# Identify the surface with the given vector equation

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Identify the surface with the given vector equation. Solution or Explanation Click to View Solution r ( u , v ) = 3 sin u i + 4 cos u j + v k , 0 ≤ v 4 hyperbolic paraboloid circular paraboloid plane elliptic cylinder circular cylinder r ( s , t ) = s , t , t 2 s 2 circular cylinder plane elliptic cylinder circular paraboloid hyperbolic paraboloid
13-11-18 HW #26 3/8 4. 1/1 points | Previous Answers SCalcET7 16.6.013. Match the equation with its graph. I II III IV V VI Determine which families of grid curves have u constant and which have v constant. u constant r ( u , v ) = u cos v i + u sin v j + v k
13-11-18 HW #26 4/8 v constant Solution or Explanation Click to View Solution each grid curve lies in a plane z = ky that includes the x -axis each grid curve is a helix each grid curve is a circle of radius (1 − | u |) in the horizontal plane z = u each grid curve is a vertically oriented circle each grid curve is a circle of radius | u | in the horizontal plane z = sin u the grid curves lies in the vertical plane y = (tan 3 u ) x the grid curves lies in a horizontal plane each grid curve is a circle contained in the vertical plane x = sin v parallel to the yz - plane the grid curves are the spiral curves a straight line in the plane z = v which intersects the z -axis the vertical planes y = kx through the z -axis the grid curves run vertically along the surface in the planes y = kx
13-11-18 HW #26
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