Identify the surface by completing the squares. x+4y - z-18x+8y+4z = 0 Describe the surface with...

   
   

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Identify the surface by completing the squares. x+4y - z-18x+8y+4z = 0 Describe the surface with equation The surface is a sphere with center (i x + y+z + 8x+4y+2z - 28 = 0 i i ) and radius Sketch the section of the surface at y = 0. 4x + 9z === 36 Find an equation of the plane indicated in the figure. Equation: 2 x 2 2 Y This exercise refers to the hyperbolic paraboloid z = y = x. - (a) Find an equation of the hyperbolic trace in the plane z = -49. (b) Find the vertices of the hyperbola in part (a). (c) Find the foci of the hyperbola in part (a). (d) Describe the orientation of the focal axis of the hyperbola in part (a) relative to the coordinate axes. The focal axis is parallel to the z-axis x-axis y-axis Sketch the domain of f (x, y) = x+y24. Use solid lines for portions of the boundary included in the domain and dashed lines for portions not included. a) 2 b) -3 c) -1 -1 -1 -1 x X d) 1 -3 -1 1 3 -1 e) 2 1 -2 -1 -1 X X Determine the graph of f (x, y) = y + 1. a) b) (0, -1, 0) (0, 0, 1) (1,0,0) (0,1,0) - c) d) X Z (0, 0, 1) e) Z Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate that using the check box. x4 y lim (x,y)(1,4) x + y = Does not exist Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate that using the check box. sin(x2+ y+22) lim (x,y,z)(0,0,0) = x + y + z Does not exist Sketch the largest region on which the function f(x, y) a) 2 x -3 -2 -1 1 2 b) -3 -2 -1 3 y 2 T X 1 2 3 = - xy is continuous. c) 3 d) -3 -2-1 2 1 y X 1 2 -1 -2 2 1 X -3 -2 -1 1 2 3 -1 -2 -3F 1 2 3 X Identify the surface by completing the squares. x+4y - z-18x+8y+4z = 0 Describe the surface with equation The surface is a sphere with center (i x + y+z + 8x+4y+2z - 28 = 0 i i ) and radius Sketch the section of the surface at y = 0. 4x + 9z === 36 Find an equation of the plane indicated in the figure. Equation: 2 x 2 2 Y This exercise refers to the hyperbolic paraboloid z = y = x. - (a) Find an equation of the hyperbolic trace in the plane z = -49. (b) Find the vertices of the hyperbola in part (a). (c) Find the foci of the hyperbola in part (a). (d) Describe the orientation of the focal axis of the hyperbola in part (a) relative to the coordinate axes. The focal axis is parallel to the z-axis x-axis y-axis Sketch the domain of f (x, y) = x+y24. Use solid lines for portions of the boundary included in the domain and dashed lines for portions not included. a) 2 b) -3 c) -1 -1 -1 -1 x X d) 1 -3 -1 1 3 -1 e) 2 1 -2 -1 -1 X X Determine the graph of f (x, y) = y + 1. a) b) (0, -1, 0) (0, 0, 1) (1,0,0) (0,1,0) - c) d) X Z (0, 0, 1) e) Z Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate that using the check box. x4 y lim (x,y)(1,4) x + y = Does not exist Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate that using the check box. sin(x2+ y+22) lim (x,y,z)(0,0,0) = x + y + z Does not exist Sketch the largest region on which the function f(x, y) a) 2 x -3 -2 -1 1 2 b) -3 -2 -1 3 y 2 T X 1 2 3 = - xy is continuous. c) 3 d) -3 -2-1 2 1 y X 1 2 -1 -2 2 1 X -3 -2 -1 1 2 3 -1 -2 -3F 1 2 3 X