问答题已知4元齐次线性方程组的解全是4元方程(ii)x1+x2+x3=0的解，(Ⅰ)求a的值；(Ⅱ)求齐次方程组(i)的解；(Ⅲ)求齐次方程(ii)的解．

问答题设，讨论f(x)的单调性，凹凸性，拐点，水平渐近线．

问答题A，B为n阶矩阵且r(A)+r(B)＜n．证明：方程组AX=0与BX=0有公共的非零解．

问答题已知，求常数a．

问答题简述要约及其要件。

问答题求函数z=x 2 +2y 2 -2x+4y+1满足条件x-2y-6=0的极值．

问答题求由方程y=e (x+y) 确定的函数y=f(x)的二阶导数。

问答题In the early 1800s, groups of English workers wrecked machines that they felt threatened their jobs. (46) They were called "Luddites" after one of their leaders, a term that is now used for anyone who puts up resistance to new technologies. (47) The odd thing about nanotechnology's Luddites is that they have started resisting before the technology has really established itself. As people start to buy products involving nanotechnology, from odour-resistant shirts to window glass that repels dirt, they will realise that many of these new things are useful and harmless. And as awareness of nanotechnology grows, they will begin to understand that it covers a range of different ways of doing things, some of which carry some risk and others do not. As a result, the technology's detractors will probably become more nuanced in their complaints. Nanotechnology has the potential to cause an industrial upheaval, just as electricity did in its time. (48) Like electricity, though, it has so many and such diverse applications that it is unlikely to arrive in one huge wave, as nanotechnology's critics fear. Instead, there will be a series of smaller waves. (49) Many of the innovations the technology may bring are a long way off, leaving plenty of time to prepare. Nanotechnology, like any new discovery, offers both risks and rewards. There will undoubtedly be some need to control its exploitation to minimize the risks, but there are also strong arguments for allowing the unfettered pursuit of knowledge, without it, innovation cannot flourish. Twenty years ago, nobody could have foreseen that the invention of a new microscope would launch a remarkable new technology, perhaps a revolution. (50) Scientists should be allowed to work with as little hindrance as possible to gain a better understanding of the object of their study-however large or small.

问答题过点M(3，0)作曲线y=ln(x-3)的切线，该切线与此曲线及x轴围成一平面图形D．试求平面图形D绕x轴旋转一周所得旋转体的体积．

问答题证明：当x≥0时，x≥arctan x。

问答题已知4阶方阵A=(α1，α2，α3，α4)，α1，α2，α3，α4均为4维列向量，其中α2，α3，α4线性无关，α1=2α2-α3．如果β=α1+α2+α3+α4，求线性方程组Ax=β的通解．

问答题设(Ⅰ)求矩阵A的特征值与特征向量；(Ⅱ)当时，求矩阵B；(Ⅲ)求A100．

问答题一枚5分硬币，连续抛掷3次，求“有1次国徽向上”的概率。

问答题设D由曲线xy=2，y=x+1，y=x-1围成，求二重积分．

问答题讨论函数在点x=2处的连续性与可导性．

问答题 Directions: Write a reply to this business letter. Office Supplies Company ABC Engineering Company, 222 Nathan Road 77 An Nei Jie, Wuhan Kowloon, Hong Kong 17th JanuaryDear Sir/Madam, I saw your advertisement in China Daily for your new fax machines. Would you please send me more information and a price list. I would also appreciate a visit to one of from sales people in the near future to discuss our requirements for business machines. Thank you. Yours sincerely, Li Wei You should write about 100 words on ANSWER SHEET 2. Do not sign your own name at the end of the letter. Use "Li Ming" instead.

问答题设y=y(x)是一向上凸的连续曲线，其上任意一点(x，y)处的曲率为，又此曲线上的点(0，1)的切线方程为y=x+1，求该曲线方程，并求函数y(x)的极值．

问答题设直线y=ax与抛物线y=x 2 所围成的图形面积为S 1 ，它们与直线x=1所围成的图形面积为S 2 ，且a＜1.

问答题设f(x)在[a，b]上连续，在(a，b)内可导(a＞0)，且f(a)=0．证明：存在ξ∈(a，b)，使得