问答题证明：(a×b)2=a2b2-(a·b)2。

问答题甲袋中有15只乒乓球，其中3只白球，7只红球，5只黄球，乙袋中有20只乒乓球，其中10只白球，6只红球，4只黄球．现从两袋中各取一只球，求两球颜色相同的概率．

问答题现有三个箱子，第一个箱子有4个红球，3个白球；第二个箱子有3个红球，3个白球；第三个箱子有3个红球，5个白球；先取一只箱子，再从中取一只球． (1)求取到白球的概率； (2)若取到红球，求红球是从第二个箱子中取出的概率．

问答题设有一根长为a的铁丝，将其分成两段，分别围成圆形和正方形，如果设所围圆形的面积为S1，正方形的面积为S2，证明：当时，S1+S2的值最小。

问答题计算，其中∑为下半球面的上侧，a为大于零的常数。

问答题已知矩阵与矩阵等价．

问答题5双不同颜色的袜子，任取两只，求其恰好是一对的概率?

问答题求∫arcsin 2 xdx．

问答题Fatigue is one of the most common complaints brought to doctors, friends, and relatives. You'd think in this era of labor-saving and convenient transportation that few people would have reason to be so tired. The causes of modern-day fatigue are diverse and only rarely related to excessive physical exertion. Today, physicians report, tiredness is more likely a consequence of underexercise than of wearing yourself down with overactivity. Physical fatigue is the well-known result of overworking your muscles. (46) Physical fatigue is usually a pleasant tiredness, such as that which you might experience after playing a hard set of tennis, chopping wood, or climbing a mountain. The cure is simple and fast: You rest, giving your body a chance to get rid of accumulated waste and restore muscle fuel. (47) Illness induced fatigue is a warning sign or consequence of some underlying physical disorder, perhaps the common cold or flu or something more serious like cancer, while other symptoms are present that often suggest the true cause. Even after an illness passed, you're likely to feel dragged out for a week or more. (48) Take your fatigue as a signal to go slow while your body has a chance to recover fully even if all you had was a cold. Pushing yourself to resume full activity too soon will certainly prolong your period of fatigue. Emotional problems and conflicts, especially depression and anxiety, are by far the most common causes of prolonged fatigue. When such feelings are not expressed openly, they often come out as physical symptoms, with fatigue as one of the most common manifestations. (49) Understanding the underlying emotional problem is the crucial first step toward curing psychological fatigue and by itself often results in considerable lessening of the tiredness. Professional psychological help or career or marriage counseling may be needed. There is a great deal you can do on your own to deal with both severe prolonged fatigue and those periodic washed-out feelings. You might try to do moderate exercise. (50) Contrary to what you may think, exercise enhances, rather than drains, engery and helps you to resist fatigue by increasing your body's ability to handle more of a workload. At the end of a day exercise can relieve accumulated tensions, give you more energy in the evening, and help you sleep more restfully.

问答题求定积分的值．

问答题设f(x)在点x=0处连续，且x≠0时，，求f(0)．

问答题设二阶常系数齐次线性微分方程以y 1 =e 2x ，y 2 =2e -x -3e 2x 为特解，求该微分方程．

问答题求微分方程y"+4y"+4y=e ax 的通解．

问答题求函数f(x，y，z)=xyz在条件(x＞0，y＞0，z＞0，常数r＞0)下的极值．

问答题就k的不同取值情况，确定方程x3-3x+k=0实根的个数．

问答题求下列函数的二阶偏导数．设z=(x+y)exy，求．

问答题If for integers C, 6＜C＜20, what is the least possible value of the equation (20-C)/(6-C)?

问答题计算下列行列式

问答题求下列极限：

问答题设a1=1，当n≥1时，，证明：数列{an}收敛并求其极限．