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 . 