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third-exam

# third-exam - l ’0 Math 3041.2 Test 3 May 5 2008 Do any...

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Unformatted text preview: l ’0 / %@ Math 3041.2 Test 3 May 5, 2008 Do any five of the following six problems. Show all work. Credit will be given only on the basis of work shown. 0 if 0 S t < 3 l 0 1. Let f0) = 2(t—3) if3 St <4 2 if t 2 4 Express f (t) in terms of Heaviside functions and ﬁnd F ( p) . .2048 mu) - 1(4'B\UqC1‘34 :2 New). ? " -2 4- - Q - 10 Angel) 9Q H\HHHB- M’ 9M l C '3 ‘ I) but“). ; “a? Crews) Ca if), IllLE-ﬁuﬂd— er— “B“Hu’ﬂ l -4(4*“ll«e£4}-:uq a} .J8 P_ :16“a l P ~M1— 10 2. Use the Table to ﬁnd the Laplace transform of each of the following functions. (a) f(x)=xs1n3x Ms ,0 a (b) g(x)_e’:'*4m 071M] ( Nil 7,» Fgg (WW—3653i 304 M tum-t! n tp i i Film] 7;. (PM? ‘ 5:1.-.“ ’ 41“.. no 9—. l J? fl" 1 sr' “l” “is"? i " ? twp Math 3041.2, Spring 2008 Test 3 3 SI ,+, 0 if05t<2 . ove = ; [O y y 1 ift22 y(0) = 0, y'(0) =1 3V5: mu} 3&0310 ,3‘Ia3zl. womb). _—J—» ”5:”. 1+ [M "L { \0 P" P f" [in \ , ”-4" 44-1) ._ 6 - uL (04“; Cd (4- I) W: H) e .1” 63 W!” I) 59?.“ P" . 6w P2 (WHM P a”) P \f: “L ‘ 1 CW2” *f— * L I"? WW) WW pt! A(/)+( .45 -_ 1 ‘ A‘ f7 C 5 P ‘ 7 ———: ,H. Airs-to ’ P A1] I)?" E Ap((lu)+ B(P-fl> n CPI - l A*€;O [Phi —-JI/+H[p‘!1 * Lly : 8'” PL» *HPVJ‘HV : '4’ 6—1:: (7’5 WW)” ~. I + 6—2” (P_*9)IY I'- /+ 6-2,; M. ‘ -. + a“ QVQ" 11.15" 3" jfﬂ= +611“ HUGO”) e” I . A‘ {‘3 = ’0 £5] A:—’ (a- [D 4. Solve y"+4y'+4y=§2(t), y(0) =0, y’(0) l 2(4-1} Math 3041.2, Spring 2008 Test 3 5. Solve y' ~3y = g(x), y(0) = 2. pY—l Jay; 036,0) Q-"SV -— 1+ MP). v—LEEL) p-‘S ’7'? ii 7] *4 the“ + (jo) 6% ___..____+7‘_ %< 6 SI x'=3x+2y ~ 5" . ove .. . /O y'=x+2y U 6‘ ‘E‘JW x"-<§>L‘ *~ (5-51): .. 0 7c" SX’ 4 H120- nu rL X: Ge”? (16 {- + 3 ”Wm: (3,: “ Math 3041.2, Spring 2008 Test 3 ...
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