问答题两个本原多项式的乘积仍为本原多项式． 两个本原多项式的和仍为本原多项式？

问答题已知函数f(x)在[0，1]上连续，在(0，1)内可导，且f(0)=0，f(1)=1，证明： (Ⅰ)存在ξ∈(0，1)，使得f(ξ)=1-ξ； (Ⅱ)存在两个不同的点，η,ξ∈(0，1)，使得f'(η)f'(ξ)=1．

问答题求微分方程y"-y"=0的满足初始条件y| x=0 =0、y"| x=0 =1的特解．

问答题已知向量组为，求该向量组的一个极大线性无关组及该向量组的秩，并把其余向量表成极大线性无关组的线性组合．

问答题设AX=A+2X，其中，求X．

问答题设平面薄片的方程可以表示为x2+y2≤R2，x≥0，薄片上点(x，y)处的密度，求该薄片的质量M．

问答题设函数y=xsinx，求y'．

问答题若p为素数，p|ab，则p|a或p|b． 若p|ab,即p|a或p|b，则p为素数？

问答题设f(x)在区间[a，b]上可导，且．证明：存在ξ∈(a，b)，使f'(ξ)=1．

问答题已知函数f(x)=ax3-bx2+cx在区间(-∞，+∞)内是奇函数，且当x=1时f(x)有极小值，求a，b，c．

问答题设对任意的x和y，有，用变量代换将f(x，y)变换g(u，v)，试求满足中的常数a和b．

问答题f(x)在[-1，1]上三阶连续可导，且f(-1)=0，f(1)=1，f"(0)=0.证明：存在ξ∈(-1，1)，使得f"""(ξ)=3.

问答题已知方程组有无穷多解，矩阵A的特征值是1，-1，0，对应的特征向量依次是α1=(1，2a，-1)T，α2=(a-2，-1，a+1)T，α3=(a，a+3，a+2)T

问答题设三阶实对称矩阵A的特征值为λ1=8，λ2=λ3=2，矩阵A的属于特征值λ1=8的特征向量为，属于特征值λ2=λ3=2的特征向量为，求属于λ2=λ3=2的另一个特征向量．

问答题已知随机变量X1，X2，X3，X4相互独立，X1与X2都在区间(0，1)上服从均匀分布，X3与X4都服从参数为的0-1分布，记Y=X1+X2+X3X4，求Y的分布函数FY(y)及概率密度fY(y)．

问答题求y"+4y'+4y=e-x的通解．

问答题设f(x)连续，且积分的结果与x无关，求f(x)．

问答题(46) History tells us that in ancient Babylon, the cradle of our civilization, the people tried to build a tower that would reach to heaven. But the tower became the tower of Babel, according to the Old Testament, when the people were suddenly caused to speak different languages. In modern New York City, a new tower, that of the United Nations Building, thrusts its shining mass skyward. (47) But the realization of the UN's aspirations—and with it the hopes of the peoples of the world—is threatened by our contemporary Babel: about three thousand different languages are spoken throughout the world today, without counting the various dialects that confound communication between peoples of the same land. In China, for example, hundreds of different dialects are spoken; people of some villages have trouble passing the time of day with the inhabitants of the next town. In the new African state of Ghana, five million people speak fifty different dialects. In India more than one hundred languages are spoken, of which only fourteen are recognized as official. To add to the confusion, as the old established empires are broken up and new states are formed, new official tongues spring up at an increasing rate. In a world made smaller by jet travel, man is still isolated from many of his neighbors by the Babel barrier of multiplying languages. Communication is blocked daily in scores of ways. Travelers find it difficult to know the peoples of other nations. Scientists are often unable to read and benefit from the work being carried on by men of science in other countries. (48) The aims of international trade, of world accord, of meetings between nations, are blocked at every turn; the work of scholars, technologists, and humanists is handicapped. Even in the shining new tower of the United Nations in New York, speeches and discussions have to be translated and printed in the five official UN language—English, French, Spanish, Russian and Chinese. Confusion, delay, suspicion, and hard feelings are the products of the diplomatic Babel. The chances for world unity are lessened if, in the literal sense of the phrase, we do not speak the same language. (49) We stand in dire need of a common tongue, a language that would cross national barriers, one simple enough to be universally learned by travelers, businessmen, government representatives, scholars, and even by children at school. Of course, this isn't a new idea. Just as everyone is against sin, so everyone is for a common language that would further communication between nations. (50) What with one thing and another—our natural state of drift as human beings, our rivalries, resentments, and jealousies as nations—we have up until now failed to take any action. I propose that we stop just talking about it, as Mark Twain said of the weather, and do something about it. We must make the concerted, massive effort it takes to reach agreement on the adoption of a single, common auxiliary tongue.

问答题已知向量组(Ⅰ)：α1，α2，α3；(Ⅱ)：α1，α2，α3，α4；(Ⅲ)：α1，α2，α3，α5．如果各向量组的秩分别为r(Ⅰ)=r(Ⅱ)=3，r(Ⅲ)=4． 证明向量组α1，α2，α3，α5-α4的秩为4．

问答题设y=arctan(1+x 2 )，求f"(1)。