1. In each of the following surface parametrizations, filling in the missing two entries. The highlighted...

 

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1. In each of the following surface parametrizations, filling in the missing two entries. The highlighted curves are "grid curves for the parametrization. Justify your work. b) The surface 2²+ y² = 2² is parametrized by FO, z)=(.. The surface 2²+y²=1 is parametrized by F(0.2)=(... The surface 2(z − 1)² + (y-5)² + 4z² = 1 is parametrized by F(0, 0) ( The surface is parametrized by F(x,y) = (..... 2. (a) Identify the surface with parametrization r = sin e 1 ...........cos(0)/2) 2= COS 2²-5²) y=u where 0 ≤ ≤ 2 and -1 ≤ ≤3. Hint: Find an equation of the form F(x, y, z)=0 for this surface by eliminating u and e from the equations above. (b) Calculate a parametrization for the tangent plane to the surface at (x, (0./3). (e) Calculate a formula for a unit normal vector field, n, to the surface in terms of u and e. Hint: n(u, v) = where (r. y.)=r(u, v). 1. In each of the following surface parametrizations, filling in the missing two entries. The highlighted curves are "grid curves for the parametrization. Justify your work. b) The surface 2²+ y² = 2² is parametrized by FO, z)=(.. The surface 2²+y²=1 is parametrized by F(0.2)=(... The surface 2(z − 1)² + (y-5)² + 4z² = 1 is parametrized by F(0, 0) ( The surface is parametrized by F(x,y) = (..... 2. (a) Identify the surface with parametrization r = sin e 1 ...........cos(0)/2) 2= COS 2²-5²) y=u where 0 ≤ ≤ 2 and -1 ≤ ≤3. Hint: Find an equation of the form F(x, y, z)=0 for this surface by eliminating u and e from the equations above. (b) Calculate a parametrization for the tangent plane to the surface at (x, (0./3). (e) Calculate a formula for a unit normal vector field, n, to the surface in terms of u and e. Hint: n(u, v) = where (r. y.)=r(u, v).

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