Final - lab-t Nam Nan-1:3 Instructor Math 15 Group Final{Fall ENE Vmiun A You an not nlluwml to mp notes hookah calculators permnul slums or cell

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Unformatted text preview: lab-t Nam: Nan-1:3: Instructor: Math 15!! Group Final {Fall ENE] Vmiun A You an: not nlluwml to mp. notes. hookah. calculators. permnul slums or cell phones. You have exactly 2 hours. This is a multiple-chaise exarii. You will 1115:: only the pmvidnd hlﬂnl: wurk pact-mt fur the calculations. At. le Ellltl of the exam yuu will turn ln the Sewn-mi. the quantiun packet and thin Wurk packet with your 11mm: ml each item. Any IIIlHEIlﬂﬂ: item may result in tllﬂciplinnry action and failurﬂ In the course. 5%” r—l l.i —-_— rig? Ir” +r —ﬁi is l u] D II} '. 1 cl - on. d} 1 rl min-acme“: 2‘ I l'uu II: _ 1i I—*'.lv : 2 is all -I iii —-—1 c] 2 ll: - 1‘. e} mint’xistmt 3' ' 1 'l Hm ..:I'.' —-.;r n... 4.1.. .n—d'l J." is:- El ii a} il‘x: Ell—r32; rl-El' ell—E f‘}--§ £2. lim :25“: .rw-nﬂr. is all + 3-: in} —ac rlil d] 1 rl mum-mum . a: I l Thin“ [1+ E) b: I ul- bj Ell-l: r} (—2 [fl £2 El t-I'I: .r’wi Eﬂf{z3=ﬂ+4thmf{:}m a1 41 h] bidir— c] I: d} 151' r] —I'E {:1 + 4F =2+4 tx=+ 4F {1:1 +4? {HHF 'r. IfI{I}—~-Isin(;) MIT—g) in «HE try—«E all can—i ﬁg 3. .Jrfm 1:“ -1}'”t1ummmjin 1.:_ 4:3 lit. m a: a} 3 {4' I] h} 31"; I} r} a—r ‘- “W: 2.: c} 2:: M1” — If” 3LT“ - 11'” 9. imﬂri if: if . a} I a] 3mm} c] ‘i 1. 1 — 5.1:? 19"]. -- F 3 u d — - L -r' 3.: } £4— 51; a} damn" I ] 19. Eng] = 21mm. than may in a} l I?) lie :1 2: d} E c} -l-l: 11L+ Thu uquutinn of tlm tangent line. tn the graph 131' _.I" Er} = v"? --|- 3:3 at (3.! {3}] is .1 _ 'r' _ 3 i’ I _ 3‘ aJy _ Era—E b}y.—r42+: cjyu4£+l 3 T’ 3 -i 12. Lul. ﬁx] ~— 1"”. mammﬁm m (15.3?” via the Iirmr appruﬂmnlinn to j baman 15 [ﬂw llmaﬁmtim off a1 15;- in :12 u: a: n2 1 a ﬁ+mﬂﬂ ﬁ__.__ c \$4....— d}2__.._ :21.— II a” 33 H 3'! 32 1 32 13. che pith-uni: Wanmz—lﬁaiﬁfﬂ} —c".tin{t} M tinn- I. umﬂwmkmhnurh: n} -r_‘2ﬁn{t}+r_‘mn[t:l b]:"sin{l1:r"¢ﬂ{t] c} 2e“ma{l} d}2r"mﬁlt} e] —2{"sinm WhinlﬂﬂcrwhidiisEEEEthHEishmaingagaimtnumﬂardihhH-is tiling am from ther walla: the ramnf4ﬂfm. 0‘1 LJ‘J—-—uﬂ—H—— “‘5’: 6 TL Warmin- Ihr- ﬁﬂt‘ all which the angle 9 {in radium] barium: the- mp uf the lad-cl” and the wall in incl-mm; m um- 51mm 3 .1 :33: 4:13 a} 2 c] d; 1-1 1 15. Lu: “:1 = :91: - 4:1”; The Mm Wm of J" m! we inn-mt 1—1-." is «1 1n #19 r: 12 d1 51“ r] 41“ 1 1E. LEII[1]=EI"-I-é.tn—3:2. Theyﬂphdfhm‘tupm. a} {-312} 5} {—13} =3 [rm- *2} .1} pm 4} am: {am} a} (—1., —2] and u, my 11'. m 1 {{2} = 41+ 5 The ﬁll]th I aminu ils ﬂhﬂllll‘lli: mum on the hue-rm] {—~m.