MATH 226 Study Guide - Midterm Guide: Medieval Commune, Iden, Tangent Space
Document Summary
Be sure that this examination has 10 pages including this cover. A gas is known to satisfy the van der waals law p = 2t. V 2 where p =pressure, v =volume and t =temperature. This equation of state is used to determine v as a function of p and t near p = t = 1. T (1, 1) and 2v (a) determine v. P2 (1, 1). (b) measurements are made and it is found that p = 1 0. 02 and t = 1 0. 02. Find the approximate maximum error in the value of v if we take v = 2. Find the points on the ellipse 2x2 + 4xy + 5y2 = 30 which are closest to and farthest from the origin. 1 x and then evaluate the integral. dx(cid:19) dy +z 2. 0 dx x (a) sketch the region of integration. (b) express the integral in polar coordinates. (c) evaluate it.
