MAT-2130 Midterm: MATH 2130 App State Spring2012 Test2
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If f (x, y) = c, then dy dx. Fy: (9 points) level curves and surfaces. (a) match the graph of the surface with its contour map. If f (x, y, z) = c, then. A (b) state the equation for the level surfaces of f (x, y, z) = x2 + y2 + z2. The level surfaces of f (x, y, z) are de ned by x2 + y2 + z2 = c (c is some xed real number). These surfaces are spheres centered at the origin when c > 0, the origin by itelf when c = 0, and empty when c < 0. Such surfaces are called spheres (at positive levels). (c) state the equation for the level surfaces of f (x, y, z) = 3x 2y + 5z. The level surfaces of f (x, y, z) are de ned by 3x 2y + 5z = c (c is some xed real number).
