曲线绕x轴旋转一周所生成的旋转曲面的方程是（）．

A . 3/7π B . 4/7π C . π/2 D . π

A . A B . B C . C D . C

A . 36π B . 54π C . 72π D . 108π

A . ['['https://assets.asklib.com/psource/2015103008412312933.jpg B . πC .https://assets.asklib.com/psource/2015103008413627903.jpg D .https://assets.asklib.com/psource/2015103008415366754.jpg

A . 4（x2+z2）-9y2=36 B . 4x2-9（y2+z2）=36 C . 4x2-9y2=36 D . 4（x2+y2）-9z2=36

A . A B . B C . C D . D

曲线y=e-x≥0)与直线x=0，y=0所围图形绕ox轴旋转一周所得旋转体的体积为()。 A．<img src='https://img2.soutiyun.com/ask/uploadfile/5757001-5760000/784bff2c580846720ac5cc8bb4e73bd0.jpg' /> B．π C．<img src='https://img2.soutiyun.com/ask/uploadfile/5757001-5760000/76698f1d07a3c7ceb7f2adf5a7d02e0d.jpg' /> D．<img src='https://img2.soutiyun.com/ask/uploadfile/5757001-5760000/ca9b02e28aced73f37e9339c8094638e.jpg' />

如图10-3,设曲线y=<img src='https://img2.soutiyun.com/ask/2020-11-30/975595449507168.png' />,过原点作其切线,求此曲线、切线及x轴围成的平面图形绕x轴旋转一周所得到的旋转体的表面积. <img src='https://img2.soutiyun.com/ask/2020-11-30/975595471682437.png' /> 答案:解题

曲线y=e-x(x)≥0)与直线x=0，y=0所围图形绕ox轴旋转一周所得旋转体的体积为（）。 <img src='https://img2.soutiyun.com/ask/uploadfile/2742001-2745000/efd235899322fda022158d0925176dc2.jpg' />

过点P(1,0)作抛物线y=<img src='https://img2.soutiyun.com/ask/2020-11-30/975595375036909.png' />的切线,该切线与上述抛物线及x轴围成一平面图形,求此图形绕x轴旋转一周所成旋转体体积,见图10-2. <img src='https://img2.soutiyun.com/ask/2020-11-30/975595390464792.png' /> <img src='https://img2.soutiyun.com/ask/2020-11-30/97559540442559.png' /> 答案:解题

A．(x+1)2=y2+z2 B．x2+y2=z-1 C．z2=x2+y2+1 D．(z-1)2=x2+y2

＞圆柱体的侧面是一条（）绕轴线旋转一周所形成的回转体 A．直线 B．曲线 C．平面 D．圆面

＞圆球体的表面是由一个（）绕轴线旋转一周所形成的回转体 A．直线 B．圆 C．曲面 D．半圆

曲线<img src='https://img2.soutiyun.com/shangxueba/ask/17664001-17667000/17665581/2015103008433015996.jpg' />围成的平面图形绕x轴旋转产生的旋转体体积是（）。 A．<img src='https://img2.soutiyun.com/shangxueba/ask/17664001-17667000/17665581/2015103008435526826.jpg' /> B．<img src='https://img2.soutiyun.com/shangxueba/ask/17664001-17667000/17665581/201510300844073703.jpg' /> C．<img src='https://img2.soutiyun.com/shangxueba/ask/17664001-17667000/17665581/2015103008442389299.jpg' /> D．<img src='https://img2.soutiyun.com/shangxueba/ask/17664001-17667000/17665581/201510300844373107.jpg' />

设过点(4,0)的直线与椭圆<img src='https://img2.soutiyun.com/ask/2021-01-10/979118507564684.png' />相切,则切线绕Ox轴旋转的旋转曲面的方程为().

求曲线<img src='https://img2.soutiyun.com/ask/2020-10-08/971032116253371.png' />绕y轴旋转所得旋转曲面方程.

求直线<img src='https://img2.soutiyun.com/ask/2020-10-29/972838000274003.png' />绕z轴旋转所得旋转面的方程，它表示什么曲面？

将直线<img src='https://img2.soutiyun.com/ask/2020-10-08/971030165366787.jpg' />绕z轴旋转,求这旋转曲面的方程,并就a和p可能的0值讨论这是什么曲面？