Math 115 final exam fall 2006: consider the surface z = f (x, y) = 2x2 + y2. Find the tangent plane to the surface at the point (x, y, z) = (1, 1, 3) and nd where this plane intersects the z-axis. Plane intersects the z-axis at z : 3 b. 2 c. 0 d. 3 e. 4 f. 6 g. 8 h. 10: find the shortest distance from the origin to the plane 2x 2y + z = 9, 1 b. 2 c. 3 d. 2 e. 5 f. 3 g. 8 h. 4: consider the function f (x, y) = x2 4x + y3 3y. S when s = 1, t = 1 is: 0 b. sin(1) c. cos(1) d. e sin(1) e. e cos(1, 2e cos(1) g. e sin(1) + 2e cos(1) h. e sin(1) 2e cos(1), evaluate. H. ln(2: in a lottery, the players select 6 numbers between 1 and 49.