MAT-2130 Midterm: MATH 2130 App State Fall2011 Test3 answer key
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If f (x, y) = c, then dy dx. /9 points) consider the surface z = px2 + y2. (a) write down an equation for the level curves of this surface. /10 points) show that the limit lim (x,y) (0,0) /9 points) suppose xz eyz = 5. /10 points) let z = f (x, y), x = u + v and y = u v. show that. X (x, y, z) = (2, 1, 1). /9 points) find the equation of the plane tangent to xyz = 2 at the point. /5 points) 3 of the follow 4 statements are true. Which direction maximizes the directional derivative? (c) given the following contour plot. /12 points) use the method of lagrange multipliers to nd the maximum and minimum value. /9 points) approximate the integral rrr x2 + y da where r = [0, 4] [ 2, 2] using 2 2. If f (x, y) = c, then dx dy.
