3.判断题(20分)设sum为有向曲面z=x^2+y^2,(0le zle 1)，其法向量与Z轴正向的夹角为锐角，则iint_(sum)(2x+z)dzdx+zdxdy=-(pi)/(2).A 正确.B 错误.

一、单选题(共50题，50.0分) 34.(单选题 1.0分) 设f(x)=}e^x,x>02,x=0x,xA. 0B. 1C. 2D. 不存在

下列命题中,正确命题的个数( )(1)若Ax=0只有零解,则Ax=b有唯一解; (2)若Ax=0有非零解,则Ax=b有无穷多解; (3)若Ax=b无解,则Ax=0一定有非零解; (4)若Ax=b有唯一解,则Ax=0只有零解; (5)若Ax=b有无穷多解,则Ax=0一定有非零解. A 1 B 2 C 3 D 4

设 z = e^u sin v, u = xy, v = x + y, 求 (partial z)/(partial x), (partial z)/(partial y) = ( ) A. (partial z)/(partial x) = (partial z)/(partial u) cdot (partial u)/(partial x) + (partial z)/(partial v) cdot (partial v)/(partial x) = e^v [y sin (x + y)+ cos (x + y)] (partial z)/(partial y) = (partial z)/(partial u) cdot (partial u)/(partial y) + (partial z)/(partial v) cdot (partial v)/(partial y) = e^v [x sin (x + y)+ cos (x + y)]B. (partial z)/(partial x) = (partial z)/(partial u) cdot (partial u)/(partial x) + (partial z)/(partial v) cdot (partial v)/(partial x) = e^v [sin (x + y)+ cos (x + y)] (partial z)/(partial y) = (partial z)/(partial u) cdot (partial u)/(partial y) + (partial z)/(partial v) cdot (partial v)/(partial y) = e^v [x sin (x + y)+ cos (x + y)]C. (partial z)/(partial x) = (partial z)/(partial u) cdot (partial u)/(partial x) + (partial z)/(partial v) cdot (partial v)/(partial x) = e^v [y sin (x + y)+ cos (x + y)] (partial z)/(partial y) = (partial z)/(partial u) cdot (partial u)/(partial y) + (partial z)/(partial v) cdot (partial v)/(partial y) = e^v [sin (x + y)+ cos (x + y)]D. (partial z)/(partial x) = (partial z)/(partial u) cdot (partial u)/(partial x) + (partial z)/(partial v) cdot (partial v)/(partial x) = [y sin (x + y)+ cos (x + y)] (partial z)/(partial y) = (partial z)/(partial u) cdot (partial u)/(partial y) + (partial z)/(partial v) cdot (partial v)/(partial y) = e^v [x sin (x + y)+ cos (x + y)]

2.计算iintlimits_(sum)x^2dS，其中sum为圆柱面x^2+y^2=4介于z=0与z=4之间的部分.

设A和B分别是m阶和n阶可逆矩阵，则分块矩阵} A & 0 0 & B

求指导本题解题过程，谢谢您！1 设α为三维列单位向量(单位向量是长度为1的向量,即分量的平方和为1)则 nabla (alpha (alpha )^2)= 1_(tr代表矩阵的迹-|||-即主对角线的元素的和).(10.0分)

下列命题一定成立的是()A. 若 AB = AC，且 A neq 0 则 B = C；B. 若 AB = 0，则 B = 0 或 A = 0；C. 若 A neq 0，则 |A| neq 0；D. 若 |A| neq 0，则 A neq 0；

17.(填空题，4.0分)iintlimits_(D)8xydsigma=( )，其中D由抛物线x^2=y与直线x=y-2围成.

设随机变量 X 的概率密度为f(x)= ) 2(x-1),1leqslant xleqslant 2 0,eeg .。