AP Calculus BC-2006

# AP Calculus BC-2006 - APE Cal-31111.15 EC EDGE Scaring...

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Unformatted text preview: APE Cal-31111.15 EC EDGE Scaring ﬂuid-3111165 AP® eALeLILua at: aaaa aename GUIDELINES ﬂuentinn 1 let E be the ahaded1eginnhnunded hy' the graph nf J' = ha I and the line .t' = .1' — 1. La ahnttn abate. [:1] Find the area ef R. hne I‘.‘ = —3. :11] Find the 't'ehune nf the aehd generated when R is natated aheut the henznntal A r [e] Waite: hut dd net evaluate. an integral eatpreaaien that can he need In ﬁnd the f} t'nlunae ef the aehd generated when R 1a :‘ntated ahent the y-aana. 111(1'] = 1' —2 when .1: = “3.151159 m131-1619. LetE=EL1iE§9am1T = 3.14619 Area {213: [Lﬂfx] — [.t— 3]] ab: = 1.15149 1:1.ﬂ'regraﬂd “ 3411113115 [1:31:13sz . 1-‘n1ume=ri;['[Lu[x;.+3;E—[x—:+3f'] m: I ,;m1eg1-and = 34 193 D134 19': 111111115. {3135111111 and mam-H « :in'regmnd 1 : 11mm and cans'raﬂt net nALeULus ee sass senalas smneuaes Iillilestian 2 At an interneetinn in Themastille. Dregnn ears turn left at the rate Lit] = ISIIIJF-z-in; Irl |. 3 tars per hnur 250 ever The time interval 0 .r 10 hauls. The graph ef I'. = £[r'] is shaun ale-ave. {PEI I"Illa. |_' I] Ellll Tn the nearest vvhele munher. ﬁnd the rural number nf ears turning left at the interneetinn ever the time mterval 0 r 10 heurs. Ii'Ill Traffic engineers will enn-z-rrler ruin restrictie-ns “30 tvhen Bit) 2 1:70 per hear. Einrl all value-:- . . . .. . . -- an :3: .+ fnrtvhJ-th mt] e 1:0 and enmpute the verage value nf L ever this time interval. U _ Lntli-tate ums af measure. .l h 0 | 1 IE Traffic engineers will install a signal if there rs any tan—ham time interval tlurmg tvhrth the predutt cf the tntal munher nf tars truning left anti the tntal number ef tun-taming traveling straight thrnugh the intersectinn greater than 300.000. In every ttva-hnur time interval. 500 nnt nnnng tars travel straight threugh the interseetren. Does this intersectinn require a trafﬁc signal“? Explain the reasening that leads ta ynur tenelusinn. Ii : setup I ﬂJlE-‘n‘ﬁ': I' lib} = ' " : Huber-3:11 when I I'r" : average value integral : 111.151.1513 wnh 11.1.11T-‘_-. : I: ﬁnders 4EJ|C| : valid ﬁlter-.111 [.H. h + , .'.|+_' _. ._ 1 t [ Em m‘ .9.- : 111151.156 and explmuim ' ll be greater than 4IIIIU 2:11 that inten'al. :21:- auj; n:.'I:I-].1::n111' -'_-.1.I.1:I1'.11ren'a1 Elf _ : 111.151.15121'.audexplauatiaﬂ Tea. a trafﬁc -'.-.ig:1::1 is requn'ed. rJiluestinm 3 An :::b_|e::tn1:::1. 'g alnng a::ttt'..'e1n the: '-pl.ane at I: tin}: at time I: where .41' - r d: =1... - 1. . [11. -1' _ ' . [it 41.1:- [1 and : :I' r Ill. Attime r = the :::h_|e::t ia- at the paint [6. —3]. (Slate: tan—:3: = a:t':::::i.n.t::: {:a] Find the a::eele1'at:i-:-n 1:eetet' and the -'_-.pee::1-:-f'the :31:_ [le The I2111'-..'E' hat: a vertical tangent hne at -::-ne pnint. At ‘.=.-'hat tune r it: the :2: _ _, dennte the al-n-pe :::f' the line tangent tn the ::tt:'-:e at the pnint I: Jill-F? 1ntern1..:::f .r and use it tn evaluate lint talk-l. I I r I'I'I - [d] The graph :::f the I2111'-..'E' hat: a hertzeuzttal rapt-ate __t' = t". '5. an hnprnpel' integral that representa- thit. . tltte -f'. _I _ 1 :.aI:-:-n31-31'a11c:11 ‘- ' |_ 1 ::-3-peed m -' = [1.593 and == [1 when r = II 44' _ 1+:3 m I: I] = H.113 11m in I: : 3| = : integrain : limits : initial value cc-nsi-z-Ienr with 1-3-‘ﬂ.