问答题求函数y=2x3-3x2的单调区间、极值及函数曲线的凸凹性区间、拐点和渐近线．

问答题求由曲线y=lnx过点(e，1)的切线、x轴及该曲线所围成平面图形D的面积A及该图形绕y轴旋转一周所生成的旋转体的体积Vy．

问答题某工厂生产甲、乙两种产品，当这两种产品的产量分别为x和y(单位：吨)时的总效益函数为 R(x，y)=15x+34y-x2-2xy-4y2-36 (单位：万元)． 已知生产甲种产品每吨需支付排污费用1万元，生产乙种产品每吨需支付排污费2万元．

问答题曲线y=(x-1)(x-2)和x轴围成一平面图形，求此平面图形绕y轴旋转一周所成的旋转体的体积．

问答题设，X是4×2矩阵，．

问答题求∫(x2-sinx)dx．

问答题3阶矩阵A的特征值为1，-1，0，对应的特征向量分别为α 1 ，α 2 ，α 3 ，若B=A 2 -2A+3E，试求B -1 的特征值和特征向量．

问答题计算定积分

问答题设随机变量X和Y相互独立且都服从正态分布N(0，1)，而X1，X2，…，X9，和Y1，Y2，…，Y9分别是来自总体X和Y的简单随机样本，求统计量

问答题{{B}}Directions:{{/B}}{{I}} Read the following passage carefully and then translate the underlined sentences into Chinese.{{/I}}44. {{U}}The Single long a stock figure in stories, songs and personal ads. was traditionally someone at the margins of society: a figure of fun, pity or awe. {{/U}}In the place of withered spinsters and bachelors are people like Elizabeth de Kergorlay, a 29-year-old Parisian banker who views her independence and her own apartment as the spoils of professional success. As the sages would say, we are all ultimately alone. But an increasing number of Europeans are choosing to be so at an ever earlier age. 45. {{U}}This isn't the stuff of gloomy philosophical meditations, but a fact of Europe's new economic landscape, embraced by demographers, real-estate developers and ad executives alike. {{/U}}46. {{U}}The shift away from family life to solo lifestyles, observes French sociologist, Jean-Claude Kaufmanns, is part of the "irresistible momentum of individualism" over the last century. {{/U}}47. {{U}}The communications revolution, the shift from a business culture of stability to one of mobility and the mass entry of women into the workforce have wreaked havoc on Europeans' private lives. {{/U}}More and more of them are remaining on their own: they're living longer, divorcing more and marrying later—if at all. British marriage rates are the lowest in 160 years of records. INSEE, France's National Institute of Statistics, reports that the number of French people living alone doubled between 1968 and 1990. Europe's new economic climate has largely fostered the trend toward independence. 48. {{U}}The current generation of home-aloners came of age during Europe's shift from social democracy to the sharper, more individualistic climate of American-style capitalism. Raised in an era of privatization and increased consumer choice, today's tech-savvy workers have embraced a free market in love as well as economics. {{/U}}Modern Europeans are rich enough to afford to live alone, and temperamentally independent enough to want to do so. A recent poll by the Institute Francois Dominion Publique, the French affiliate of the Gallup poll, found that 58 percent of French respondents viewed living alone as a choice, not an obligation. Other European singles agree. "I've always wanted to be free to go on adventures," says Iris Expender, who lives by herself in Berlin.

问答题求

问答题(1)证明：利用变换可将方程化为；(2)求原方程的通解．