问答题设区域D=(x，y)|x2+y2≤1，x≥0，计算二重积分。

问答题设P(A)＞0，P(B)＞0．证明：A，B互不相容与A，B相互独立不能同时成立．

问答题求的收敛域及和函数．

问答题(本题满分11分)设随机变量X与Y相互独立，且X服从区间(0，1)上的均匀分布，Y服从参数为1的指数分布．(Ⅰ)求概率P{X+Y≤1}；(Ⅱ)令，求Z的概率密度fZ(z)．

问答题设0＜k＜1，f(x)=kx-arctanx．证明：f(x)在(0，+∞)中有唯一的零点，即存在唯一的x 0 ∈(0，+∞)，使f(x 0 )=0．

问答题71.Vacations were once the prerogative of the privileged few, even as late as the 19th century. Now they are considered the right of all, except for such unfotrunate masses as, for example, the bulk of puplation in certain countries, for whom life, save for sleep and brief periods of rest, is uniterrupted toil. Vacations are more necessary now than before because today the average life is less well-rounded and has become increasingly compartmentalized. 72. I suppose the idea of vacations, as we conceive it, must be incomprehensible to primitive peoples. Rest of some kind has of course always been a part of the rhythm of human life, but earlier ages did not find it necessary to organize it in the way that modern man has done. Holidays and feast days were sufficient. With modern man's increasing tensions, with the stultifying quality of so much of his work, this break in the year's routine became steadily more necessary. 73. Vacations became mandatory for the purpose of renewal and repair. And so it came about that in the United States, the most self-indulgent of nations, the most tense and compartmentalized, vacations have come to take a predominant place in domestic conversation.

问答题已知A是m×n矩阵，m＜n．证明：AA T 是对称阵，并且AA T 正定的充要条件是r(A)=m．

问答题设，证明：级数条件收敛．

问答题设函数处处连续，试确定常数a，并求f"(0)与f"(0)．

问答题设

问答题设a1=1，试证：1.级数收敛；