MATH 200 Midterm: MATH 200 2008 Winter Test 2

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

Document Summary

Rules governing examinations: each candidate must be prepared to produce, upon request, a. Let f (x, y) = x2y x4 + 2y2 . (i) find the tangent plane to the surface z = f (x, y) at the point (cid:18) 1, 1, 3(cid:19). (ii) find an approximate value for f ( 0. 9, 1. 1). Let f (x) and g(x) be two functions of x satisfying f (7) = 2 and g ( 4) = 1. T2 when s = 2 z = h(s, t) = f (2s + 3t) + g(s 6t) is a function of s and t, nd the value of and t = 1. A solid is bounded below by the cone z = px2 + y2 and above by the sphere x2 + y2 + z2 = 2. It has density (x, y, z) = x2 + y2. (i) express the mass m of the solid as a triple integral, with limits, in cylindrical coordinates.