问答题计算积分。

问答题设方程组为矩阵A的分别属于特征值λ1=1，λ2=-2，λ3=-1的特征向量．

问答题设，其中f为可微函数．证明．

问答题若(a1,a2，…，an)=1，则(a1a2-an,b)=(a1,b)(a2,b)…(an，b). 若a1，a2，…，an互素，则[a1a2…an，b]=[a1，b][a2，b]…[an，b]?

问答题设函数，问函数f(x)在x=1处是否连续?若不连续，修改函数在x=1处的定义使之连续．

问答题设f(x)在[0，a]上一阶连续可导，f(0)=0，在(0，a)内二阶可导且f"(x)＞0．证明：

问答题You've had a problem, you've thought about it till you were tired, forgotten it and perhaps slept on it, and then flash! When you weren't thinking about it suddenly the answer has come to you, as a gift from the gods. Of course all ideas don't come like that, but the interesting thing is that so many do, particularly the most important ones. They burst into the mind, glowing with the heat of creation. How they do is a mystery. (46) Psychology does not yet understand even the ordinary process of conscious thought, but the emergence of new ideas by a "leap in thought" is particularly intriguing, because they must have come from the somewhere. For the moment let us assume that they come from the "unconscious". (47)This is reasonable, for the psychologists use this term to describe mental processes which are unknown to the subject, and creative thought consists precisely in what was unknown becoming known. (48) It seems that all truly creative activity depends in some degree on these signals from the unconscious, and the more highly intuitive the person, the sharper and more dramatic the signals become. But growth requires a seed, and the heart of the creative process lies in the production of the original fertile nucleus from which growth can proceed. (49) This initial step in all creation consists in the establishment of a new unity from disparate elements, of order out of disorder, of shape from what was formless. The mind achieves this by the plastic reshaping, so derived from a new unit, of a selection of the separate elements derived from experience and stored in memory. Intuitions arise from richly unified experience. (50) This process of the establishment of new form must occur in pattern of nervous activity in the brain, lying below the threshold of consciousness, which interacts and combines to form more comprehensive patterns. Experimental physiology has not yet identified this process, for its methods are as yet insufficiently refined, but it may be significant that a quarter of the total bodily consumption of energy during sleep goes to the brain, even when the sense organ are at rest, to maintain the activity of ten thousand million brain cells. These cells, acting together as a single organ, achieve the miracle of the production of new patterns of thought. No calculating machine can do that, for such machines can "only do what we know how to design them to do", and these formative brain processes obey laws which are still unknown. Can any practical conclusions be drawn from the experience of genius? Is there an art of thought for the ordinary person? Certainly there is no single road to success; in the world of the imagination each has to find his own way to use his own gift.

问答题在第Ⅰ象限内的曲线上求一点M(x，y)，使过该点的切线被两坐标轴所截线段的长度为最小．

问答题计算定积分

问答题λ取何值时，线性方程组有惟一解、无解、无穷多解?在有无穷多解时，求其通解．

问答题设函数f(x)对于[a，b]上任意两点x1与x2恒有|f(x1)-f(x2)|≤q|x1-x2|(其中q为常数)，且f(A) f(B) ＜0，证明：至少存在一点ξ∈(a，b)，使得f(ξ)=0．

问答题在曲线y=sin x(0≤x≤π)上求一点，使该曲线在该点的切线平行于过点(-2，0)和点(0，1)的盲线。

问答题求所有(0，+∞)上的正连续函数g(x)，使得对任意x＞0有

问答题设α是n维单位列向量，A=E-αα T ．证明：r(A)＜n．

问答题向量组α1，α2，…，αs的秩为r，则其中任意r个线性无关向量部分组构成它的一极大无关组. 若向量组α1，α2，…，αs的秩为r，则其中任意r个向量构成一个极大无关组？

问答题(工)求ι与C的准线的交点坐标；(Ⅱ)求|AB|．

问答题求曲线y=ln(1+x 2 )的凹区间．

问答题设f(u)具有二阶连续导数，且，求.

问答题设矩阵A与B相似，其中．