Math 220 Final Exam-December 10, 2022 %100 Correct Questions and Answers.

Math 220 Final Exam-December 10, 2022 %100 Correct Questions and Answers. Instructions: • During the exam, you may not use your books, notes, reference materials, or any electronic devices, including calculators and cell phones. Violating this rule will result in expulsion from the exam and a score of zero (0)! • No form of reproduction or provision of this exam, or any part thereof, including, but not limited to, copying for personal use, sharing with current or prospective students, or posting on the Internet in open access or restricted selective spaces is permitted without the written permission of the course coordinator, Prof.Alexey Cheskidov, Math 220, Fall 2015. • You are required to show your work on each problem on this exam. Mysterious or unsupported answers willnot receive fullcredit. A correct answer, unsupported by calculations, explanations, and/or algebraic work will receive no credit; an incorrect answer supported by substantially correct calculations and explanations will receive partial credit. Scores: 1. /15 points 2. /10 points 3. /10 points 4. /15 points 5. /15 points 6. /10 points 7. /15 points 8. /15 points 9. /15 points Total: /120 points L e at t n (s) = n! (s − a) n+1 , L e at sin(bt) (s) = b (s − a) 2 + b2 , L e at cos(bt) (s) = s − a (s − a) 2 + b2 , L f 0 (t) (s) = sL f (t) (s) − f (0) , L f (t − a)u(t − a) (s) = e −as L f (t) (s) , L δ(t − a) (s) = e −as . PLEASE LEAVE THE REST OF THIS PAGE BLANK! 1. (15 points).Solve the initial value problem y 00+ 2y 0 + y = sin(t) − δ(t − 1) , y(0) = 0 , y 0 (0) = 1 . 2. (10 points).Compute the Laplace transform of the function f (t) = te −2t sin t + π/2.