MATH 105 Midterm: MATH 105 2013 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. 9 (a) let q : x + 5y 3z = 2 and r : 3x . R are parallel, orthogonal, or identical. y 4z = 0 be two planes. Answer: (b) the volume of a right circular cone of radius x and height y is v (x, y) = the level curve v (x, y) = . Answer: (c) let f (x, y) = sin(xy). Page 3 of 16 pages (d) use sigma notation to write the midpoint riemann sum for f (x) = x8 on [5, 15] with n = 50. 1 f (x) dx, where f (x) ={ 3 if x 3 x if x 3 (f) if f (1) = 2 and f (2) = 3, nd 2. Page 4 of 16 pages (g) evaluate cos 1 y dy.