Spring 2007 - Ebenfelt's Class - Practice Final Exam

# Spring 2007 - Ebenfelt's Class - Practice Final Exam - Name...

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Name: PID: TA: Math 208. Final Examination March 22r 2006 Turn off and put o,way gour cell phone. No calculators or any other deuices are allowed on this efran1,, You mag use one page of notes, but no boolcs or other ass'istance on th'is efiarn' Read, each question carefully, answer each question completelg, and show all of gour work. Write your solutions clearlg and, legibly; no cred'it will be gi'uen for illegi'ble solutions. If any question i,s not clear, ask clarification. 1. (6 points) Find a function y : A(t) that satisfies the following differential equation subject to the given initial condition. a' 4te-u s(t) o rJt "e*-F' dt gY d1 = lfr Q'-5 :-4t c.'c,l I 'tt.i t .''- I \v5 ^r L,, # ll Score t\ Y-3 o ta J' t\ :ztz+ C t=\ t 1"4 -t-^ ( et*+ t) o = {o (a- \'+ ,l,fA hc"dg C:*l \ \s 1 2 3 4 5 6 7 B T { ? t!-n (}tL*-I)

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2. (12 points) The integral of sin2(r) may be found using several different methods. (a) Find /sin2(r)dr using the double-angle identity for cos(2r), 5;'ntx' 5 l-cu52{ "*, t# r | -' d , >rrr*\t'{ X '= {u5; { t 4r* d ,* a- +t (b) Find Le-{t rt I t *J- l7 4 ,fi -?Y '-[ + L,4-i<>X{i F / sin2 (r) dr using integration
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• Spring '08
• Justin
• Math, Trigraph, Complex number, differential equation subject, gour cell phone, gour work. carefully,answereachquestion, dr usingintegration parts

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Spring 2007 - Ebenfelt's Class - Practice Final Exam - Name...

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