问答题计算，其中D是由圆x2+y2=4与直线x=0所围的左半圆．

问答题设，B为三阶非零矩阵，为BX=0的解向量，且AX=α3有解．(1)求常数a，b的值；(2)求BX=0的通解．

问答题已知u=ax 2 +by 2 +cz 2 ，其中a＞0，b＞0，c＞0．求在条件x+y+z=1下的极小值．

问答题设f(x)是区间[0，+∞)上具有连续导数的单调增加函数，且f(0)=1．对任意的t∈[0，+∞)，直线x=0，x=t，曲线y=f(x)以及x轴所围成的曲边梯形绕x轴旋转一周生成一旋转体．若该旋转体的侧面积在数值上等于其体积的2倍，求函数f(x)的表达式．

问答题计算二次积分

问答题[习题1.27] 证明：(a+b，b+C，c+a)=2(a，b，c)。

问答题计算二重积分，其中D是由曲线x=，直线y=x及x轴所围成的闭区域．

问答题求曲线段y=x 2 (0≤x≤1)上一点处的切线，使该切线与直线y=0，x=1和曲线y=x 2 所围成图形的面积最小．

问答题{{B}}Directions:{{/B}} 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. It is astonishing how little is known about the working of the mind. But however little or much is known, it is fairly clear that the model of the logic-machine is not only wrong but mischievous. There are people who profess to believe that man can live by logic alone. If only they say, men developed their reason, looked at all situations and dilemmas logically, and proceeded to devise rational solutions, all human problems would be solved. Be reasonable. Think logically. Act rationally. This line of thought is very persuasive, not to say seductive. 1) {{U}}It is astonishing, however, how frequently the people most fanatically devoted to logic and reason, to a cold review of the "facts" and a calculated construction of the truth, turn out not only to be terribly emotional in argumentation, but obstinate before any "truth" is "proved"{{/U}} -- deeply committed to emotional positions that prove rock-resistible to the most massive accumulation of unsympathetic facts and proofs. 2) {{U}}If man's mind cannot be turned into a logic-machine, neither can it function properly as a great emotional sponge, to be squeezed at will.{{/U}} All of us have known people who gush as a general response to life - who gush in seeing a sunset, who gush in reading a book, who gush in meeting a friend. They may seem to live by emotion alone, but their constant gushing is a disguise for absence of genuine feeling, a torrent rushing to fill a vacuum. It is not uncommon to find beneath the gush a cold, analytic mind that is astonishing in its meticulousness and ruthless in its calculation. Somewhere between machine and sponge lies the reality of the mind - a blend of reason and emotion, of actuality and imagination, of fact and feeling. 3) {{U}}The entanglement is so complete, the mixture so thoroughly mixed, that it is probably impossible to achieve pure reason or pure emotion, at least for any sustained period of time.{{/U}} 4) {{U}}It is probably best to assume that all our reasoning is fused with our emotional commitments and beliefs, all our thoughts colored by feelings that lie deep within our psyches.{{/U}} Moreover, it is probably best to assume that this stream of emotion is not a poison, not even a taint, but is a positive life-source, a stream of psychic energy that animates and vitalizes our entire thought process. 5) {{U}}The roots of reason are embedded in feelings - feelings that have formed and accumulated and developed over a lifetime of personality-shaping.{{/U}} These feelings are not for occasional using but are inescapable. To know what we think, we must know how we feel. It is feeling that shapes belief and forms opinion. It is feeling that directs the strategy of argument. It is our feelings, then, with which we must come to honorable terms.

问答题已知ξ=[1，1，-1]T是矩阵的一个特征向量．