Review of Functions - Lt, 1.31 Lil] 1.5, La 8mm .0: m Tm;...

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Unformatted text preview: Lt, 1.31 Lil] 1.5, La 8mm .0: m Tm; FORUM» A = 'zrr‘z For: 7715 0:751? a): :9 cMcLE IS A RULE can'ch 19550049735 WIT” EBCH P0677105 REHL NUDBER I" EXfiCTL‘i om: omen NUDBEI? F)’ NfiI'IELy) THE MEI? or n CIRCLE OF mamas r, n REfiL-VflLUED FUNCTION 9f Q 3531. vegans ( 0k JUST Fumcnom Fol? SHORT) cow’s-rs 0F Two mmsg: u) A SET D 0F R891. NUDBERS CfiLLED THE Darwin) w.) n RULE wmcfi 935000155 mm EVERY 8513).. NUUBER x "u THE Donaw D EXDCTLY ONE HUNGER y craLLea "WE VALUE OF THE FUNCTION AT 7L. Tiff SET OF flu. VBLUES OF 7715 FUNCTION (5 cfiLLED ITS Rimes _ THE RULES flRE GENERfiLL)’ GWEN NHnES LIKE ptg, “'! F363". IF rm: Nana IS P, ms» ms VALUE 0; P m x :5 orrsm wmrmu ch) L "PoF at") 891195)? Wm)! : y : ch) SonE SPECIBL Fumcnmvs HfiVE NBflES RESERVED FOR THE”) E. 6., sm , cos, , In, 2.173).", swim)“, sons new»; or DESCRIBING FUNCTIONS : 1. FDRUULHS 1 l-x‘ 6.6., Pox) = IN THIS c1955 mt Donmm IS camstaauy THKEN TO BE THE NfiTURBL Donnw , 125., THE Lfificfisr 557 OF REHL munBERS x To wmcfl ms Fannum cam BE flPPuED To VI-xt GIVE Amman INS/9L Nansen. FOR ch) :- Th‘ls wouLD I36 u 1 4 )( 4 1.. EXCEPTMN: THE Foknum nfiy ARISE w Sane CONTEXT mm PLBCES FURTHER RESTRICTIONS am 1775 Donemv, E. c. , l ,4) IN :1an; PERFECT SENSE FoR r s o, BUT CUPCLES no war mews sucu R190”. A Few SPECML 01.19555; 0F Fumcnows DESCRIgsD By FDRDULBS : 5. PowEn FUNCTIONS : x """" ' 3. 3 x ’* (= (1/37) ) 3 43! L = 1/3 x ) -14 X xv v t I X“. .1; PoLYNanmLs : 5x + 3 xl-ax +1 6x3-7 8 ‘qu- §x3+7xl+ 5x -.2 l anx +q" x +---+qzx “1.x +a° RfiTIoNfiL FDNCTIo/vs : 5X * 3 ...__.._-— (011635 Fax) r-mo QCX) IM’E POLYMOUIBLS' V y: x" «I . GRHPHS c PHRHBDLF) ) fiLL FUNCTIONS HfiVE GRfiPHS’ E. 6., x Y , .L - x L ( HYPERBOLH ) X ETC, \ . on THE OTHER 079nm, Hwy cunuE IN THE xy-PLHNE “mar P195555 7'»: “ vEfiTlcm. LINE 72557 " DEFINES A FUNCTION wh‘OSE vBLUE HT 7: 15 m5 HEIGHT 0F me CURVE neouE (0R BELow) X , Y «no-c BHNGE u.--- t l O i I DOHBM) 3. GEOHETRICHLL)’ F0)? ExnnPLE , cas x an») 5:» x ME DEFINED By THE PICTURE (Cosx, Sm x) /;m ) '1 = 38C LENGTH ( cLOCk’MSE CIRCLE or: w; >5 RHDIDS 1 BBOUT m IF )C‘ O ) THE 08mm} f (50) / THEN THE REST: I sm - ._._.—— {max-.