Parametric Surfaces

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  1. Identify the surface with the vector equation

    ruv=2sinui+3cosuj+vk

    where 0v2 .

  2. Match the equations with the graphs, explain.

    1. ruv=cosvsinvu
    2. ruv=ucosvusinvu
    3. ruv=ucosvusinvv
    4. x=u3,y=usinv,z=ucosv
    5. x=usinucosv ,
      y=1cosusinv ,
      z=u .
    6. x=1u3+cosvcos4πu ,
      y=1u3+cosvsin4πu ,
      z=3u+1usinv .
    1. parametric surface
    2. parametric surface
    3. parametric surface
    4. parametric surface
    5. parametric surface
    6. parametric surface
  3. Find parametric equations for the surface obtained by rotating the curve y=ex , 0x3 , about the x-axis and use them to graph the surface.
    x=x,y=excosθ,z=exsinθ,0x3
  4. Match the shown surfaces with their parametrizations. Justify your choices.

    r1uv=sinucosvsinusinvcosu

    r2uv=uvu2v2

    r3uv=ucosvuusinv

    r4uv=ueucosveusinv

    r5uv=u1+u2cosv1+u2sinv

    r6uv=uvu3+v3

    mystery surface
    Surface 1.

    mystery surface
    Surface 2.

    r4 and r2 .