MATH 200 Midterm: MATH 200 2012 Winter Test 1

• School: UBC
• Department: Mathematics
• Course: MATH 200
• Professor: All

Document Summary

Total: candidates must follow any additional examination rules or directions com- municated by the examiner(s) or invigilator(s). Assume that the function f (x, y, z) satis es the equation the mixed partial derivatives. G( , s, t) = f ( + s, s, at). [10] 3. xyz + x + y2 + z3 = 0. Suppose that a function z = f (x, y) is implicitly de ned by an equation: (i) find. Find the absolute maximum and minimum values of the function f (x, y) = 5 + 2x x2 4y2 on the rectangular region r = {(x, y) | 1 x 3, 1 y 1}. Find the direction in which the function w = f (x, y, z) has the. Y f (x, y) dx dy. (i) sketch the domain of integration. (ii) reverse the order of integration. (iii) evaluate the integral for f (x, y) = Hint: you may use the fact that /2.