Calculus 1 Topics Covered: - Three-Dimensional Space; Vectors - Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces - Planes in 3-Space - Quadric Surfaces

Instructions: Answer the following problems by showing the complete solution. In return, I will give you a good and high rating. Thank you so much! Special Note to Tutor: Please be careful with the units and measurements in calculations. Thank you!

The blue icon "I" means "exact number, no tolerance"

1.

Identify the surface by completing the squares. x2 + 4y2 - z2 - 18x + 8y+ 4z = 0 O A hyperbolic paraboloid. O A hyperboloid of one sheet. O A hyperboloid of two sheets. O An ellipsoid. O An elliptic cone. O An elliptic paraboloid.Describe the surface with equation x2 + 12 + z + 8x + 4y+ 2z - 28 = 0 The surface is a sphere with center ( HI ) and radius\fb) + 6 -4 -2 X 2 4 6 -4 a C) - ON 2 -6 -4 X 1-2 4 6 -2 -4 -6\fFind an equation of the plane indicated in the figure. Z 2 Equation: 2 2This exercise refers to the hyperbolic paraboloid z = y2 - x2. (a) Find an equation of the hyperbolic trace in the plane z = -49. O y = z- - 1 O x 2 = 1 49 49 X z = 1 49 49 O Z = - y + 49 O x2+ y = 49 (b) Find the vertices of the hyperbola in part (a). O (0, + 7\\/2, 49) O (+7, 0, - 49) O (0, + 7, 49) O (+7, 0, 49) O (+7\\ 2, 0, - 49)(c) Find the foci of the hyperbola in part (a). O (0, + 7, 49) O (+7, 0, - 49) O (+7\\ 2, 0, - 49) O (+7, 0, 49) O (0, + 7\\/2, 49 (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-axisSketch the domain of f (x, y) = \\x2 + y - 4. Use solid lines for portions of the boundary included in the domain and dashed lines for portions not included. a) -3 -2 -1 2 3 -1 -2\fDetermine whether the limit exists. If so, find its value. If the limit does not exist, indicate that using the check box. lim (2,y)-(1,4) 202 + 22 Does not existDetermine whether the limit exists. If so, find its value. If the limit does not exist, indicate that using the check box. sin(x2 + 32 + 22) lim Does not exist (z,y,z)-(0,0,0) Vac? + 32+ 22Sketch the largest region on which the function f {.x'. y) = ' Xx y is continuous.