The goal of this quiz is to see if you are comfortable with the geometric interpretation of gradients. Let S be the surface given by the cartesian equation ele+y2+zg (a) There are two ways we can visualize this surface. First, since we can isolate the variable 3:, we can think of S as the graph of the function f(y,z) : 111(1 + 342 + Z2). The vector Vp) in this case represents the direction in the yz-plane for which the corresponding path on the surface S at the point P sees the largest increase in the x direction. Sketch the surface 3, mark the point P 2 (111(2), 0, 1) and draw the path on S in the direction of Vf(P). (b) Now, let's think of S as the zero set of the function g(x, y, z) = ex - 1 -32 - z2. As we saw in class, a normal vector to S at the point P is given by Vg(P). Use this to find the cartesian equation for the tangent plane to S at the point P = (In(2), 0, 1)