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Fat bans12). Orinept View Go To Zoom Selection Favorite. Settings Help |Page 1/2 + - |806 120 0 Find: Rules: This exam is open-notes and open book. You may not communicate with others in any way or use any electronic resources (such as the internet) during your exam. except a physical graphing calculator. Each problem is worth 10 points. 1. The depth of a pond at the point (x, y) is given by h(x, y) = x2 + 2y' with a. y. and h measured in meters. A swimmer is floating at the point (2, 4). (a) If the person swims in the direction 27 + 37, at what (instantaneous) rate is the depth changing? (b) Which direction should the person swim to have the depth of the water in- crease the fastest? Give your answer as a unit vector. 2. Consider the function f(z,y) = 213 - 3x2y - 1212 - 3y? This function has three critical points at (0,0), (2, -2), and (-4, -8). Classify each one as a local max, local min, or saddle point. 3. Let F(x, y, z) = (x2, 3y + 2, z), and let S be the top half (where z 2 0) of the disc of radius 2, centered at the origin, lying in the zz-plane. Compute the flux of F through S, in the positive y-direction. 4. Let S be the sphere of radius 3, centered at the origin, oriented with outward facing normals. Let G(x, y, z) = (x, 3z cos z +y, a2y? - erv). Compute 5. Let C be the curve comprised of four line segments in R3, all lying in the yz- [[ G.as to (0,0.0) (so they make a rectangle). plane. From (0.0,0) to (0,2,0), then to (0,2, 1), then to (0,0, 1), and then back Let F( I, U. = ) = (ex sina + 1)7 + (2 +)3+ (ex - a2)k. Compute & F - dr