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)。

问答题设函数f(x)=xlnx+x．(I)求曲线y=f(x)在点(1，f(1))处的切线方程；(Ⅱ)求f(x)的极值．

问答题设证明：f(x，y)在点(0，0)处可微，但在点(0，0)处不连续.

问答题设α 1 ，α 2 ，α 3 为四维列向量组，α 1 ，α 2 线性无关，α 3 =3α 1 +2α 2 ，A=(α 1 ，α 2 ，α 3 )，求AX=0的一个基础解系．

问答题讨论下列级数的敛散性：

问答题设曲线f(x)=x 2 -x+2在点(x 0 ，f(x 0 ))处的切线垂直于直线y=-2x+1，求过点(x 0 ，f(x 0 ))的曲线的切线方程。

问答题计算，D：ε2≤x2+y2≤1，并求此积分当ε→0+时的极限．

问答题设X～U(0，2)，Y=X 2 ，求Y的概率密度函数．

问答题设求f(f(x))．

问答题求一个正弦曲线与x轴所围成图形的面积(只计算一个周期的面积)．

问答题就k的不同取值情况，确定方程x 3 -3x+k=0根的个数．

问答题确定常数a和b的值，使．

问答题设曲线y=xn在点(1，1)处的切线交x轴于点(ξn，0)，求