AS.110.202 Final: Practice Final No Solutions Fall 2017
Document Summary
Instructions: this exam has 10 questions and is out of a total of 200 points. No graphing calculators, books, or notes are allowed. Be sure to show all work for all problems. No credit will be given for answers without work shown. If you do not have enough room in the space provided you may use additional paper. Be sure to clearly label each problem and attach them to the exam. I certify that i have taken this exam without the aid of unauthorized people or objects. Compute the following limits. (a) (b) lim (x,y) (0,0) (x2 + y2) ln(x2 + y2). lim (x,y,z) (0,0,0) sin(xyz) xyz. Question 2 (20 points) (a) find the rate of change to the function f (x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 1). 3 (b) recall that f : r2 r is harmonic if 2f.
