设球面∑:x^2+y^2+z^2=1,则曲面积分∫∫(x+y+z+1)^2dS=

A . ['-2https://assets.asklib.com/psource/201510271143121366.jpg B . 2https://assets.asklib.com/psource/201510271143121366.jpg C . 2D . 0

A . 4/3π B . 8/3π C . 16/3π D . 32/3π

A . 3 B . 3.5 C . 4 D . 5

A .https://assets.asklib.com/psource/2015102908452594024.jpg B .https://assets.asklib.com/psource/2015102908454251607.jpg C .https://assets.asklib.com/psource/2015102908455530519.jpg D .https://assets.asklib.com/psource/2015102908460720236.jpg

计算三重积分<img src='https://img2.soutiyun.com/ask/2020-10-30/97291958752518.png' />其中Ω由圆锥面<img src='https://img2.soutiyun.com/ask/2020-10-30/972919603836112.png' />和球面x²+y²+(z-1)²=1所围成.

A.3 B.5 C.4 D.5

设<img src='https://img2.soutiyun.com/ask/2020-12-21/977437317641057.png' />为球面x²+y²+z²=1，取外侧，则<img src='https://img2.soutiyun.com/ask/2020-12-21/97743872424051.png' />

是 否

A、条件(1)充分，但条件(2)不充分． B、条件(2)充分，但条件(1)不充分． C、条件(1)和条件(2)单独都不充分，但条件(1)和条件(2)联合起来充分． D、条件(1)充分，条件(2)也充分． E、条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分．

设z=f(x，y)由方程x-yz+cosxyz=2确定，求曲面z=f(x，y)在P₀(1，1，0)处的切平面方程与法线方程

设L是从点（0，0）沿y=1-｜x-1｜至点（2，0）的折线段，则曲线积分<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17672640/2015102616112131846.jpg' />-ydx+rdy等于（） A．0 B． -1 C． 2 D． -2

利用三重积分计算下列由曲面所围立体的质心(设密度ρ=1): (1)z²=x²+y²,z=1; (2)<img src='https://img2.soutiyun.com/ask/2020-11-25/975183822416377.png' />,<img src='https://img2.soutiyun.com/ask/2020-11-25/975183835201108.png' />(A＞a＞0),z=0; (3)z=x²+y²,x+y=a,x=0,y=0,z=0.

设曲面∑:|x|+|y|+|z|=1,则<img src='https://img2.soutiyun.com/ask/2020-08-05/965487145513117.png' />=()。

设球面方程为(x-1)2+(y+2)2+(z-3)2=4，则该球的球心坐标与半径分别为() A．(-1，2，-3)；2 B．(-1，2，-3)；4 C．(1，-2，3)；2 D．(1，-2，3)；4

设习是球Ω的表面x²+y²+z²=a²的外侧,<img src='https://img2.soutiyun.com/ask/2020-11-02/973176956181061.png' />计算曲面积分<img src='https://img2.soutiyun.com/ask/2020-11-02/973176967115687.png' />的过程如下: <img src='https://img2.soutiyun.com/ask/2020-11-02/973176983472622.png' /> 问上述计算是否正确？为什么？若错了,则改正之.

A:对 B:错

A．Y.是 B．N.否

A．x+y B．x C．y D．2x

<img src='https://img2.soutiyun.com/ask/2021-01-11/979216841161532.jpg' />,S为圆柱体[x²+y≤a²,0≤z≤h]的表面.(计算曲面积分)

设Ω=|(x,y,z)|x²+y²+z²≤1|则<img src='https://img2.soutiyun.com/ask/2021-01-10/979150367436964.png' />=().