-'El'1:i.1rlit AP' :' CALCULUS EC 20156 SCORING GUIDELINES rJiluestian :1 vi : _| I: feet per -'.-1':I:.‘:'_'Ill-:1::| Recl-tet .--1 has FIE-51TH? t'elctcit': t-'[t] launched upward ft'ctnt an initial height cf El feet at tinte r = U SE The t'elu:ucit'_-..' c: f the 1'cu:l-:et recei'ded fei' -'.-.ele-:-ted values. cf t -:-'-.'E1' the inten'al U t ' ec:::n-:l-'.-.. aza- cn. 111a the table a t__a__| Find the at'et'ag celeraticn -:-f1't'.:-:‘1:Et.-l -::-'..'er the time intert‘al [2| ‘ lmlicate units. at" measure. . TI) {13) Using ceﬂ'ect explain the meaning cut" llr| eff] [-1,- :i_1_1 net-mg EIfthE- rackets. ﬁght. Ute a mdpmur Riemann thin with submten‘alt. cf equal length tc- apprex i.1.t:Iate [1; Hit) tit. end per tecamd. At tinte- t = 0 recent. the initial hetgh cf the 1'cu:l-:et " "I feet, ' ' ' - -' - 7' feet per sec-end. Which cf the t1.‘.'-::- incl-Lets i‘: trace-hag 1' at tune I = ED -'_-ecc:n '.-5' Explain j.-'I:Itti' ﬂJl-E-‘ﬂ 1'. I 31131.1’61' : EKplﬂJlﬁTi-"I Rie 111m 311m 1-' '. + 1-14 21+ ' + + 44] = ' 1.1::1it1::: :1 : ﬁll-13134} :nmpmea 1:2: 1-42.30}, and drau- r: L :2: :1-.-]11.-3il:::1 : in :31) and [13} AP' :' CALCULUS BC 29135 SCORING GUIDELINES Questian 5 LTI:I:1-'.-.1I:1er the ehﬁiﬂeunal etpjatmu — = in" — — . t-z-r _1' at Let L]! = _.I' l_.‘l.'_ll be the particular -'.-.-::-lut1:::ﬂ ten l' . -:1:iﬂ‘e1‘eut:iale-;1uati::lﬂwith the initial eaﬂdﬂmu fl 1] = —-4. and '57" at [—1: —-'1]. II'I. . . aﬁ' {ale Evaluate {111 la it pl'laaible fer the .‘J.'-'£1..1.'.i-'.- tc: be tauge at t-:- the graph-31‘3" at acme paint? Explain why :31' why n-a-t. Find the wanna-degree Taylet pI:Ilj.-':1-:!-mial :7 __ abmtt .:r: = —l. {d} L'ae Eulefa metll . matting at .1. = —l with 11.1.. L: -'.-.tep=_. of equal seize: t-a a}.1p:'-:-.1::i1m1te _.I'"[|I|]. She-1.15 the war]: that leads t-:I j_-'-:-1.u'aua1a=er. _!1:\$=Um1d 1-:0 '--=1 (11' ' I_ 1 : .- 31.1:5-1' and explauancm . . _ _. ., I. ._ 1- _ I it] Flag] = —-1-+ E‘I_.i'.'+ 1J — 3|}: + 1}" I _ | 1 : quadrant and centered at .:r: = —1 L ' L 1 :-:-I:Ieﬂ‘i-:-ient=_. . . _|- 1 :Eulei’s meme-:1 with 7' “5'15"” L ' I"__ 1 :Euler's apprtlximariclntc: __ AP'E' CALCULUS 5-: zone SCORING GUIDELINES Question 5 The ﬁlﬂetienn _.I'" deﬁle-:1 by The FIG-1.1.7121 -'_-.e:'ie:-3 far all real number-2. .:r: ‘::I:' which The series. :: -.-_ _; L_i -. 5'-"-"1 3+4! EH + far all real number-2 'whj-eh The sene‘: I:-:-1:I1.'E'I'gee. {3] Find The lure: . 1] wet =.~e1‘1e=.~ fi::1' r" Jueriff-r' ‘fnur 311-1 ' {hj The graph elf I‘ll = ._ '- _.-' 2 Thrc-ugh the paint {'1}. —1]. Fin-:1 1-"'[|I|] and __1""I"U"I. I}ete1'nJ.1'hev.'herhe1'_]-' a relative nunimuu; a felam'e maximum, at neither at 1' = El. Gite a tea-243:1 f::nrj_.r::n_u'.aue1.1.'er. : eete up :‘atie : -:-I:I1.up11te-'_-. limit C-ffﬂtiﬂ : identiﬁer;- radius ‘ '16:": alien-:11. ' I-ﬂﬂ-ﬂi} ' ' I:h.1t31i'_'lﬂf:E-I' hath Eﬂdpﬂlﬂt‘: When J: = —1. the =.«e1'1e-'_-. 15 + % + 3 + - -- _' é- Tlti e: 1::ew:.a1.t£~e the limit -:-f the ind: .. :dual term; is nut 21:1.1 Thu-2.: the lﬂtEﬂ'ﬂl ef I:-::-1J'-.'ei'genee 1:: —1 c: .t' : -:-I:I:1-:111-'.-.1v::u : Since __t-' LEI] = [II and __1 ' __1' 1.1.1:. a relative at .t' = U. ...
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