问答题设函数z=f(x，y)在点(1，1)处可微，且φ(x)=f[x，xf(x，x)]，求

问答题设f(x 1 ，x 2 ，x 3 )=X T AX，r(A)=1，A的每行元素之和为2，当X=β=[2，4，0] T 时， 求f(x 1 ，x 2 ，x 3 )=X T AX在β处的值，即f(x 1 ，x 2 ，x 3 )| X=β =β T Aβ．

问答题求由方程所确定的隐函数的偏导数或全微分

问答题简述善意占有与恶意占有。

问答题设n维向量α1，α2，…，αs线性无关，而α1，α2，…，αs，β线性相关，证明β可以由α1，α2，…，αs线性表出，且表示方法唯一．

问答题有6个会计和一个Controler组成一个四人小组，问Controler必然保存在组内的概率。

问答题求微分方程xy'=3y-6x2的一个解y=y(x)，使得曲线y=y(x)与直线x=1，y=0所围成的平面图形绕x轴旋转一周所得旋转体体积最小。

问答题设函数y=y(x)是由方程cos(xy)=x+y所确定的隐函数，求函数曲线y=y(x)过点(0，1)的切线方程．

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。