MAT-2130 Midterm: MATH 2130 App State Fall2012 Test3 answer key
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If f (x, y) = c, then dy dx. /10 points) let f (x, y) = x2 + 4y2. Fz (a) write down a general equation for the level curves / surfaces of f (circle the correct term). Brie y describe these level things. (b) write down the equation of the trace of z = x2 + 4y2 in the xz-plane. (c) make a rough sketch of z = x2 + 4y2. /10 points) consider x and y as independent variables and z as a dependent variable where. /10 points) take it to the limit. (a) show lim (x,y,z) (0,0,0) x2 + 2y2 + 3z2 xy + yz + xz does not exist. (b) show lim (x,y) (0,0) 3x2 + 3y2 + 5y4 x2 + y2 exists (and nd the limit). /10 points) suppose that z = f (x, y), x = u + v, and y = u v. use the chain rule to show that.
