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1、微积分初步形成性考核作业（一）解答函数，极限和连续一、填空题（每小题2分，共20分）1函数的定义域是解：， 所以函数的定义域是2函数的定义域是 解：， 所以函数的定义域是3函数的定义域是解： ， 所以函数的定义域是4函数，则 解： 所以5函数，则 解：6函数，则 解：，7函数的间断点是 解：因为当，即时函数无意义 所以函数的间断点是8解：9若，则解： 因为 所以10若，则解：因为 所以二、单项选择题（每小题2分，共24分）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既奇又偶函数解：因为 所以函数是偶函数。故应选B2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
2、偶函数解：因为 所以函数是奇函数。故应选A3函数的图形是关于（）对称A B轴C轴 D坐标原点解：因为 所以函数是奇函数 从而函数的图形是关于坐标原点对称的 因此应选D4下列函数中为奇函数是（）A B C D解：应选C5函数的定义域为（）A B C且 D且解：，所以应选D 6函数的定义域是（）A BC D解：，函数的定义域是，故应选D 7设，则（ ）A B C D 解： ，故应选C8下列各函数对中，（）中的两个函数相等 A， B， C， D， 解：两个函数相等必须满足定义域相同函数表达式相同，所以应选D9当时，下列变量中为无穷小量的是（ ）.A B C D解：因为，所以当时，为无穷小量，所以应选
3、C10当（ ）时，函数，在处连续.A0 B1 C D 解：因为， 若函数，在处连续，则，因此。故应选B11当（ ）时，函数在处连续.A0 B1 C D 解：，所以应选D12函数的间断点是（ ）AB C D无间断点解：当时分母为零，因此是间断点，故应选A三、解答题（每小题7分，共56分）计算极限 解：2计算极限解：3 解： 4计算极限 解：5计算极限解：6计算极限 解： 7计算极限解： 8计算极限 解： 微积分初步形成性考核作业（二）解答（除选择题）导数、微分及应用一、填空题（每小题2分，共20分）1曲线在点的斜率是 解：，斜率2曲线在点的切线方程是 解： ，斜率 所以曲线在点的切线方程是：3曲
4、线在点处的切线方程是解：，斜率 所以曲线在点处的切线方程是：，即：4 解：5若y = x (x 1)(x 2)(x 3)，则(0) = 解：6已知，则=解：，7已知，则=解：，8若，则 解：， 9函数的单调增加区间是 解：，所以函数的单调增加区间是10函数在区间内单调增加，则a应满足 解：，而，所以二、单项选择题（每小题2分，共24分）1函数在区间是（ D ）A单调增加 B单调减少C先增后减 D先减后增2满足方程的点一定是函数的（ C ）.A极值点B最值点 C驻点D 间断点3若，则=（C ） A. 2 B. 1 C. -1 D. -24设，则（B ） A B C D5设是可微函数，则（ D ）
5、 A B C D 6曲线在处切线的斜率是（ C ） A B C D 7若，则（ C ） A B C D 8若，其中是常数，则（ C ） A B C D9下列结论中（ B ）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. C可导函数的极值点一定发生在其驻点上. D若在a，b内恒有，则在a，b内函数是单调下降的.10若函数f (x)在点x0处可导，则( B )是错误的 A函数f (x)在点x0处有定义 B，但 C函数f (x)在点x0处连续 D函数f (x)在点x0处可微 11下列函数在指定区间上单调增加的是（ B） Asinx Be x Cx 2 D3 - x12.下列结
6、论正确的有（ A ） Ax0是f (x)的极值点，且(x0)存在，则必有(x0) = 0 Bx0是f (x)的极值点，则x0必是f (x)的驻点 C若(x0) = 0，则x0必是f (x)的极值点 D使不存在的点x0，一定是f (x)的极值点三、解答题（每小题7分，共56分）设，求 解：2设，求.解：3设，求.解：4设，求. 解：5设是由方程确定的隐函数，求.解：两边微分： 6设是由方程确定的隐函数，求. 解：两边对求导，得： ， 7设是由方程确定的隐函数，求.解：两边微分，得： ，8设，求解：两边对求导，得： 微积分初步形成性考核作业（三）解答（填空题除外）不定积分，极值应用问题一、填空题（
7、每小题2分，共20分）1若的一个原函数为，则 。2若的一个原函数为，则 。3若，则4若，则 5若，则6若，则78 9若，则10若，则二、单项选择题（每小题2分，共16分）1下列等式成立的是（）A B CD解：应选A2若，则（ ）. A. B. C. D. 解：两边同时求导，得：，所以应选A3若，则（ ）. A. B. C. D. 解：应选A4以下计算正确的是（ ）ABCD 解：应选A5（ ）A. B. C. D. 解：，所以应选A6=（ ） A B C D 解：应选C7如果等式，则（ ）A. B. C. D. 解：两边求导，得：，所以，故应选B三、计算题（每小题7分，共35分）1解： 2 解：
8、 3解：4解： 5解：四、极值应用题（每小题12分，共24分）1 设矩形的周长为120厘米，以矩形的一边为轴旋转一周得一圆柱体。试求矩形的边长为多少时，才能使圆柱体的体积最大。 解：设矩形的一边长为厘米，则另一边长为厘米，以厘米的边为轴旋转一周得一圆柱体，则体积为：，即：，令，得：（不合题意，舍去），这时由于根据实际问题，有最大体积，故当矩形的一边长为厘米、另一边长为厘米时，才能使圆柱体的体积最大。2 欲用围墙围成面积为216平方米的一成矩形的土地，并在正中用一堵墙将其隔成两块，问这块土地的长和宽选取多大尺寸，才能使所用建筑材料最省？ 解：设矩形的长为米，则矩形的宽为米，从而所用建筑材料为：，
9、即：，令得：（取正值），这时由于根据实际问题，确实有最小值，故当矩形的长为米，宽为米时，才能使所用建筑材料最省五、证明题（本题5分）函数在（是单调增加的证明：因为，当（时， 所以函数在（是单调增加的微积分初步形成性考核作业（四）解答（选择题除外）定积分及应用、微分方程一、填空题（每小题2分，共20分）1 解：2解：3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 。解：由得所求的曲线方程由确定 因为曲线过，所以，解得： 因此所求的曲线方程为4若 解：5由定积分的几何意义知，= 。解：由定积分的几何意义知，就等于圆在第象限的面积，即 圆面积的，因此6 .解：07= 解： 8微分方程的
10、特解为 . 解：由得，两边同时积分，得 因为，所以，所以 从而，因此微分方程的特解为9微分方程的通解为 .解：， ，即 所以微分方程的通解为10微分方程的阶数为 解：微分方程的阶数为阶二、单项选择题（每小题2分，共20分）1在切线斜率为2x的积分曲线族中，通过点（1, 4）的曲线为（ A ）Ay = x2 + 3 By = x2 + 4 C D 2若= 2，则k =（ A ） A1 B-1 C0 D 3下列定积分中积分值为0的是（ A ） A B C D 4设是连续的奇函数，则定积分（ D ）AB CD 05（ D ）A0 B C D6下列无穷积分收敛的是（B ）ABCD 7下列无穷积分收敛的
11、是（B ）AB CD8下列微分方程中，（ D ）是线性微分方程 A B C D9微分方程的通解为（ C ） A B C D10下列微分方程中为可分离变量方程的是（B ）A. ；B. ； C. ； D. 三、计算题（每小题7分，共56分）1解：2 解： 3解：4解： 5解： 6求微分方程满足初始条件的特解解：微分方程的通解为 这里 ， 代入得微分方程的通解为 将初始条件代入上式，解得 所以微分方程的特解为7求微分方程的通解。解：微分方程的通解为 这里， 代入得微分方程的通解为四、证明题（本题4分）证明等式。证明： 考虑积分，令，则，从而 所以 ag an employment tribunal
12、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 action your employer has taken against you your employer dismisses you and you think that you have been dismissed unfairly.
