Test 1 Solutions

# Test 1 Solutions - 02HGTI2008 15:9? IFAH...

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Unformatted text preview: 02HGTI2008 15:9? IFAH scannerllimail.mathmcmasterta + Donnie ﬂosterlin 001E005 MATH lAAB Test 1 Name: Student No.: 1)(i)—(v). Multiple choice questions. Indicate your answers to questions (i)—(v) by circling only ONE of the letters. 2 (i) [3] Consider the rational function Gm. Indicate the correct form you would use to express this rational function in partial fractions. a) Arc-MB +CI+D 2 332—43+4 \$2+4 x rtl'lfLi '1 {DKPQJ A B C D b):c—2+a:—2+m—2+:r+2 QLL'I‘Ll' f]; CWQJKHLLP, ) A + Bm+C+ D C _, ' _ 2 2 :r: 2 (I 2) 3 +4 PAL-l A a (:5th d) A + B + _....___,_.___ _._.....,._. : —"—— F...— _..|?- 1*- ——2..-.—-. cc—2 (3—32 \$2+4 @onwﬂxaﬂ In; (1-2.) M +‘t. ) A + B + C ' e a:—-2 (cc—2)2 m2+4 oi”. A(a:— )+B(z+1)+CI+D m—ﬂ 3—2 \$2+4 (ii) [3] Indicate the integral that you would use to ﬁnd the volume of the solid formed by rotating the region bounded by the graph of y = c'”, the line a: = 1 and the line y = 1 8:0qu the line a: = 1. -‘*l :L 3) fol WU - Hy)? do 1 1 ‘8 13)]; 71'(1— e"y)2 dy t k 1-.l 2) [01m — my)? dy 1H 'N (Fania d) 1 m—Inonﬁdy if 1 \1 :e-x :7“) at I *ﬂﬁﬂl) - a“ e) [3 mama)? dy k aﬁewu—mﬁdy w’w = {r (l- Lfr'nil 0‘7 @ \le Continued on next page 02HGTI2008 15:9? IFAH soannerliimeil.methmcmasterte + Donnie ﬂosterlin 002E005 MATH 1AA3 Test 1 Name: Student NO-: (iii) [3] Indicate the integral which is equal to / 313+ 1 d1: after applying a trigonometric substitution. seceﬂ) _' a ﬁfth-13(7); d5 lit—"taﬂlal I Mfﬂiwl d9 13‘“ : tame) + l 1 Set 9 tan (9) c) d6 g : SELL 9' tanﬂ?) Willi) *T“ l *1 L9 9 d) taﬂzwﬂa S J91 u die : Jsec. 9 cu: at 1032(9) 1‘ kanQ c0309) _ mew mfg-lama? Hg aka-:9 019 (‘9 (iv) [3] Indicate the integral which is equal to [332111 a: ( ) dz. a) £333 ln(:1:) — \$332 d3: 5-} {Lou/é " 1 1 LL :- 20" 3 3 J. 3 I 4! ‘MM —. M M) —[ .n m a E) gag if \$3: 111(1) d1: K 1 ﬁ 3 1 f) 3:2 — j 3:2111(:c) do: @ DD (v) [3] Indicate the limit or limits which can be correctly used to calculate A.) 111(1) d3. t ‘ " O a) lim ln(:r) da: 0'“ (all c" M a“ ' t—>o-o c b 1' ?:1 d r c“)1 d he: a “(3” We: 1 I“) I (a) I I1 I t c) \$131+ I 111(3) dzt+tllhrgjji 1110:) d3: #03 d) lim 11101:) d3: t—+U+ f Continued on next page QEIUTIECICIE 15:0? IFAK soannerllimail.math.momaster.oa + Bonnie ﬂosterlin 003;“005 MATH 1AA3 Test 1 Name: Student No.: In the following questions, you must show all your work to receive full credit. You may use integrals from the Table of Formulas, but you should refer to them by number. 2) Calculate the following integrals or explain why the integral does not exist. a)[5] fsinz(r)cos2(m) d\$ gag 8 RB} Q %1“L(1\: Hana“) N Milli =i(l~m(lx\) 2.. 3 TI; Cl“ m1(‘l“\) queen me (lo: I; ( l~ mum) bllﬁl [SJ-“(Val d1? SKlDS'l\\Twl‘ c k .: H .. F El : pg. _ ‘3 Mb ﬁll-"(ﬂ all ltd'lr ; clnL Wm —_ 954’: ) all" 0L —.- Mr V t, m m n :—21Jrcm[t3 - \- agent VJ :‘ “Rtmbltl 1‘ AVA“) ’cC. : rQELQJow'iJ to}. TC. Continued 011 next page 02f0'r‘f2008 15:0? IFAK eoannerlﬂmail.math.mcmaeter.oa + Bonnie IIIoeterlin UMIUQE MATH 1AA3 Test 1 Name: Student No.: 3) CalCulate the following integrals or explain why the integral does not exist. 2 1 ﬁlial/0 I—ldE k“ ‘ d ‘ {LP-L— J :lihf 3': 1 'i' lkH J gal 3‘ {ﬂit c) "Edd-r i ‘C‘ 4c [We r +1—- ‘1"‘ 1 (in Ll'arll ~of 0 1! -Pwr [ \o 1 lien (omit-Q F" Lh‘l tﬁﬁ" :2 am. 356—7 93: Q: 32m, : mmwB’au—U M1l, —% :-AB \$21 .21.:"5 a : 3A AH P “gm—1L "‘ I 3 ,,( ‘ ——-— elm : H 1— ‘: J “l 1 "Ta-:3 J 1—3 A 1 Continued on next page 02x’0'r'f2008 15:0? IFAK eeannerlﬂmail.math.mcmaeter.ea + Bonnie ﬂoaterlin 005E005 MATH lAA3 Test 1 Name: Student No.: 4) [6] Calculate the average value of the function f (3:) = a“: sin(a:) on the interval [0, 7r]. ! 7? (TU/:6 Villa-L : 150 expllulle Jo fell J1 _: __ exmbijj-g- Ifmjfx)cn A hum: J 3“ t I; - e (Zulu) ﬁﬁpl'ﬁm(’)l] *‘gexﬁfw(1tlllll Home lama-0mm = L LDLKWW)‘C“{“\\ 14:" 9-; "R aura“ um,me _- if. g: '51 em‘ {Wth- CdtfnﬂXD '1 iLHCQKeq‘ 5) [6] Calculate the volume of the solid formed by rotating the area enclosed by the graphs of y = m2 and y = 25:: — 1:2 around the :n-ame. Cwlhs ml‘ Lab-wk 3- D- : (elk—ah?" O 2 9.2L — slat L “3L 1 C? M 7"- 1- l THE END ...
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## This note was uploaded on 11/25/2009 for the course MATH MATH 1A03 taught by Professor Dr.lozinski during the Fall '09 term at McMaster University.

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Test 1 Solutions - 02HGTI2008 15:9? IFAH...

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