MATH 1172 Quiz: MATH 1172 Ohio State University Math 1172 14AU Quiz 6 Solutions

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

Problem 1 [6 points] and the interval of convergence. For the power series that is given, nd the radius of convergence. Solution: let us use the ratio test to determine the interval of convergence and radius of convergence. 2k+1(x+5)k+1 (k + 1)4 (cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) 2k |x + 5|k (k + 1)4 k4 k + 1(cid:19)4 k(cid:19)4. By the ratio test, the series converges when 2 |x + 5| < 1. 2 , and the radius of convergence is 1. Solution: 63 = 216 and 73 = 343, so i will chose a = 216: find the taylor polynomial of order 3 for the function f (x) using the center that you chose in part a. [note: f (a) should f (x) = x. 27 : approximate 3 218 using your taylor polynomial of order 3. 6. 01846165661: find a bound for the magnitude of the remainder for your approximation.