题可知,当底半径与高 时可使用料最省。一体积为V的圆柱体,问底半径与高各为多少时表面积最小? 解: 本题的解法和结果与2-1完全相同。生产一种体积为V的无盖圆柱形容器,问容器的底半径与高各为多少时用料最省? 解:设容器的底半径为,高为,则无盖圆柱形容器表面积为 ,令 , 得 ,由实际问题可知,当底半径与高 时可使用料最省。2-2欲做一个底为正方形,容积为32立方米的长方体开口容器,怎样做法用料最省?(0707考题)解: 设底边的边长为,高为,用材料为,由已知,表面积 ,令,得, 此时=2由实际问题可知,是函数的极小值点,所以当,时用料最省。欲做一个底为正
10、方形,容积为62.5立方米的长方体开口容器,怎样做法用料最省? 解: 本题的解法与2-2同,只需把V=62.5 代入即可。类型3 求求曲线上的点,使其到点的距离最短曲线上的点到点的距离平方为 , 3-1在抛物线上求一点,使其与轴上的点的距离最短 解:设所求点P(x,y),则满足 ,点P 到点A 的距离之平方为令,解得是唯一驻点,易知是函数的极小值点,当时,或,所以满足条件的有两个点(1,2)和(1,2)3-2求曲线上的点,使其到点的距离最短解:曲线上的点到点A(2,0) 的距离之平方为令,得, 由此, 即曲线上的点(1,)和(1,)到点A(2,0)的距离最短。08074 求曲线上的点,使其到点
11、A(0,2)的距离最短。解: 曲线上的点到点A(0,2)的距离公式为 与在同一点取到最大值,为计算方便求的最大值点, 令 得,并由此解出,即曲线上的点()和点()到点A(0,2)的距离最短ag an employment tribunal clai Emloyment tribunals sort out disagreements between employers and employees. You may need to make a claim to an employment tribunal if: you dont agree with the disciplinary act
12、ion 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 organisations listed underFur ther help. Employment tribunals are less formal than some other courts, but it is still a legal process
13、 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 to an employment tribunal, you should get help straight away from one of the organisations listed underFurther help. ation
14、 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 taken against you. However, if you win your case, the tribunal may reduce any compensation awarded to you as a result of yo
15、ur 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 happened. If your application is received after this time limit, the tribunal will not usually accept i. If you are worrie
16、d 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 compensation if you win the case. This is known as adamages-based agreement. In England and Wales, your solicitor cant charg
17、e 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 example, at a Citizens Advice Bureau. To find your nearest CAB, including those that give advice by e-mail, click onnearest CAB
18、. 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 anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Prem
19、ier 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 like to speak to him first to find out what his experience was. Uefa hasopened disciplinary proceedings against CSKAfor the
20、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 actions. CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We fou
21、nd 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 the same day; May be back in the past, to oneself the paranoid weird belief disillusionment, these days, my mind has been
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