问答题已知二元连续函数f(x，y)满足，g(x，y)满足y)=1及g(0，0)=0．求二重积分，其中D是由曲线x=y2及直线x=1围成的平面图形．

问答题设p(x)是f(x)的导数f(x)的k-1重因式，证明： (i)p(x)未必是f(x)的k重因式； (ii)p(x)是f(x)的k重因式的充分且必要条件是p(x)|f(x)．

问答题若xy=-6，那么xy(x+y)的值可以唯一确定． (1)x-y=5；(2)xy2=18．

问答题某厂家生产的一种产品同时在A，B两个市场销售，每件产品售价分别为p1和p2，需求函数分别为q1=3-0.5p1和q2=2-3p2，总成本函数为．如果A市场的价格对B市场的价格弹性为2，且p2=1时，试问：厂家如何确定两个市场的售价，能使其获得的总利润最大？

问答题解下列微分方程：

问答题设二阶常系数线性微分方程y"+αy"+βy=γe x 的一个特解为y * =e 2x +(1+x)e x ．试确定常数α，β，γ，并求该方程的通解．

问答题设f(x，y)为连续函数，二重积分在极坐标系下的二次积分为，请将它化为直角坐标系下的二次积分．

问答题设f(x)在[a，b]上连续，在(a，b)内可导，且|f"(x)|≥1，求证：若f(a)=f(b)=0，则．

问答题假设某种商品一周的需要量X是一随机变量，其概率密度函数为假设各周对该商品的需要是相互独立的．

问答题{{I}}Directions: Read the following text carefully and then translate the underlined segments into Chinese. Write your pieces of Chinese version in the proper space on your Answer Sheet Ⅱ.{{/I}} In May 2004 the United Nations Food and Agriculture Organization (FAO) released its 2003-2004 book-length report, The State of Food and Agriculture: Agricultural Biotechnology: Meeting the Needs of the Poor? It immediately attracted significant press and media attention. In fact, while reporting on its survey of existing examinations of risks posed by agricultural biotechnology, the FAO report concludes that "biotechnology is capable of benefiting small resource-poor farmers" and that in numerous situations the benefits clearly outweigh the risks. In addition to attempting to re-orient biotechnology discussions and lessen the polemics attendant to them, {{U}}1. the FAO report offers and illuminates much factual information that is encompassed by biotechnology research, applications, and distribution{{/U}}. In fact, report lays out a coherent understanding of what biotechnology is, and offers a clear exposition for general readers--as well as policy and scientific specialists--of essential biotechnology concepts and methods such as market-assisted breeding, cell as well as genetic engineering. {{U}}2. Of particular importance, the essay has a thoughtful discussion on the health and environmental concerns associated with biotechnology{{/U}}. While concluding that, as to health concerns, there is a scientific consensus that biotechnology-altered foodstuffs are safe, the report stresses the scientific consensus on the need for case-by-case studies for all biotechnology products and processes. Regarding environmental concerns, of which the reports describes the science community's call for more scientific research and investigation, the FAO report surveys and describes the international instruments that are beginning to direct policy and regulatory standard development for biotechnology, such as the International Plant Protection Convention and the Convention on Biological Diversity. Notwithstanding its multi-faceted examination of biotechnology for the 21st century, {{U}}3. the FAO report's other major emphasis--alongside the potential of biotechnology for poor farmers--is that the mode for bringing this biotechnology potential to poor farmers is woefully deficient.{{/U}} Although some obstacles are indeed formidable for bringing biotechnology potential benefits to the poor, the report does not despair, and it offers ideas and even an agenda for reorienting the biotechnology enterprise for greater technology transfer and benefits for the poor. To overcome technology transfer and development obstacles, {{U}}4. the FAO report calls on all countries and the international community as a whole to: "establish transparent, predictable science-based regulatory procedures; establish appropriate intellectual property rights to insure that developers can earn an adequate return of investment."{{/U}} Along with these supportive measures, more direct measures for bio-technology need to be taken, and these include a dramatic increase in public research, a fostering of public-private partnerships, greater focus on the crops that poor farmers grow, and the emergence of developing world regional centers of biotechnology research and dissemination. The FAO report is hopeful that this can be done. {{U}}5. Underlying its propounding of this hopeful vision is not only an examination of what is currently amiss, but also important case studies in which biotechnology is actually helping poor farmers{{/U}}, in terms of economics and also human health, as is the case with biotechnology-modified cotton in China.

问答题设f(x)在[1，+∞)上有连续的二阶导数，f(1)=0，f'(1)=1，且二元函数z=(x2+y2)f(x2+y2)满足，求f(x)在[1，+∞)的最大值．

问答题求微分方程(y+x2e-x)dx-xdy=0满足初始条件y|x=1=0的特解。

问答题设a1＜a2＜…＜an，且函数f(x)在[a1，an]上n阶可导，c∈[a1，an]且f(a1)=f(a2)=…=f(an)=0．证明：存在ξ∈(a1，an)，使得