ﬂ} nt :1] -2 w -2-'='3 c} 4*" a; 4-”! c} —3 18. is a} 1.3:“ +16-- 17 5} -_= r} “'1‘ + IE it]. H” M“) £05 I 1 Jr “'1 rim is - a] u b] i c] 1 d} 2 t} -. 21. a ' 1 1 Ed: ‘5 f q E: a}: mi EMF—I d}; a)? 22. . 1,!” 1 [mm] + 9'12“; is - - a] 5 b1 — :1 i .n a. r} :1" 23. Thumul'dwreginnmwkmdhy Llwgraplmafy:rgmuiy:2:—x’iﬁ 1 1 1 u] E b} E n} 3 d] ﬁll-III raj]; 2i. Witt-ﬂ llambdlyufmohjml Iminthhex-uis'ssin(¥) a: ﬁn:- t. Th:- am: trawler! hf thu- nhjad mm the rim:- iﬂlﬂ‘lﬂl \$11.5; in 3 w 12 n} 3- Fa} E :1] “3T— d}-1 n] 12 25. 3.3mm than. 1—3! - r”? nudym : -1 11m an} isThmyinh. .. - 1 I _ _ r z A}: —:;2_ run , -r.r2 _ Fm 0"] 2 a F +n H2+e P c} 2+§£ —2r d} -2+2r"""2-2€_l” c} 44:”? +2c—W—2 Sulutiuna 2. 2 ___.1 _. _. ,_ 2 am Ir 1 um Itx 2Hm+21| # “m trr 2:: tx+ 1| _ “mi”? ‘ 4 z—-'.'~ arr-y r—2- 3*? :2— 1-2 :4 The mm in h 3. ﬂy L‘Hmmital’s mic, siniiiw} +3: . Enwﬁﬂrﬁ __ . -9Mn[~l1]_ 51 hlnlfix} _ 9 EﬂT‘ FELT SET - abs: 3: “5 The ml!!! in d. 4. By L‘liﬁpitnl‘n Ulla. . a _I [int 112"”: H131 31” v um sli— = lim '4: r—-1-;1-: :I'-+-r-:n ('1 l—r—r-h: __r___rm x -+-m c-lﬂ 2 - lim F4 = hm b — — I'll. J—ww_ _1_” :— lump-“1T2 +1: Them'ﬁc. 5.thaw \$30 + é): = .mmﬁlﬂ“ 2%)) "—W(,E'ﬂx"“(l I 2%))- By L'Hﬁgmiml's ruk'. iimxxh:(l+i)— Hm -———'—u — Em Thnmfore. - i t_ r — a _ 1:2 imbue.) (“MDWW ‘ The answer in b. 6. FM 2 Ed; :. ; _ “21:1”: mamm'ﬁd. 7. I'm - E(4nn(§)) =4(M(%) ‘£m(5) 11mm, The nnswur is a. B. —i “ L”__I_ _ 4;: _ 1: rmﬁtﬁw ]} "3'11: '1 [hi—31:1 112?:- “Emu-3'51 9. d 1 3 E {at} = "131—13512 m _ _v’I_—Ef3 Thu mlawer in: c. [H.1-‘hrelmw -—-2:llﬂ{II-I-I. ThI-mﬁm. f'{€}=3cln{£1+e=2¢+c 3c. Timmixb. ILWulmmre -' ._d- 31.“!_] u 'u-if': ____._.Ir-_ Hal—EU”) —§{;+;} {22: Thﬂmfnrm a II3J=4mn1f[3?‘l~ Thus. 3 a _' a mamigd_ 1'2. We haw: If 1 1 I'm -_ Elm ._. 11-an __ hm Therefan Hm} = 1ﬁ'“ 2 “d 1 ' i 1 1 '__..:I|r.‘_ = I_—=— - 4-13 II": 4:21}! L=1E 321 so that I L11} '—- H161 when“ IE} =2+E¢r— Iii}. Thcrcfum, a- L [1' s} - a _ ‘E. “15—3) - a. _ ﬂ '11:»;I m is d. 13. W32 have d "m = a“ "mm = -r“s'mtt1 +£"ms{t}. Ind uh} = 3% = ghiﬁinﬂ] — c-I'mﬂ1’_ Fri mu} H ﬂ—t sin {n 2 _2E" min} The answer is t. 14. I B “In haw.