SKKU-Calculus-Sec-15-6 Surface Area by SGLee with 김유경
15.6 Surface Area by SGLee with 김유경
1-3. Find a parametric representation of the surface.
1. 
Let the parameters 
and 
,
we find that parametric surface is given by equations 
, 
and 
.
Therefore, the plane is described by the vector function
.
2. 
.
Let the parameters 
and 
,
we find that parametric surface is given by equations 
, 
and 
.
Therefore, the plane is described by the vector function
.
3. The portion 
from 
to 
.
4-5. Find an equation of the tangent plane at the point on the surface corresponding to the given parameter values.
4. 
, 
, 
, 
, 
.
At 
and 
, the point on the surface is 
. The surface is defined by the vector function
, then
, 
and
.
The normal vector 
to the surface at 
and 
. An equation of the tangent plane at that point is
or 
.
Note : 처음에 a,b,c를 x,y,z를 놓지않아야 한다. x,y,z라고 놓게 되면, tangent plane이 u,v에 관한 함수로 나오게 되어서 제대로 답을 구할 수 없다.
5. 
; 
, 
.
6-8. Calculate the area of the surface.
|
6. The surface with parametric equations 
, 
, 
, 
, 
.
and then form the cross product
The area is
.
7. The part of the plane 
that lines in the first octant.
8. The part of the plane 
tha lines inside the cylinder 
.
