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AP Calculus BC 2007 - Copy

# AP Calculus BC 2007 - Copy - AP“ Calculus BC 20f Scaring...

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Unformatted text preview: AP“ Calculus BC 20f}? Scaring Guidelines Quinlan 1 Let R hethe regionihtheﬁret end eeeend quadteuts hemdedahneehy the glephef y = i”, and l + I" helew h]; the haimmal line 1; = l (3} Find the area nf R. [h] Find the ernllme efﬂ'e euhd generated when R iereteted eheut the I-eeie. {e} The regieu R is he hue efe enhd. Fer this. solid, the ewe; eeetime papemhnﬂar tn 1h: .e-eeie are eeniehelee. Find the erehzme ef 1111's eelid. 13:2 =2whu1x=i3 1:1:cnectlinﬁtsinaninmgralin {a}: {b}: M {E} 2!] 1+1?“ Am .1 — 1] til." = 31951 at 31952 Quinlan 2 Themmmtﬂfnatainaﬂmgemuhingaﬂomismudelad hyawminunmﬁmctimnnthetinimuwl (1515?, when: tismmmaﬂinhnmslnttﬂsmudelﬁtesmagivm asfullnm: [1} Ihemteatwlﬂthmtermmetmkis m}: 1013mm galkmperhmnfurﬂits T. (i1) mmmmmmmmg Emma r: galluns hum. 3” {Mixing 1’” m...“ Thegmphmffandgmhiﬂintmﬂat I‘=1.ﬁ1?|| and t: 5.9%, areshuminﬂnaﬁgmeabnveﬁt time I =ﬂ, mammﬂfwﬂﬂmtehnkisﬁﬂmm {a} Huwmmygaﬂmsufmtﬂmterﬂetankdmiuglheﬁnmiutmml HEM T? andymranswertn tenemastgalku fa} Fnrﬂits T, mummdmmgmmmﬁmmmmmm Gitrearaasnnfuraachanswar. {c} Fm [ISIS T, atwhattime fistheammﬂnfwatﬂmthehnkgeatesﬂhttemstgaﬂm, mnputethemﬂnfmtﬂatﬁnisﬁnmlmﬁfywamwu (3)1: mar SEE-Elgaﬂum (In) Themmtufmterinttetankisdmuﬂngmite internals DEtSLﬁlT mdSEfEiﬂTﬁ Ila-cause ﬂi}ig{£}fﬂtﬂ5hﬁl.ﬁl? andhtﬁma lit} Simf{t}-g{ﬂchmwsignﬁnmwﬁtiwtmgaﬁw mly‘at if: 3, ﬁnnmﬁuhtafmtheahmlutemaﬂnnmam at 1: 11,3, and? “— . 5mm} j—ﬂﬂm 25:43]: 31215591 5125.591+I L ﬁrm—211mm}: 4513.30? Themtufmterinttetankisgmﬂtestaﬂhmﬁt ﬁlatﬁnJheammmmfwatﬂinﬁmtankmmdaimﬁm mat gallon, is 511? galluns. Liningmnd l:mmmlcrfwatﬂatt=3 Lajmmﬂcrfwatuath?’ 1::011chmim {human 3 Thegmphsﬂfﬂlepularcmresr=laudr=3+lmsﬂ meshuwnin meﬁgumabummmmmma=1§mda=% {a} Let R mmmmgmmmdn 1 atﬂalsuinside ﬁ1egmphufr=3+2msﬂ asshadaﬂintteﬁgmeabmreﬁndﬁle maﬂfﬂ {b} Apmﬁclemﬁngwﬂhnmzmvelmityalmgﬁmpulmmgivm by r= 3+ 2cm? haspusitim [:{r},;{:}} attime I, ma =9 whenf=ﬂ. Thisparticlemmsalungtheummmthat£=£. d! dfi Fiudthevﬂnenf\$ atfi =§mﬂintu1ntwamweriutenmnfthenmﬁwafthepmﬁda (11} Fmthepmﬁdedmihedmpmm}, % =%. Findﬁmvalmnfg 3H3 =%1ndin1&prﬂjrnm amwuiutmmnfthenmﬁunﬂfthepﬂﬁde. 4 3 . (3} Am; =%g{2f +%I2:3[3+Emsﬁ]1 da 1 :amanfmtnlarsectc: -lﬂ37ﬂ lintegralfmmﬁmnflinngnn ' - Limegml l:lim1tsandmtan1 | = d” 5:113 ‘13 5:;le {h} % = —1.?32 Thpmﬁcleismuingcluﬂtuﬁmuﬂgﬁsmm —~f.