问答题已知平面上三条不同直线的方程分别为 l 1 ：ax+2by+3c=0， l 2 ：bx+2cy+3a=0， l 3 ：cx+2ay+3b=0． 试证：这三条直线交于一点的充分必要条件为a+b+c=0．

问答题已知z=f(xlny，x-y)，求

问答题设随机变量(X，Y)在区域D={(x，y)|0≤x≤2，0≤y≤1}上服从均匀分布，令

问答题计算．

问答题设表示不超过1+x2+y2的最大整数，计算二重积分

问答题求微分方程x 3 y""+2x 2 y"-xy"+y=0的通解．

问答题求一曲线通过(2，3)，它在两坐标轴间的切线段均被切点平分，求此曲线方程y=y(x)．

问答题已知F(x)是f(x)的一个原函数，而F(x)是微分方程xy'+y=ex满足初始条件的解，试将f(x)展开成x的幂级数，并求的和．

问答题计算

问答题设β1=α1，β2=α1+α2，βl=α1+α2+α1+α2+…+αl，且向量组α1，α2，…，αl线性无关，证明向量组β1，β2，…，βl也线性无关．

问答题{{B}}Directions:{{/B}}{{I}} In this section there is a passage in English. Translate the five sentences under-lined into Chinese and write your translation on ANSWER SHEET 2.{{/I}}56. {{U}}When you are in the business of sending spacecraft to other planets, it is probably wise to do everything you can m keep your space-probes sterile (无菌的){{/U}}. NASA, America's space agency, certainly does so. After all, you would not want hugs from one planet to contaminate another where they might possibly thrive. But according to Curt Mileikowsky, of the Royal Institute of Technology in Stockholm, this may already have happened naturally billions of years ago when the solar sys- tem was young. For Dr Mileikowsky has taken a century-old idea called panspermia (有生源说), and shown that it is plausible. 57. {{U}}Panspermia is the theory that life does not start independently on each planet that has it (assuming that other planets do). Rather, it hops from place to place, "infecting" new worlds as it goes{{/U}}. Supported by experts in biology, geology and celestial mechanics, Dr Mileikowsky argued to the American Astronomical Society meeting in Atlanta that this is not as outlandish as it sounds. 58. {{U}}Bungling (笨手笨脚) space organizations apart, the only mode of travel open to microbes seems to be meteorites (流星). Most of these are small bits of junk from the asteroid (小行星) belt that have gone off course{{/U}}. But some are rocks that have been flung into space from the surfaces of planets as a result of those planets having been struck by even larger bits of rock--decent-sized asteroids or comets. 59. {{U}}If there is life on such a planet, microscopic forms of it will probably live deep in- side rocks, as they do on earth. The acceleration of lift-off would not kill something that size{{/U}}. 60. {{U}}If a rock is large enough, the heat generated as it is thrown clear will be negligible except at its surface--where, ii anything, melting may even produce an airtight skin to protect any microbes deeper down from the unpleasant vacuum of space{{/U}}.

问答题设f(x)连续且f(0)=0，f"(0)=2，求极限

问答题设曲线f(x)=xn在点(1，1)处的切线与x轴的交点为(xn，0)，计算

问答题忙碌的推销商驾驭在利润与亏损之间的一条细线上，特别是在确定价格上，例如，对当地电影院的影片准入闭路电视议价．根据连续记录，影院测定，如果入场票时20元，则影院取1000人为观影的平均人数．但是每提价1元，影院就从平均人数中失去100个顾客．每位顾客在让价上平均花费1.8元．为使总利润最大化，影院应当确定的入场票价是多少?