- ﬂ I it I 1 I Tbnwfmq «*3 _ 1 E ' 3mm hi the iﬂﬂlﬂn‘l- H = 1‘33, ﬂ 1 2 'l'henuswurisd. 15. We have N J i: .5— 5; Ha: [:L' — } + 21:3 8:172 — f-I-J: 89: [:r: — 3} _ 4] - Thrmfmu. LILL' critical pnlnLn‘ if f are [El1 3 and 4-. W}! have ﬂ—l'] — 53”, ﬂan = H4}. = D and H3} _ u. Thnﬁ'fﬂﬂh the. Flhﬁﬂiutﬁ' maximum nf f cm The interval [—1,-1; 15 EL The mmwur '15 b. '5. r E f 16. We have d I fir] — E(1]—2:L’1+%LH— ﬁr )—%m" +ELJ—ﬁj and E H .. l._.'i;l..2_ .. __,.'_P I_ ._ p _ “_r’ nil-(3A ' 2t '3‘") -L +-£ h {J.+.i][.¢ _.':| Therefore, I” :.- {I if :1»; E [—00, —3} or :r. E [2, +00}, Thus;1 the graph of f is mucmre up on the illtt‘l'VﬂIti f m.- 3} and {2! 'r Tlm Euwwru' 15 d- , d . 1 _ a Ih—hJ—l 2.9+! “*1 E(“‘+;)—‘-";-T"?" mm!'{xl—Dif EIJ+IHBﬁIa=vgﬁm=—§:ﬁ Wu hm mm] :- u in: q 4"“ and I’m a: u H inrnutsing un [ —':r.;. -T”“I and disarming m1 I—E' '5 maximum-mtI—mﬁ] at —2‘”"‘. Them is b. "I" 4:: 1 c. {L Thatch-1'me 1. Thus. {attains its aim-alum IB- 1 f£(:—1 d:_1:—1l _-l-1_1-I___3_ , at 11+: ‘13“ 1‘16“ 1+1‘I7 Thuansw-rise. I'D. d I 3-; ﬁn"+lﬁrfu: .r‘+lﬁ —| THREE-“whit. ﬂkﬁmu=¢§wtmdn—U[2mdx.ﬂm I,“ ml” 1 m I .= . :2 ‘ .w‘” =2 1—-)=I ﬂ .1: 2 "Emmi", (minnm) ( 2 ﬁnal Timmnnmiﬁc- 21. J l 1 ,= _1 _ 2 '1 [ Era-“m, aim—4 2 The mm is e. '22. We 29:11: 1:. = 3:1: 5:: that riu = 3&5. Tlmﬁ. ml 1 l 1 I it"! _ 3 4 I”. I +91?" 1 1 Hash"— J (mwwILJ-écz+\$)—e- Thn mmwer ih IL 13. We have zizh—xgulxﬂ-Eﬂ:-ﬂﬁ:flx_1]=u“_z_ﬂmz: L Thu m 111’ the rug'km unuimmi by the. graphs of y z :2 and y = 2:1: — 9:“ is J 1 I 1 . 2 3 LIH‘h—ﬁ} -.-:.~3}d.1;_ £'{2x_2::2}dw:;2(i_-fﬂ_ Thn I‘J-J'lﬁwcr 5,5 {L The distant!!! 1mm hr urath mu than Iliml' interval [H.ﬁl is ll 3'1 | [H‘si11(:—1)dt—fain(T—:)dt 4( _ :t—mi:}+mstﬂ]}--:~( ¢w(3—:-)+m{=j) = LLE -' 3r 11' 71' The mm is c. a]: If: yum 2: y[l} + fed“: —2 :- ft"”du '— —-2 —2f cwdw I d". i _tlrli —. —2- 25'“ + 2.3”“ _ sax-“‘1 +2.:' W J mam-nuke. 11 ...
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This note was uploaded on 04/23/2008 for the course MATH 150 taught by Professor Shen during the Fall '08 term at San Diego State.

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Final - lab-t Nam Nan-1:3 Instructor Math 15 Group Final{Fall ENE Vmiun A You an not nlluwml to mp notes hookah calculators permnul slums or cell

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