电大《微积分初步》复习题及答案小抄.doc

微积分初步模拟试题一、填空题（每小题4分，本题共20分）函数的定义域是若，则 曲线在点处的切线方程是微分方程的特解为 二、单项选择题（每小题4分，本题共20分）设函数，则该函数是（）A偶函数B奇函数C非奇非偶函数 D既奇又偶函数当（ ）时，函数，在处连续.A0 B1 C D下列结论中（ ）正确 A在处连续，则一定在处可微. B函数的极值点一定发生在其驻点上. C在处不连续，则一定在处不可导. D函数的极值点一定发生在不可导点上.下列等式中正确的是（）A . B. C. D. 微分方程的阶数为（）A. 2； B. 3； C. 4； D. 5三、计算题（本题共44分，每小题11分）计算极限设，求. 计算不定积分计算定积分四、应用题（本题16分） 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？参考答案一、填空题（每小题4分，本题共20分） 2 0 二、单项选择题（每小题4分，本题共20分）ACCDB 三、（本题共44分，每小题11分）解：原式 解： 解：= 解： 四、应用题（本题16分）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，时用料最省。 一、填空题（每小题4分，本题共20分）函数，则 当时，为无穷小量.若y = x (x 1)(x 2)(x 3)，则(1) = 微分方程的特解为 . 二、单项选择题（每小题4分，本题共20分）函数的定义域是（）A BC D 曲线在处切线的斜率是（ ） A B C D下列结论正确的有（ ） A若(x0) = 0，则x0必是f (x)的极值点 Bx0是f (x)的极值点，且(x0)存在，则必有(x0) = 0 Cx0是f (x)的极值点，则x0必是f (x)的驻点 D使不存在的点x0，一定是f (x)的极值点下列无穷积分收敛的是（）A B C D 微分方程的阶数为（）A. 1；B. 2；C. 3； D. 4三、计算题（本题共44分，每小题11分）计算极限设，求. 计算不定积分计算定积分四、应用题（本题16分） 用钢板焊接一个容积为4的底为正方形的无盖水箱，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？试题答案（供参考）一、填空题（每小题4分，本题共20分） 0 二、单项选择题（每小题4分，本题共20分）CDBA D三、（本题共44分，每小题11分）解： 解： 解：= 4解： 四、应用题（本题16分）解：设水箱的底边长为，高为，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，当时水箱的表面积最小. 此时的费用为 （元） 一、填空题（每小题4分，本题共20分）函数，则 曲线在点处的切线方程是若，则 微分方程的阶数为 二、单项选择题（每小题4分，本题共20分）设函数，则该函数是（）A非奇非偶函数B既奇又偶函数C偶函数 D奇函数当时，下列变量中为无穷小量的是（ ）.A B C D下列函数在指定区间上单调减少的是（ ） A B C D 设，则（ ） A. B. C. D. 下列微分方程中，（ ）是线性微分方程 A B C D 三、计算题（本题共44分，每小题11分）计算极限设，求. 计算不定积分计算定积分四、应用题（本题16分） 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？参考答案（供参考）一、填空题（每小题4分，本题共20分） 5二、单项选择题（每小题4分，本题共20分）DCBCA 三、（本题共44分，每小题11分）解：原式 解： 解：= 4解： 四、应用题（本题16分）解：设长方体底边的边长为，高为，用材料为，由已知 令，解得是唯一驻点， 因为问题存在最小值，且驻点唯一，所以是函数的极小值点，即当，时用料最省. 一、填空题（每小题4分，本题共20分）函数，则若函数,在处连续，则 函数的单调增加区间是 微分方程的阶数为 二、单项选择题（每小题4分，本题共20分）设函数，则该函数是（）A奇函数 B偶函数C非奇非偶函数 D既奇又偶函数当时，下列变量为无穷小量的是（ ）.A B C D 若函数f (x)在点x0处可导，则( )是错误的 A函数f (x)在点x0处有定义 B函数f (x)在点x0处连续 C函数f (x)在点x0处可微 D，但 若，则（ ）. A. B. C. D. 下列微分方程中为可分离变量方程的是（）A. ； B. ； C. ； D. 三、计算题（本题共44分，每小题11分）计算极限设，求. 计算不定积分计算定积分四、应用题（本题16分） 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可使用料最省？参考答案一、填空题（每小题4分，本题共20分） 2 4二、单项选择题（每小题4分，本题共20分）BADCB 三、计算题（本题共44分，每小题11分）解：原式 解： 解：= 4解： 待添加的隐藏文字内容3四、应用题（本题16分）解：设容器的底半径为，高为，则其表面积为，由已知，于是，则其表面积为 令，解得唯一驻点，由实际问题可知，当时可使用料最省，此时，即当容器的底半径与高分别为与时，用料最省 "If we don't do that it will go on and go on. We have to stop it; we need the courage to do it."His comments came hours after Fifa vice-president Jeffrey Webb - also in London for the FA's celebrations - said he wanted to meet Ivory Coast international Toure to discuss his complaint.CSKA general director Roman Babaev says the matter has been "exaggerated" by the Ivorian and the British media.Blatter, 77, said: "It has been decided by the Fifa congress that it is a nonsense for racism to be dealt with with fines. You can always find money from somebody to pay them."It is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. It is all nonsense."We can do something better to fight racism and discrimination."This is one of the villains we have today in our game. But it is only with harsh sanctions that racism and discrimination can be washed out of football."The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifa's anti-racism taskforce, is in London for the Football Association's 150th anniversary celebrations and will attend City's Premier League match at Chelsea on Sunday."I am going to be at the match tomorrow and I have asked to meet Yaya Toure," he told BBC Sport."For me it's about how he felt and I would like to speak to him first to find out what his experience was."Uefa has opened disciplinary proceedings against CSKA for the "racist behaviour of their fans" during City's 2-1 win.Michel Platini, president of European football's governing body, has also ordered an immediate investigation into the referee's actions.CSKA said they were "surprised and disappointed" by Toure's complaint. In a statement the Russian side added: "We found no racist insults from fans of CSKA."Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather 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 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 kilometers), 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.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, he'll be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes it's not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it won't. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).cause there