M231SP24_FinalExam-BLANKTemplate

BLANK TEMPLATE Math 231 Final Exam Blank Template Spring 2024 Name (printed clearly): UIN (9 digits): Directions: . Do not open the exam booklet until you are told to begin the exam. / • Please clear your desk except a writing utensil and your i-Card. No exam will be accepted for grading without a photo ID. • All cell phones and electronic devices (including smart watches and AirPods) must be turned o ↵ and put away for the entire exam period. Please remove any hats, put away all books and notes, and keep your book bags closed for the entire exam period. • Calculators are not allowed on this exam. • Academic honesty is required and expected. If you are seen using any electronic device, using any notes or course materials, or talking to another student during the exam period, it will be construed as cheating and you will be asked to leave. • The exam is double-sided and there are 15 questions on the exam for a total of 80 points. • Do each of the free-response problems and show all work within the indicated margins. Box or circle Box or circle your final answer. Partial credit will be given for partially correct work on free-response questions. • Do each of the multiple-choice questions and fill in only one bubble only one bubble for your final answer. Multiple-choice questions will be graded on accuracy with no partial credit awarded. • When you finish the exam: ? Make sure that your name is written in the space provided in the top right corner of each page. ? If you finish with more than 10 minutes remaining , you may quietly turn in your exam and leave. You must show your ID to the proctor at this time. No exam will be accepted for grading without an ID. ? With 10 minutes remaining, all students who are still taking the exam must remain seated until the end of the examination period. At that time, everyone will be instructed to stop working on the exam. Your writing utensil should be put down and the exam booklet closed. Anyone who does not follow these instructions will earn zero points on the page they have open. You will then show your ID to the proctor. • If you have any questions during the exam, please raise your hand and a proctor will come to you as soon as possible. Read each question carefully, write your solution clearly, and check your work. Good luck on the exam, and please wish the people near you good luck as well! I certify that I have read, understand, and agree to abide by the above exam directions. Signature:

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BLANK TEMPLATE Math 231 Spring 2024 Final Exam Blank Template Name: F Free-Response Questions (54 points) Directions: Show su ffi cient work to justify your answer. Box or circle Box or circle your final answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. (14 points) Find the radius of convergence, R , and the interval of convergence, I , for each of the following power series. (a.) 1 X n =1 a ( n ) (b.) 1 X n =1 a ( n ) ⑮ (X-2)" an = x * " Ant = x + IX =O (113(15) ... Ent 1)/(3/(5) -- (2n + 1) (1) (31(5) .. (2( + 2) + 1) Plant 1 = tiscets / I # . = 0 , / = = = (21x0 = 04 - Into An + 1 = 1 (3x- 2 , n + n + 1 Elan = : /* Bx 2) n I (n + 11 ((x 2) = (3x2/0 = (3x 2141 = (x 5145 - 143x 24/ X = 1 Is I or 123x3 R = 5 (x = 1 < X 13(1)-2 div . I = [ B , 1) = an um lam = = (1 . it = ( x0 = 0 < 1 R = 1 = 1 0 , 0 - An = In - Tim lat = ) = / 4 = (x- 3/ = ( 314 - 1<x - 34 (2 - 3) 2 - 12 --- cr - 2 x dir In + x" an = in + yxhR , tim1 = (x) = (x(x R = 1 1 = ( . 1, 1)