MATH 241 Midterm: MATH 241 UIUC Math241_Spring08_Exam3

• School: University of Illinois
• Department: Mathematics
• Course: MATH 241
• Professor: All

Document Summary

Math 241 exam 3 version 1: (5pts) determine if the following statement is true or false. Everyone starts with 1 total point and the lowest possible total score on this problem is zero. (a) z 2 (b) z 1. 3 dydx = z 2 x2ex+y dydx = z 1. Brie y justify your answer. (3pts) show that f is a gradient eld by nding a function f (x, y) such that f = f : (5pts) let r be the rectangular region [ 2, 1] [0, 1]. 1 x2 + y2 + 4 da. (5pts) find the image of the unit square s = [0, 1] [0, 1] under the transformation. T (u, v) = (u2 v2, 2uv). In other words, sketch the region r = t (s) in xy-space. (b) (5pts) using a double integral in uv-space, compute the area of the region r. (remark: You can do part (b) whether or not you were successful in part (a). )