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exam1pracBsol

# exam1pracBsol - 1(8 points The graph of y = f:c is given(a...

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Unformatted text preview: 1. (8 points). The graph of y = f (:c) is given. (a) Is f even, geld, or neither? Newer. Tine. 8%"ch is “01’ Symmei'fic. ounﬁ‘i: We, . Quaxfs or We car-Cam : (b) Is f one-twone? Explain. If so, estimate f‘1(5)? Yea} We 8‘11ng Passes We “0&3th lama ﬁsi 3mg :Hodzg We * 150-253: '5] ' ' £“(§‘\ 211% -~ 163: ' (c) Sketch the graph ofy= f(—a:) —3. . I Firsﬂr ghégai ’2 . C‘X) Cinema/e We ET?“ C39 "1C" CGOFC-Biwwi‘e S‘ .' ‘ SIECOc-mn \$4139: ‘6': §(~X\ ~— 3 _ Decree-6:2 ~23, ~ CCDWJQMCK‘L‘C-E b7 ‘3 g“ . 2. (5 points) Show that 111%(2m — 4) = 2 by ﬁnding a 6 > 0 such that |(2:c~«4)——2|<e Whenever 0<|x—-3|<6. \ (Zr-LN“ < E 43> l‘Zx-Gl<5 go EQCJLQAJ 52: FE» (Gr OAY‘H/‘(o’iﬁ _ S‘MerPV} 3. (25 points) Find each of the following limits. If there is an inﬁnite limit, then determine whether it is 00 or —00. ‘ ~i \ \ ,, - .. \$+1 . Lasts We “5' ; so We cm MHW+E (find: (a) iim ; aha—2 (\$+2)2 ' - - ‘ '2. Since, WHO {30:- x‘ 01696 to «2 We? Qua) >0 CliU—‘ClYS' Q0? )C ff: “-2) We (lmciiom .{g negd‘wde Vke‘ar- XE») S’s Hie Kemw :5 ”my ﬂ 2+5—3)( 7- 5- 3) ' \(ngwq (la. bimL 9w“ :w - 7"? 03 g we ”M we (We) Kim 04 NW5“) WWW =2 6:“ Come if Aways HY suing-Hi-Uﬁom QEFS+J AKSG‘ \$308626 I‘m/“ECWI‘M (909%? QEJFij Eecqugf You Ccm_ .Gm\)\/ Wag? We Cami-Com between 4mm m Admjﬂﬂgr ""(d')"'1im"1+'3in'\$ r r‘—r\~r£ rrééwx éi Se 7 C) E H Simx" é 2 m—wo :1; ' \+ Sin X 2’ 4 . __. SO O _ _ X - K .. gm - at o .—. 3 w 1 m w I 0 by RPM Kayo We Sim ee'cc ﬂieorem e lim _____4y2 _ 3y+7 ' ' i ‘ y—’°° W92"y+1 QQOUKQW’RMET‘ U3? saw {a k“ 5‘” {\C’) ' ‘(le+ ‘0'“ 7:5; K"? m X 4. (8 points) Show that the equation 2 sins: = :1: has a root in the interval [7r/2, 7r]. You may use the fact that 3 < 7r < 4. Tim-5 }3 We 5T1 ME (BIS ﬂeet“ VLCJ “k“ 6 Cum (+60 V1 §(X\: 23M K'-—-—)( MOS q red- }m We , ”Were ere , O ,,,ue\$, kaQﬁdéem §(-E~\Qmﬂ g (1T3 gimce '? \$5 COWLMKJOUS}. «(W EMPMecft‘a‘Fe \I’qbe, W909: E’VL {'eﬂé US ‘1’6‘9‘79 “:5 Ct («dumber _ C 6 [TI-E} Tr] wﬁ’h. €(C‘A :- 0, Mcj‘K-ei +6 See “HZ/(Q4 §(g}>0 W’s {3mg +0 Ufé , om approzkrwxq+r0m Ute TFN N 31W. bo‘E tk’g EMPoﬁ'QvK‘E Cit/MD QCQi/KOQJKQORSQ WC?“ %[3 E5 C991 4&3 VeCoamize N “g“ uro'E-’.m‘§--Com , my? equdi’); Sc: eij N is CorreC+' Sod-42' '5; i5 ﬂd‘? M W6 CQSQ, 5. (5 points) Let P(t) be the population in year t of a certain country (in thousands). The following table gives values of P(t) for certain years. Interpret and estimate the ' value of P’ (1970). t 1950 1900 1970 1980 1990 P(t) 123 121 125 128 130 The: get-at“? om L h P’( \Cf7G\ ES ‘H‘Q \$731+? 09 iAQﬁ‘C/T‘QS‘E 0C- ‘H’AE POFQ[@+€G¢A (\M HGUQGuCﬂS /yecm‘\ ‘M [CW0 \H a“ " m3 Eé M m \ Poo - 12g , ‘ . : 6M ._____.___.. . ? (”W03 tam t ._ Hm. We com 3€+ q reqsomabl-e esHMd—e \07 (Neal? {:- M'QS dose 4m H110 a; we Com 313+ 6‘? , M 119—417: . 2 oz 5? ((CW3) "’ 118046110 ° or 9mm 2: 111—115“ {Cleo—(C1910 Hawker oi: Wage {S meager-ELY ‘m thee We?” H19 56 04 be‘a'er’ \[Q‘i- @émeai? “1% We“. ﬁ’ﬂ‘t‘uﬂ it §_(0.3+o,ng; (535 : out Moi—e: as Em “ELL it’s {wages—+016? +0 E'é’[email protected]‘/Ifze when You‘re Male-{913 qm GS‘Q‘fM/jmgfg: (AA—13 01me Cut-1’41 VQQHY ERMA/k W0 3,4004de (1P3 esivqt (2:) 6. (10 points) Sketch the graph of a function f with all the following properties. 