You must show work for credit; answers with out support will receive no credit. Leave all answers in exact form: unless stated otherwise, answers given with a decimal approximation (like from a calculator) will not receive full credit. You do not need to give a copy of this sheet when you turn in your homework. Please write your homework on a clean sheet of paper and include your full name, class you are in (Math 1720), and your recitation section number (check your schedule for your recitation section number). If you use more than one sheet of paper your sheets must be stapled together. This assignment covers section 10.3, 11.2 and 11.3. This assignment will be due at the beginning of class on Thursday, Nov 29. Please note the due date. This will be due a week after Thanksgiving, but it two weeks of material on this assignment. So please work ahead to make sure you finish. 1. Find the Taylor series for the following functions at the given center. Then find the interval of conver- gence. a) f(x) = cos r, centered at a = b) f(x) = e, centered at a = Ins c) f(x) = 1-2r centered at a = 0 2. Give three alternate representations of the point in polar coordinates: (37). 3. Express the following points in the given coordinate system. a) (3.) in Cartesian coordinates b) (6.) in Cartesian coordinates. c) (1,-1) in polar coordinates. d) (-12,5) in polar coordinates. 4. Find the area of the region shared by the circle r=2 and the cardiod r = 2(1-cos).