MAT-2130 Midterm: MATH 2130 App State Spring2012 Test3 answer key
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If f (x, y) = c, then dy dx. If f (x, y, z) = c, then. /9 points) level curves and surfaces. (a) match the graph of the surface with its contour map. C (b) state the equation for the level surfaces of f (x, y, z) = x2 + y2 + z2. Such surfaces are called (c) state the equation for the level surfaces of f (x, y, z) = 3x 2y + 5z. /9 points) show that the limit lim (x,y) (0,0) x2 + y2 x2 + 3xy + y2 does not exist. /10 points) the volume enclosed by a pipe of radius r and length l is given by v = r2l. Use a di erential to approximate the maximal error in measured volume if the measurement of the radius r is o by at most 2% and measurement of the length l is o by at most 3%.