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Purdue MA 22300 - Lecture notes

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1MA 223 Even Answers31 and 1 60) )118()13(2 48))131(or )3(31 30) )23( 26))32(2 24) 123 22)93636 16) 81415 12)1.2Section 2422/12/13/13/12322222==++---+-+-+---xxxxxuuuuxxxzxzyxxxxxxx3434 )463 and 85 )44 2521 )342 32) 2521 30)larperpendicunot are lines ,61 and 2 are slopes 22)31 14) 6) 4) 2)1.4Section +==-=--==+-=-=xybmxyxxy- mbdc$12000/yr. d) $48000 c) section graph See b) 12000012000 )a 70) )[0, ),,1[ ,sectiongraph See 42)),3()3,1[ 34) ),1()1,( 24) 2)4( 0)2( 1)0( 2)2( 12)2.1Section +-=•••»•»-•====-nVgggghhxxxxxx21 44) 2)2( 34)10124 3 1x2 28) 423 34203 26)2.2Section 222-=++++++++]40,0[ ,40)( 60) yr 215in 28)$128,000 24) mg 118 )2020000 ,28000 d) 1000006)( c) 20)( b) 10000014)( a) 18) 6 1 16)2.3Section 2xxxAxxPxxRxxCbm-=--==+==-=2 0 76) )- (toexist not does ), (to 1 68) 1 are limitsboth 66)existnot do limits 64) 1 62) 4 60)existnot doeslimit 56) 21 34) exist not doeslimit 14)existnot doeslimit 8) 3 6) exist not doeslimit 4)2.4Section ••2 and 0at except continuous 70) 1at except continuous 60)1 and 3at except continuous 58) right) (from 3 left), (from 1 40) exist not doeslimit 6)2.5Section ====-=xx-xxxoard$200/surfb c) oard$100/surfb b) 30020 a) 34)ft/sec 2140 c) ft/sec 20.5 b) 820 a) 32)sectiongraph See c) 4341 b) )2(1 a) 26) 323 22)43 18) 54 16) 4- 12)2.6Section 2+---=--+-=+-=+xxyxxyxyxgadvertisinon $100000 isspent amount when ratefaster aat increasing dollars usand$46000/tho b) dollars usand$61000/tho a) 56)26 c) 24 27, b) 15123 a) 54) )27256,38( ),0,0( )4647163 44) 311316 42) 23 b) 1 a) 36)29)(' 34) 415)(' )3032320)(' 26) 44)(' 20))(' 14) 4)(' 10) 0)(' 2)3.1Section 22/342342/13/132/32++--+=+=--=++-=-+-=-=-===------ttxyxyxxxfxxxxfxxxxfxxxfuufrrrfxfp3million/yr $5.71 ,million/yr $17.04 ,million/yr 4.38$ 56) 0.024%/hr - 0%/hr, 0.096%/hr, b) )1()t-0.2(1 a) )50)21,1( and )21,1( 46) 1229 )442)1(' 32) )322(142)(' 26) )1(1)(' 20) )2(23)(' )16134)(' )1048108815)(' 8) )13(2)(' 6)3.2Section 22222222222342342+--+-==+++--=+-=+-=--+=--+=--=txyhxxxxxfuuufxxgxxxxfxxxxxfxxxf( )222256472422325222)8(1600 80)th$80000/mon- onth,$336,000/m c) 25950009)(' b) 92003202710)(' a) 78) 6)0(' 56))1(8 52) )23()35)(12(4)(' 42) )1()1(10)(' 34))21()1)(1126(2)(' 32) 122)(' )18)1(16)(' 16) 3216)(' 12) )1(3)(' 2)3.3Section ttrrxRtttrhxxdxdyttttgxxxfuuuuugxxxfxxxfttttfxxf+=+-=+-=-=+=+--=-+-=-++-=--=--=--=--=-0.0194 0.0024,- b) 6000002.0000004.0)(' C a) 16) $760 b) $750 a) 12)400)5000(' c) 80008.0)(' b) 80004.0)( a) 10) 5000)(' C b) 25000)(C a) 6)$138 $120, $114, b) $138.12 ,06.120$ ,114$ a) 4)3.4Section 222xxxRxxRxxxRxxxx--==+-=+-=-=+=40)8(,16)4(,0)0( e) 8)8('',4)4('',8)0('' d)8643)('' c) 