1. The problem statement, all variables and given/known data (a) Sketch the level curves of z = (x^2 - 2y +6)/(3x^2 + y) at heights z = 0 and z =1. (b) Sketch the surface (x−1)^2 + (y+2)^2 + z^2 = 2 in R^3. Write down a point which is on the surface. 2. Relevant equations -- 3. The attempt at a solution (a) From the question, I assume that you would draw the equation in 2D on the xy-axis and then mark the curves z = 0 and z =1. However, what I am unsure of how is to how to actually sketch the level curves and then find at what values would z = 0 and z = 1 be drawn. (b) From the equation, I recognise that the surface will be a sphere. But is R^3 the xyz-plane? If so, then how would I be able to sketch this as a sphere (on paper)? Would sketching it within a cube be appropriate? Moreover, how would I find a point which is on the surface? Would a point on the surface be an integer solution? (For example, x=0, y=-3, z=0 so, (0,-3,0)).