英文版-微积分试卷答案-(1).doc

1、 (1) 0 . (2) (3) (4). .(5) 26/3 2、 (6) The right proposition in the following propositions is _A_.A. Ifexists anddoes not exist thendoes not exist.B. If,do both not exist thendoes not exist. C. Ifexists anddoes not exist thendoes not exist. D. Ifexists anddoes not exist thendoes not exist.(7) The right proposition in the following propositions is _B_.A. Ifthenexists. B. If thendoes not exist. C. Ifdoes not exist then.D. Ifdoes not exist then the curedoes not have tangent at.(8) The right statement in the following statements is _D_. A. B. C. D. (9) For continuous function, the erroneous expression in the following expressions is _D_.A. B. C. D. (10) The right proposition in the following propositions is _B_.A. Ifis discontinuous onthenis unbounded on.B. Ifis unbounded onthenis discontinuous on. C. Ifis bounded onthenis continuous on.D. Ifhas absolute extreme values onthenis continuous on.3、Evaluate （考点课本4.4节洛比达法则，每年都会有一道求极限的解答题，大多数都是用洛比达法则去求解，所以大家要注意4.4节的内容。注意洛比达法则的适用范围。）4Find andif. （考察微积分基本定理与微分，书上5.3节）5、 Find= （凑微分求不定积分，积分是微积分的重点及难点，大家一定要掌握透彻。）6、 Given that. (1) Find the intervals on whichis increasing or decreasing. WhenTherefore, the increasing interval is, the decreasing interval is (2) Find the local maximum and minimum values of The function is increasing in interval, decreasing in interval, therefore, the function exist the local minimum value, it is (3)Find the intervals of concavity and the inflection points.Therefore, the concave upward interval are, the concave downward interval are, and the inflection points are ,(4) Find the asymptote lines of the cureTherefore, the line is a horizontal asymptote（考点：4.3节，4.5、4.6节。近几年经常会考一道作图题。这种题目应该在注意的点主要包括函数的定义域，对称性，增减区间，极值点，凹凸性，拐点，以及渐近线等。大家参照课本的4.5节进行作图）7、Let R be the region bounded by the curve , and the line and.(a)Evaluate the area of the region R. R=(b)Find the volume of the solid generated by revolving the R about the y-axis. V=（考点：求面积以及体积，课本6.1、6.2节。这类题目是常考题，较简单。望同学一定要做相应的题目加以巩固。）8、 Determine the production level that will maximize the profit for a company with cost and demand functionsand.Solution Let since x0, then x=400When x=400 Therefore, when the production level is 400 that will maximize the profit 35350 （考点：经济函数，课本4.8节。此题型为常考题，属于送分题，大家可以做相应的4.8节的练习加以巩固） 9、State the second derivative test theorem testing maximum and prove it.Suppose is continuous near c If and , then has a local maximum at c .Proof: Because near c and so is concave downward near c. This means that the graph of lies below its horizontal tangent at c and so has a local maximum at c. 10、Show that the equationhas at most one root in the interval. Suppose the equation has two rootin the interval.Let then there exist Using the Rolles Theorem we can know that there exist one number c can satisfy But, Therefore,