Think over these questions, please feel welcome to discuss them on Yellowdig. At the end of the week, one of them will be randomly assigned to you with a 30-minute quiz. 1. (a) Suppose we want to answer the following question: how close to the origin does the surface ry + z2 = 4 get? Explain why it would work to minimize D(x, y, z) = x2 + y + 22 (the square of the distance function). What is the constraint for this optimization problem? Solve. (b) What function would we minimize if we wondered how close the surface got to the point (1,2,3)? (Do not solve.)2. It's important to remember what you are computing when you see / / f(x, y) dA. Each integral below is computing the volume of a geometric object. Sketch the volume in question, then use your knowledge of geometry to evaluate the integral! (This shouldn't require "actual integration.") al 4dA, where D = [-3, 1] x [1, 4] = {(1,y) : - 3