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 .




                    그림입니다. 원본 그림의 이름: P8060672.JPG 원본 그림의 크기: 가로 3648pixel, 세로 2736pixel 사진 찍은 날짜: 2013년 08월 06일 오후 2:10

 

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