ﬂ andrbﬂwtmﬁ=i (a) y=rsinﬂ={3+3mﬂ]sinﬂ lzexprasimﬁxyintﬂnmnfﬂ iv = 4‘ = 'U' 5 Elﬁaﬂ 5'9 5:115 Thparﬁcleismﬁngmyﬂnmttex—aﬂs, sinne E J mbﬂandylbﬂwhenﬂ 3. ﬂunettnn 4 Let fhe the ﬁnretinn deﬁned fer r ‘n t], with He} = E and I”, the ﬁretderiratitre nfj; giaenhjr f L1") = fine: (a) 1Write an equatim fer the line tangent tn the Jgraph at f at the pnint. (e, l]. (la) la the graph nf f enneatre up nr enneatre linen en the interval 1 a r e: 3 it Give a retreat fer j'ﬂttt' arewer. [e] The entidifferentiatien tn ﬁnd ﬁr]. [at rte} = at a . t1 : ftet :— . L 1 : erInntinn nf tangent. line An nquntinn fer the line mgr]! tn the graph nf f at the paint Le, a} e y —e = 214;“:— e]. {h} j“{x} = I + 2x111 I. Furlixii xbﬂandlnxbﬂ,snf'[x}}ﬂ.1hm, ﬁlegraphuffismwupunﬂj}- smuef{a]=2, 2=%—%+cmC=2—%E. Thus,f[1'}= 1—;hx—éxj + 2 —%e3_ f ﬂ-IIIﬂI 5111 5.? 2.11 1.2 11.5 WWW“) lull“. 1‘11511111111115515 Whamhﬂnmmmmmmdehhﬂnmmhutﬂ 111515111115511115 haﬂmmfeetﬁmdﬂedhyamrim-diﬂ‘ﬂmﬁableﬁmcﬁm rafting 11511515 115111555111111111111111111155. F111: (11:15:12 ﬁ15g15ph51r155-5115555111111rn.Ihetableahuwgimmlectedwluaufthemteofuhﬂge, 131:1}. ufttemdhmnfﬂaehaﬂnmwertheﬁmimmral 115 1511 "115115111115 11111511151111111115311111511511511 f=5.[Tv11115:T115155111111511f55p11m11115111m r15g11re11hjr 1": gin-3.} [5} E511111515’d1515111115 1111151115111151111111:51511= 5.4 115111g11151511gmt|1|155p1111151111511m511 =5. 1531:1111 Hﬁmtegrmtﬂﬁnnmmthmthemm16ﬁmarﬂ5mfmymrm. [h] Findthemtwfchangenfthewlmmnfthghaﬂummthmpeﬂtuﬁmwhent =5.In111:51:5111111511f 11155511115. [5} 1.155 aﬂghtﬁmmmmnndmmﬁwmhmmmhmﬁumﬂbfﬁmlhhmthehbkmappmm 1:11:11] :5. 1.15111gm115511111115, mphinthenmminguf 1:55} 5: 51555551551515.55me 11511111111. [11] hymappruﬁmaﬂnninparﬂc]greaterthanurlmttunllfr'ﬂldt? Ghmareunnfurymranmer. [3} £15.11] w r{5] + r’[5]ﬂf = 30+ BEL-1} = EELS ﬂ; Simethegmphnf r ismnmrednwnnnthninmml 5:: Hi4, thisesﬁnnteisgmaterthan r{5.4]. w \$3M aﬂlir = min}: 2 = um: ﬁ‘fmin d: r=5 {c} Kimmi-2{4_u}+3[2_u]+2{1_2]+4{ﬂ_ﬁ}+1{u_5] 2:{1:appmjmﬁm = 19.3 ft 1 WW“ II In r’{t}dtisthectungiuﬁ1eradius,infeet,ﬁtm 1: ﬂ tnt=12 ﬂljﬂlltES. [:1] Sim: riscnnmreduwn, r’isdmnmingmﬂﬂfill Whawmﬂm, 19.3mislessttﬂn j 51:} at. Mufﬁn inpmtfbhudﬂiupaﬂc} l:1m1tsin(h}and(c} mm theﬁminngivenhjr ﬁx] = 2-11. (1} Wﬁteﬁleﬁmﬁmrnmtﬂmanﬂﬂemﬂtumﬂfte Taylnraeriesfurfahum I =ﬂ. I—E—HIJ 4 {h} Useynmanswertnpartﬁﬁnﬁnd Iim HI] I (E}Wﬁ1eﬁ1eﬁmﬁmrnmtﬂmnflheTayhsuimfmfra"ldt ahmt 1' =1]. Uaeﬁleﬁrstmru _ 1:141 temuﬂfjwamwertuﬁhnutejlﬂ 3 d1. 11': 42 (a) mmmmrmmmqmmmmmmjﬂ a drhylﬁsthan i am [- INN-1”] +-I{ "‘j=l+—! + 4 1.1” lnr+2 3! 2t Ii 5 Usingtheﬁrsttwntamnfthisseriamesﬁmmat I'ﬂe-W-ILJIAJJ n E 3 E 14' 1f 1 =TﬂT-um [all mm 1' -Eﬂ_1_1‘{[%] in { 11"[1 ]2n+1 ”'1 41 W ' f L. E blimi Hieswithindhddlmltemsttntdeﬂminabmhtewlne tuﬂ. whichisanaltamﬁng ...
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AP Calculus BC 2007 - Copy - AP“ Calculus BC 20f Scaring...

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