MATH 215 Final: finalw03
Document Summary
Please do all your work in this booklet and show all the steps. Write your nal answer in the corresponding box. Problem 1. (10 pts. ) (a 5 pts. ) Find the area of the parallelogram spanned by the vectors u = h3, 2, 1i and v = h1, 2, 3i. (b 5 pts. ) Find the rate of change of the function f (x, y) = x2y + y3 at the point (2, 1) in the direction of the vector h3, 2i. (a) Three quantities x, y, and z are related by the equation x3zez. Using any method you like (for example, the distance formula, lagrange multipliers, etc. ) Nd the distance from the point a(17, 4, 3) to the point on the plane 6x 3y + 2z = 10 closest to a. The great greek mathematician archimedes in his treatise on. Spirals gave the following de nition of a spiral:
