MAT 2322 Final: MAT 2322 University of Ottawa Final Exam exam 3
Document Summary
Print your name and student number on this page. Verify that your copy of the exam has all 10 pages. There are 9 questions worth a total of 60 marks. Write your answers in the spaces below the questions. You may use the backs of the pages if necessary. Basic scienti c calculators only - graphing and/or programmable calculators are not permitted. Find and classify all of the critical points of f (x, y) = x2y x2 y2 + 3. Evaluate the following integral by changing to spherical coordinates: Y2 (x2 + y2 + z2) dz dx dy. ~f (x, y) = 4x + 6y along the path c, where c consists. Calculate the line integral of of the straight line from (0, 0) to (2 2, 2 2) and then a circular arc (part of the circle x2 + y2 = 16) from (2 2, 2 2) to (0, 4).