13、 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 and you will need to give evidence under an oath or affirmation. Most people find making a claim to an employment tribu
14、nal 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 about dismissal and unfair dismissal, seeDismissal. You can make a claim to an employment tribunal, even if you haventa
15、ppealedagainst 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 your failure to appeal. Remember that in most cases you must make an application to an employment tribunal within three mo
16、nths 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 worried about how the time limits apply to you If you are being represented by a solicitor at the tribunal, they may ask you t
17、o 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 charge you more than 35% of your compensationif you win the case. You are clear about the terms of the agreement. It might be
18、 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. For more information about making a claim to an employment tribunal, seeEmployment tribunals. The (lack of) air up the
19、re 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 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 t
20、old 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 racist behaviour of their fans duringCitys 2-1 win. Michel Platini, president of European footballs governing body, has
21、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 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 t
22、o 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 very messy, in my mind constantly. Always feel oneself should go to do something, or write something. Twenty years of l
23、ife trajectory deeply shallow, suddenly feel something, do it.一字开头的年龄已经到了尾声。或许是愧疚于自己似乎把转瞬即逝的很多个不同的日子过成了同一天的样子；或许是追溯过去，对自己那些近乎偏执的怪异信念的醒悟，这些天以来，思绪一直很凌乱，在脑海中不断纠缠。总觉得自己似乎应该去做点什么，或者写点什么。二十年的人生轨迹深深浅浅，突然就感觉到有些事情，非做不可了。The end of our life, and can meet many things really do?而穷尽我们的一生，又能遇到多少事情是真正地非做不可？ During
24、 my childhood, think lucky money and new clothes are necessary 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
25、alumni in peace, suddenly found that isnt really grow up, 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 a
26、gain stood on the pitch he has sweat profusely, looked at 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
27、 calm - winds less than 2 mph, with no precipitation or humidity 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 k
28、ilometers), drifting even higher than the cruising altitude 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
29、; instead of letting the world soften us, we let it drive 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
30、let the world soften us.生活发生不幸时，我们常常会关上心门；世界不仅没能慰藉我们，反倒使我们更加消沉。我们假装一切仿佛都不曾发生，以此试图忘却伤痛，可就算隐藏得再好，最终也还是骗不了自己。既然如此，何不尝试打开心门，拥抱生活中的各种可能，让世界感化我们呢？ Whenever we start to let our fears and seriousness get the best of us, we should take a step back and re-evaluate our behavior. The items listed below are six
31、ways you can open your heart more fully and completely.当恐惧与焦虑来袭时，我们应该退后一步，重新反思自己的言行。下面六个方法有助于你更完满透彻地敞开心扉。Whenever a painful situation arises in your life, try to embrace it instead of running away or trying to mask the hurt. When the sadness strikes, take a deep breath and lean into it. When we run
32、away from sadness thats unfolding in our lives, it gets stronger and more real. We take an emotion thats fleeting and make it a solid event, instead of something that passes through us.当生活中出现痛苦的事情时，别再逃跑或隐藏痛苦，试着拥抱它吧；当悲伤来袭时，试着深呼吸，然后直面它。如果我们一味逃避生活中的悲伤，悲伤只会变得更强烈更真实悲伤原本只是稍纵即逝的情绪，我们却固执地耿耿于怀By utilizing our breath we soften our experiences. If we dam them up, our lives will stagnate, but when we keep them flowing, we allow more newness and greater experiences to blossom.深呼吸能减缓我们的感受。屏住呼吸，生活停滞；呼出呼吸，更多新奇与经历又将拉开序幕。16