0 The domain of f is all of R except :c = —1. o f is continuous on its entire domain except a: = 4. o f is not diﬁerentiable at :1: = 2. o f has asymptotes 5:: = —1 and y = 2. o f is decreasing and concave up on (—00, ~—2). -o f isincreasing and concave down on (4, 00).” o f has an inﬂection point at (—2, 3). i i knew.” Cure MQWY PaSSEloiliN’iE’S. Here’s OWE ‘1 Notes on (2,63%me Mési-QQeS‘i a Is: [Ads +6 be (gee-{Mod} ai- ‘Kil’l ordse th ism“? EDQr-‘i‘ of; We domain _ \ @‘To \Acwe q kéritowi'd Q§YMP+E3+€ Laxil, ectbxw \CM §GC§21 0? [CM god-:2, Kano )(x—e “'00 7 " °' fat— I‘k'g me,“- QﬂOUjL‘ (‘3— K&—-Z 4Q ﬂax 'g’V-e' Q A“ {M‘GIQC‘l—fom PGaA‘i' IS wkewe fCGlﬁCQUi C, 0mg 5! VACA' or \Gch WKQXEMUM of MEniMUMt (325 q seed-Peg 1(in 7. (6 points) Match the graphs of the functions shown in (a)—(f) with the graphs of their derivatives in (A)~(F). You do not need to explain your answers. D (a) (b) , - (c) . (d) 8. (8 points) Let f (2;) 2 2f. (a) Calculate f’(a) using the limit deﬁnition of the derivative Z'W)QL+‘A ”1F ,___ 2 {CM lthLl/L“ ~t’ﬂhwm}: 3 (0L\: “LA/(:2 1A [Avac h @qu W) ._ [t m 1 2 m d; I l 15:; Mina-+14 1162? two 0‘1“" “a ,._ "Z 1,. _1_- ‘“ 3:152 13 5&3; Kid’s Emcawed- to; 0,0 ‘HNE [‘M SYMLDOI Segre you d6? OLC'R-LJQUY' GUM lumieoEPDP't‘I/le [(Md— (:9 whit" \‘PAE‘G‘Q are 5+3“ \AL: CLL'GUMQ} P 90:3 H“) ”WLS (FEM akgo hedges/1a (£1.34 3C (Cd’ ﬂ £13540. X—Q 1 ' (b) Using your answer to part (a), ﬁnd an equation of the tangent line to y“ .— f(.’12) Mx=4 WE [Me (31395 wreak ('11: E01“: ((1. L.” QM Ms: sex £(Ll\-— Jr?- 2; :12 ~ ~ ‘5'” : 41— (My \(5 VH4: WMS‘L’ML lime. 9. (20 points) Find the derivatives of each of the following functions. \$2 ‘.‘_ ‘2; _ ' (7.; 2- .” 714% EC x7“... Gav—2 " @033" g (m: A—x (m x- + 6 (KW ””"' q€x( 3M x '- Cos x) (d) ﬁt) = Atant + Btsint § ((6: A 560.1%: + . B mt fr ‘8 t cert,- 10. (5 points) Circle True or False for each of the following statements. You do not need ' to explain your answers. (a) True / False If f is differentiable on an open interval, then f is continuous on t at interval. 8‘66 WM€GFGW Ll OSIA ‘7, lél I (b)@ / False If f is one—to-one and 1 is in the range of f , then f ( f‘1(1))= 1. “Vim": Caz-Mes OliveCilY \QwiM We CQQQim-‘Hcm on f 5“ See, Wiscl ecroqifcms Li cm (c) True / If f is an even function, then g(m) = — f (9:) is an odd function. %€-x\ =-—§-C—— 2A :- *- E‘Cxl (Since 39 as em) ' ,, , ,, “-5 {Jim ,4 , S's, c5; ,, is, sexist/5,, mi 0&9- , ,, (d) @ / False If f is undeﬁned at m = a, then f cannot be continuous at \$:CL. See We dis: d\$§£b"\ HSN aCier- beﬁmyh,‘ \ GM P. ll? (e) True / False For any function f, f(a,b) = f(a)f(b). The, is- €0.ng ‘chﬁ‘ ﬁg twee/(s; V0F moi/leis, EC 962:5: Ml). 39919, :3 at“; looir some -: (61+ l\ ( bit-IS -: ab toil) H. 3639 We, S‘ec‘i-Covl “ enevwific/ i: CowaWlVe-z“ an the Leela {a 3 “COMM/1m err-Uri; "M umCDéWﬁa'dUQ‘ie - 3L Mathew/lair? rag 'f ...
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exam1pracBsol - 1(8 points The graph of y = f:c is given(a...

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