问答题设A为n阶矩阵，证明AT与A的特征值相同．

问答题试证方程x=asinx+b(a＞0，b＞0)至少有一个正根，且不超过a+b.

问答题设函数f(x)在[0，c]上具有单调减少的导数f(x)，f(0)=0．证明：对于满足不等式0＜a＜b＜a+b＜c的a、b，恒有f(a)+f(b)＞f(a+b)

问答题计算∫ L (xy 2 +y)dx+(x 2 y+x)dy，其中

问答题设有曲线，过原点作其切线，求由此曲线、切线及x轴围成的平面图形绕x轴旋转一周所得到的旋转体的表面积．

问答题设求f(x)并讨论f(x)的连续性与可导性．

问答题{{B}}Directions:{{/B}}{{I}} Read the following passage carefully and then translate the underlined sentences into Chinese.{{/I}} The world's long romance with speed may finally be ending. Even if Concorde (协和式飞机) flies again, its antique nature was revealed as soon as the Paris accident made people scratch their heads and ask quite why these odd aircraft were still flying. Much of the technology that surrounded us has, when we look at it afresh, a Jules Verne quality-solving problems that once seemed important in ways that are ingenious but not necessarily efficient or safe. The reorientation of science toward the biological and computer frontiers is now an old story, but the 19th century fascination with motive power has retained a powerful hold on our imaginations and our economies. 71. {{U}}Advances in motive power were for a long while the main way in which progress and national competition in technology were measured. First at sea, then on the railways, then on the roads, in the air and finally in space, more and more rapid movement was seen as an Carefree good and also, in some vague way, as a key to a fuller understanding of the world.{{/U}} So intoxicating was this ultimate way in which the growing speed and reach of manmade vehicles could be used that when an unknown rocket enthusiast called Hermann Oberth published his By Rocket To Interplanetary Space in the 1920s, it represented such an escape from the difficulties of the present to the anxious citizens of Weimar Germany (德国魏玛共和国) that it became a bestseller overnight. 72. {{U}}For individual sportsmen, pilots and drivers, speed had the status of a privileged substance to which, in those early days, only a minority had full access. Mechanized speed made men, and a few women, into heroes, and it remains a commodity to which males, in particular, are attracted.{{/U}} The front of the Boys Own annual of half a century ago would typically feature a speeding train in the middle ground, a fast aeroplane above, and a racing car in the foreground. Disentangling the genuine advantages of speed from its cult aspects has always been a problem, and this was certainly the case in the era in which Concorde was conceived. Land, air and sea speed records had mattered since the 20s in a way inconceivable today. This manic race was run on three tracks-of celebrity sport, of competition between civil industries, and of military development. All three were littered with casualties, whether spectators at Le Mans, Donald Campbell on Coniston Water, or numerous test pilots and astronauts through the years. Britain was slowing down on all three courses when Concorde came along. Indeed the Concorde project survived in part because, as Harold Wilson explained in his memoirs, the agreement with the French was embodied in an international treaty, and they refused even to consider abandoning or postponing the work. "We had little choice but to go on," the then prime minister concluded. His lack of enthusiasm suggests that, long before Concorde flew, some those responsible for it knew that it was not going to be a practical aircraft, and also that the technical spin-off would be less than advertised. The reason was that speed was such as dominant consideration that everything else had to take second place. The result was an aircraft that was both ahead of its tie and behind the times, since the era of small-scale luxury air travel was over. A preoccupation with speed has always gone hand in hand with a preoccupation with safety, the two standards between them providing a way in which advanced states calibrate the state of civilization. Increasing speeds have world lives in constant fear of regression, of losing the scientific and organizational edge that enables it to be both fast and safe. That is one reason why air and sea accidents can attain such mythic status. The disparate treatment of first and third world accidents in the Western press is probably due more to the feeling that accidents are indicators of technical health than to any devaluation of American or Asian lives. Speed still has its kingdom, but it is shrinking. Its limits have long ago been reached on the roads, and its value in the air, even for manned military aircraft, is diminished- agility and protection are as or more important. 73. {{U}}It is still marginally attractive to make trains go faster. The pursuit of physical speed has been replaced by the pursuit of near instantaneity on the Net, an aim which we may in time come to regard just as skeptically.{{/U}} It is hard to imagine the mood in which David Lean's The Sound Barrier was made in 1952. breaking that barrier seemed to hold the key to a mystery. But there was no mystery. Man can go faster, but that does not mean it is worth doing so.

问答题编号为1、2、3的3台仪器正在工作的概率分别为0.9、0.8和0.4，从中任选一台。 (Ⅰ)求此台仪器正在工作的概率； (Ⅱ)已知选到的仪器正在工作，求它编号为2的概率。

问答题设f(x)，g(x)可微，且f'(x)=g(x)，g'(x)=-f(x)，f(0)=0，f'(0)=1，证明：f2(x)+g2(x)=1．

问答题求常数a，b使得在x=0处可导．

问答题设曲面及平面π：2x+2y+z+5=0．