MATH 230 Midterm: Math-230-Spring-Test-2
15 Feb 2019
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De ne a function f on the plane r2 by f (x, y) = s x2 + 2y2. 8y x2 . (a) (5 points) describe or sketch the domain of the function f . (b) (5 points) sketch the level curve f (x, y) = 1 on the coordinate axes below. A cannon res a ball at the angle of 30 to the ground. Use the gravitational acceleration constant g = 10 m/s2. Problem 6 (14 points) a function f (x, y) satis es. F (0, 1) = h3, 5i (a) (4 points) find the polar coordinates (r, ) of the point (0, 1). (b) (10 points) compute. The picture below shows some level curves of a function z = f (x, y). Use the level curves to decide the sign (positive, negative, or zero) of the following partial derivatives. (a) (2 points) fx (b) (2 points) fy (c) (2 points) fxx (d) (2 points) fyy.
