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AK-MATH225F10-WS1

AK-MATH225F10-WS1 - MATH225 Fall 2010 Name 0 Q 7045...

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Unformatted text preview: MATH225, Fall 2010 Name: 0( Q 7045 Worksheet 1 (Review) Section: t For full credit7 you must show all work and box answers. 1. Find the roots of the following polynomials. (Solve for 'r.) V —1\ l—fi—‘I (a)r2—4r--!4=0 IA:— L~ ‘0’ [AC- CF 2); 3C: 2—“ 1" Z -0 Hip Z i @Fc—fayi 200% (13)?” _g,«_3—0 LBP'¢)CF‘/f>2)'o fl] Q“ 34L) O1 + 12.5 C) IS (1:65;) _L\[3)[5) :W“ Z; : Efz— 2. Use exponential and logarithmic rules to simplify the following. 3'1 376+ ~Zt: 2t (a) e’e : C ‘6 a €225 (we 4ln(.1 : and LXL’) l L >(>O (0)1(3J)-1%)+1H()= Qa<%-L): (Ed—3,1 3’ y >50 3. Verify the giw n lunction :(1‘y)satisfies the given d1fielent1cff'equat10n 6 (' . (a) y=——-—)e 20’, y’+20y=24 5 5 -Zo‘(: ’12 7 L'iC 21.5; 7/507 2 W+Zoz~ gag“) ~2L1 ; as (b) y = 2coslf). y’ ’—l—y— - 0 : ”ZSM‘E/ ”3—‘2C056 £135: 7” +7 1 ‘25::ch +ZC65fB1CDr'Si‘x (C) y: —e’3’cos(2t) y’ ’—6y’ +13z/=0 17’ : ~3539coséze) + 2855 .5(26) 7” : :fi astcsséaé) 1' L5 afi$>fl£2fl + é5‘g sImCZt)+Lf¢3 quilt) Mvgé asCZ—b)—f/Z¢St~5/H(Zi) 915:7” 47’ +13; :~§¢\3tQ(:-+> 15%) (\ofikfig (894% 4. Evaluate the following integrals. + 1 1%“: (at): —0: (“kg (a)/11n—1~d1::3 LAalc/L:U —— :;l ’ [M595 L1: QAX 01b, —'—.,l>( 1 2 .. X5691: firiQ’O/ X=€,.' U3Qn[&->'2 4.41, b) L. 075 PAVE ‘ Invuww'é; DOW-(I {’5 ’ A—Ingr~l Chwc 4;.“ 2;;540567‘15 U 1 x7— ; » Z (by/3111mm = TrQnX- 37:; A)?” ”-éwanxv 8 {ET/()6 I t. 6 Pat; 2' Z W Av: 14% :fii T '— W; 31%;»; Sui:):iu=u+< my)“ - , : 9+,TC : ngiyfif Z:/ Z .0 t :3; (£2 41%;: ”if WW JZté—szb)’; MW 1 3: ~24 +25: (2—042) Z = #CXM) 1’ 80‘") AX+HTBX B; Z “Max + [A 8) Z \-. , W... ... Algebra and Calculus Review In MAT H225 you will need to use algebra, trigonometry, and calculus as tools to solve ordinary differential equations. Based on prerequisites, it is expected that you are skilled in these areas of mathematics already. Small arithmetic and calculus errors may be graded more intensely than what you may have been accustomed to in your previous math classes. This paper is intended to help review these topics but it should NOT be viewed as an all-encompassing review. Quadratic Formula: ' —b :: \/ b2 — 4m: 2 a, If arz + bi" + c = 0, then 'r = Exponential Properties: ,. , . , .fi a“ ,i _, 1 a"‘+y = amay, a'l "1 = —, (a‘l')y : a”, a y = —, co = 1 (my ay Note: a can be any positive real number including (2. Natural Log Properties: 111(35) + ln(;g) =1n(.1u). ln('J;) » ln(y) 2111(3) , yln($) 2 1mm?!) , (2111(1) : 50, 111(1) 2 0 Note: at, y can be any positive real numbers. u-substitution: EX: ,2 1, l, ,,2 /$e“' dac = /§c“du=§e“+C= 6“ +0 [\Dlr—l [\J du = Q$d$ H a. Let u Integration by Parts: /udv = no — /’u du EX: ' ' /te*dt = tet—/e’dt=tet—et+C Let u = t, dz} 2 at (it (in = clt7 v 2 ct Partial Fraction Decomposition: EX: 82 + S + 4 A B C s(s—1)(s+2) Z §+§——1+ 3+2 52 +s+4 A . B . C D s(s—1)(3+2)2 : .3 '3—1's+2 + (3—1—2)2 82 + s + 4 A B 03 + D man 1x32 +2) = 2 + g: +2 Completing the Square: EX: 9 9 _2 2 _2 2 s‘——23+5 = s‘—28+ (—2— +5—<7>:(5—1)2+4 9 9 9 r 1 ‘ 1 1 ‘ 19 ,2 . r = '2 ' _ '_ _ = _ _ .5 +s+o S +S+<2) +) <2> (8+2) +4 ...
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