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Q1_1130

# Q1_1130 - MATH 415.01 QUIZ 1A SHOW ALL YOUR WORK GOOD LUCK...

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Unformatted text preview: MATH 415.01 QUIZ 1A Jan 13, 2010 SHOW ALL YOUR WORK! GOOD LUCK! NAME: 1. (5 pts.) Determine whether the members of the given set of vectors are linearly independent. If they are linearly independent, ﬁnd a. linear relation among them. xu)=(1,1,0), ai..(2)=({},1,1), z(3)=(1,0,1) Fu- than): Inc-inftméaxcag: r i '0 i Live. Xo‘.=’o “LC/1.. x: ‘ i O a ° “ ‘ N- l O i ’0 Jl-tf'li’rl l o l 0 r2. i | .13 {j ,4} Cl 1 .1 0 r3 1: I i o O M 0 I" 1" O/er { 0‘ ]U\ ‘L‘K . J a”? w 0 A“ w—x a)“, U L‘i O O 0‘ Q i . #533) l 00 mi. +13er 0 o *- 2. (5 pts.) Write down a differential equation of the form g? = ay + 1) whose solutions approach y = 3 as t—>oo. \“ “DE/WE": A2“ :cL-L— :‘é in iag‘tl’i L :‘L TC": Gal-gab 9‘- Qi— O'Uvbvk‘: = C- Q. .1. 5 : 1 Ce.“ "1° :2. 39 0‘40 _ (/Lowr__ a=’\ WL ! 5; as 1,. and? - we...“ ,1, -'“ " .—. 5:J_(C.e.——lo\ 2. 5,—5.2.- [Efﬁe '1 g: L, “st—.50: MATH 415.01 QUIZ 113 Jan 13, 2010 SHOW ALL YOUR WORK! GOOD LUCK! NAME: 1. (5 pts.) Verify that each given function is a solution of ﬁle differential equation. 1‘. y” + 3y' + 2y = 0: 916) =64, 3:20) = 6" \$1.4 _ 5| “6' 5.“: 4., £2" 9.": 4"“ 11 1+ -24 ﬂu — _ 5"...sz‘15‘ -_— {9 +3.44; +2.2- : e. (‘4—£+11 :W‘ .3- ‘3‘L5 5:4. ﬁt: '64- ”: :- 8' .—‘~ _.L 4“,..— 31.113..*251 - e“ ”Ba” fléinD 1. 2. (5 pts.) Find the general solution of the given differential equation, and use it to determine how solutions behave as t. —) oo. ty’+2y=cost, t>0 - __ yL Bug—E, __ 59f ’ 30 {GI-'7: 5p. -3: 7.-_.[,.l. ”A 1- A.:— e-S + : 941‘ :"+ I” 415 = S *Lfﬁiti-L = 5 i? “'4'“, :‘LS'I'A' —Sfln-LJ-+ 4"" a J.” Lulu :- 4—smt- +95%” +5, v:5m#1¢ TIN“, +213 :: +504“ tend-1C. r -2—- Sn"" .1. C495;- 1- 9;“ = +s-<~t~s+ ”A —- 4:- ‘TL +=— f1” RI \0 N30 \er 5'_ *v 90/ “‘5 L amp MIL—W;- 3—95? aawilﬁ Aoal- ~40 Jami-‘9 4.. O ...
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Q1_1130 - MATH 415.01 QUIZ 1A SHOW ALL YOUR WORK GOOD LUCK...

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