MATH 105 Midterm: MATH 105 2016 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 (0, 3, 2) with a normal vector h2, 1, 4i. Answer: (b) let z = 2 cos(x + y). Is the point ( , 3 ) on the level curve z = 2? (c) let s(x, z) = z2 tan xz. Page 3 of 16 pages (d) let f (x, y) = 4x2 + 8y2 3. Find the critical point(s) of f (x, y), and determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. Find the derivative f (x) of f (x). Page 4 of 16 pages (g) evaluate x3ex4+1 dx. 2 (h) evaluate z sin 1 y dy, where sin 1 y = arcsin y. (i) evaluate z sin5 x dx.