0)8(',0)4(',0)0(' b) 8341)(' a) )34)1()3(2)('' )1(1)(' )18)14)(12(12)('' )12)(18()(' )14)1335(4)('' )145)(1()(' 10)3.5Section 22332222222322====-==+-====+-=+-=++-=--=--=-+-=+-+=hhhhhhttthhhhtttthuuuufuuufuuuguuugxxxxhxxxxhft/sec 3.75 60) sec/cm 1.6 cm/sec, 0.0064 a) 56)ft/sec 3.04 54) ft/sec 40.6 52)in/seccu 7.5 48) k tires/wee500- 42)ft/sec 14.18 40) )(2'' )363532 34) 16168' )26'18) )43()1(2' )162552' 14) 133' )12)1(1' b) )1(1' a) 4) 43' b) 43' a) 2)3.6Section 35333/22222yyxxyxyxyxyxyyxyxxyyyyxyxyyxyxyxyyy+-=-=+-+-=˜¯ˆÁËÊ-=--=++-=+-=--=--=-=-=3344/3cm 0.076 32) cm 270 )300056.36.81,41 24) 125.417,2 )2003315.0 c) 03333.0 b) 12 a) )182973.0 c) 3.0 b) )26( a) 16)3.7Section ±ª=ª==Dª+=-=D-ª-=-dxxdyxdxdyydyxdxdyydydxxdy54.1),4000( :decreasing ),4000,0( :increasing 74) )610,10( :minimum relative )66)8,3( :minimum relative )4,3(:maximum relative )64)44,2( :minimum relative )84,2( :maximum relative )60),2()0,( :increasing ),2,1()1,0( :decreasing )34)1,1( :increasing ),,1()1,( :decreasing )26),23()23,( :decreasing )24),1()0,1( increasing (0,1),,-1)(- :decreasing )22•----•»-•»-•»--••-»--••»-»•4.2(0,0) :minimum relative 68))24,2( :minimum relative ),24,2( :maximum relative 56) )847,43( :minimum relative )54)21,21( 44) ),2()2,( :downward concave )40)1,0( :downward concave ),,1()0,( :upward concave )26),( :downward concave 22) 12) )10---•»-••»-••-•cb4.3answersgraph See 56,54,52,44,342,2 : vertical,horizontal no 20) 2 : vertical,0 :horizontal )12 =-=-== xxxy4.4AM 30:11 56) 380)3( :maximum absolute 8)1( :minimum absolute )261)0(,1)3( :minimum absolute ,3)2(,3)1( :maximum absolute )20)5,4( :maximum absolute )4,1( :minimum absolute )16==-=-=-=-=-fggggg4.56mph 56.57 24) e trees/acr20 16)in. 10by in. 5 10) ft. 5by ft. 2by ft. 2 8) in. 3by in. 6by in. 6 6)in. 35by in. 335in.by 314 4) yd. sq. 750,000 A , yd. 1500 x yd. 500 )2 =5.1answersgraph See 32,281 26) 3,0 24) 3 )22 ===-= xxxx5.26620.33.03ln 42) 4931.54.09ln 40) 3311.037.2ln 36)answersgraph See 34) )1log(21log 22) 3ln )1822ª=ª=-ª-=+-tttxxzyx5.31.47698) to(1.47746higher isA investment 34) $15,000 28) yr. 2.8ely approximat 18)13.75% 12) $12,518,26 ,$37,518.26 10) $26,496.48 )25.40.021- 0.151, (b) 0.075 0.094, (a) 54) answersgraph see )48),2( :upward concave ),2,( :downward concave )38),2()0,( :decreasing )2,0( :increasing 36) 32 )34)4(9 22) 2 20) 2 4) 3 )22332)2/1(2•---••»-•+-=------eeyeexeeexxxxx5.5answersgraph See 64) kg 2.78ely approximatby increases )58)1067.3,5( :maximum absolute ),( :minimum absolute )56)23,( 54) ),( :decreasing ),0( :increasing )5012 14) 3 10) t10 6) 122 )432.32eeeeeexxx---•---+5.6mg 80 )8198,176$)6


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Purdue MA 22300 - Lecture notes

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