填空题设，f(x0)=5，则f[f"(x0)]=________．

填空题函数z=x2+xy-y2-3的全微分=________。

填空题定积分________．

填空题[A] The Need for Science[B] The Methods of Science[C] The Challenge of Unsolved Problems[D] The Specific Features of the Laws of Science[E] The Steps in Establishing a Scientific Theory[F] The Rapid Increase of Scientific Knowledge It is the business of the scientist to accumulate knowledge about the universe and all that is in it. and to find. if he is able. common factors which underlie and account for the facts that he knows. He chooses, when he can, the method of the "controlled experiment".41. ______. In the course of his inquiries the scientist may find what he thinks is one common explanation for an increasing number of facts. The explanation, if it seems consistently to fit the various facts, is called a hypothesis. If a hypothesis continues to stand the test of numerous experiments and remains unshaken, it becomes a law.42. ______. The "laws" of science differ from the "laws" of a country in two ways. First, a scientific law is liable at any time to need modifying. This happens when a fact is discovered which seems to contradict what the "law" would lead one to expect. The "law" may, in fact. have to be abandoned altogether. Second. a scientific "law" says, "This is likely to be the explanation", or "This accounts for the facts as far as we know them". But the "law" of the country says, "You must..." or "You must not..." The scientific "law" has no moral force; it is not binding on human behavior nor approved or opposed by human conscience.43. ______. The evidence as to the vastness of the universe and the complexity of its arrangements continues to grow at an amazing rate. The gap between what we know and all that can be known seems not to diminish, but rather to increase with every new discovery. Fresh unexplored regions are forever opening out. The rapidity of the growth of scientific knowledge, in the nineteenth and twentieth centuries, is apt to give students and teachers the impression that no sooner is a problem stated than the answer is forthcoming. A more detailed study of the history of science corrects the impression that fundamental discoveries are made with dramatic suddenness. Even in our present age no less than fifty years separate the discovery of radioactivity from the explosion of the first atomic bomb. The teacher, giving his brief accounts of scientific discovery, is apt to forget the long periods of misunderstanding, of false hypotheses and general uncertainty, which almost invariably precede the clear statement of scientific truth.44. ______. The vast mass of information which scientists have gained has provided the answer to the fundamental questions which, through the centuries, have puzzled and sometimes tortured the human mind. There are many such questions. The study of parasites has provided evidence that organisms which could be self-supporting have become parasites, but hardly any light has been shed on the problem of why they should have done so. What enables an organism to respond to the poisonous secretions of harmful bacteria and organize its resources to defend its life?45. ______. To raise the standard of living in any country, two things are required, scientific knowledge, and a population sufficiently educated to understand how to apply it. Without the latter, the expected benefits will not come. Notes: ado 麻烦，忙乱。be binding on 对......有约束力。parasite 寄生虫。shed light on 使某事物更清楚些。 secretion 分泌物。

填空题设随机变量X和Y均服从且D(X+Y)=1，则X与Y的相关系数ρ=________．

填空题设z=z(x，y)是由方程确定的隐函数，则________．

填空题若，则φ(x)=______．

填空题设A=，B≠O为三阶矩阵，且BA=O，则r(B)=________．

填空题设变换可把方程简化为，则a=______．

填空题函数的定义域是________，极________值是________．

填空题设f(x)为连续函数，且f(1)=1，则

填空题1______

填空题设，则t=0对应的曲线上点处的法线为________．

填空题已知则Ax=0解空间的规范正交基是

填空题设f(x)在x=a的邻域内二阶可导且f"(a)≠0，则

填空题曲线y=2x 2 -x+1在点(1，2)处的切线方程为______．

填空题设f(x，y)可微，且f"1(-1，3)=-2，f"2(-1，3)=1，令则dz|(1,3)=________．

填空题设A是m×n矩阵，E是n阶单位阵，矩阵B=-aE+A T A是正定阵，则a的取值范围是_______。

填空题设f(x)二阶连续可导，且f(0)=1，f(2)=3，f"(2)=5，则

填空题设线性相关，则a=________．