MATH 105 Midterm: MATH 105 2015 Winter Test 2

• School: UBC
• Department: Mathematics
• Course: MATH 105
• Professor: All

Document Summary

Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal di culty. (a) find an equation of the plane that passes through the point ( 1, 0, 3) with a normal vector h3, 5, 2i. Answer: (b) find the domain of the function f (x, y) = ln(4 x2 y2). (c) let f (x, y) = x sin(xy). Page 3 of 14 pages (d) determine whether the following statement is true ( you do not need to justify your answer) : The function f (x, y) could have both an absolute maximum and an absolute minimum at two di erent points that are not critical points. You do not need to justify your answer. (f) evaluate. Z 1 f (x) dx, where f (x) =(cid:26) 2x + 4 if x 3 if x < 3.