- x SECX' rosx COS X I cal’x= cosx CSCX= smx Sm X SODE SPECIBL VBLUES YOU DUST KNOW 3 1' I. I 11: x O a q .3 a. "- J— E. I: 51» X o A 1 3‘ I o E. ’37 .1. cos X I .1 .3: 1 a 4 $005 IDENTITIES you DUST gmaw : 2. cos x + sma‘x = I 2. I + hw‘x = 88:. x snle = RSINXCOSX 1. Z. casax=cosx—swx Coszx 1" sm‘x -.-. fu- cos-2x) HERE '5 ANOTHER (seemmmy coo, Bur vsny mponmmr ) GEonETmcaL way or DEFINING FUNCTIONS: SUPPOSE pm) >, 0 on) sane INTERVBL I mvo FIX $0115 a. no I. In. nus-udo-ooupcuh For: [my x W 1' DEFINE anal) UNDER y=pcx) PROD a To x , :F X b a. FLY.) : ~ muss uwosn y=flcx2 mm x Tea 1" X‘OL 3 5.6., n= y: Rx) = fix on) .7: = Logan) vwm 0L: 0 ‘ Y=FLXJ=-_{-x sPEcmL c955 : wE lulu. SEE LBTER “rm-)7 m5 “ PROPER " DEFImmom 0F ms NBTURfiL Losnmmn Fumcnom In x, Fm? x >0, IS As 7775 " ARE/9 Fumcnon" F0}; ch J = '5‘; on) cafe) wm-I a: l [9850 = In X X ALL OF THE "usum." PROPERTIES or we NBTU/ML Loam?!an c come» you nusr «mow ) cmv BE PROVED Fkon 'nm DEFINITION : Y y:’nx nu... x um) In (I) = O In Lab) : Ina. + Inb a . |n(-'-°- : “IQ.” In!) I" lnLa ) = rlna. H, fiPPLlCH TIONS 909an I A SOUP Conmmy wmv'rs TD DBNUFACTURE A Tm cm (N THE snaps OF A man czxcuLnR cyLwDER ( ) war 3 mm. How 500 an 0F SOUP, EXPRESS TII‘E MOUNT 01: TM) REQUIRED TO BUILD THE 019m 35 a FUNCTIoN 0F THE Ramos r OF THE CBN L nwo THINK 313007 77-h? PROBLEn 0F mema n 0001625 0F r' Th‘fiT wru. mMmtE THE finovm' 0F nHTEmFJL REQUIRED ). ll 1 l suns/9c: HPEI? )9 m MW 4- .2er B = .211'rz+ .2er h 6’00 voLunE : 500 = m3}, .1; I, = 7;;- 2, $00 Aer) = .211? +.21rr~(-——-w,_) I! THE any?” 0F 19m Looks RovcHLV ms rms A ' r \ THIS vfiLuE 0F 1‘ www Remake THE 1.59:7" 1900va OF TIN. WE («ALL Fwo rr LflTER. 5'. INVERSES fl FUNCTION P wmi 00mm) D IS smo 12: BE ONE-[q-oms om D n: ms GRfiPfl passes ms " Homzommz. LINE rssr ". 7 Y ONE — TO - ONE Ivor ONE-TD- ONE IF P (S ems-To-oms, mm we emu DEFINE mvomE/e FUNCTION, -' ; wmrrsro P awn CflLLED m5 mvERSE 0F P wHICH "umboss,' fl : 3 5.6., IF Pa) = X om (-°°,°°), WM F a) = Vx BECfiUSE .v 3 p(pLX)) '-' F (X3) : 1/ x3 z x. MIDPORTHNT EXBDPLE : PLX) : In x on; (o’eo) Y THERE IS IUD SIDPLE FORDULH FOR THE on INVERSE In 0F In J BUT IT my; 3 “,0; warns BNO B synom. (i-Jc'rumwJ Two synBoLS ) -I In :5 ammo T7125 EXPONENTIHL FUNCTION nmo n5 vmus 197‘ My x w (Juno) :5 meTEN exp (X) 0R x 8. amp»; 0F vaRsE FUNCTIONS fiRE 037‘me BY " BEFLECTWG 50 y:€x nanoss Th‘E Lwe y = x ' x SINCE lnx fin») e 1905 wususss, In): E =X , O<XLoo ln(e")=x -°°‘X<°° ’ THE PROPER'UES OF In x LISTED EBRUER mnwsmrc‘ mm Tms FfinILmR PROPERTIES OF THE EXPDNENTML FUNCTION ( L0Hch You HOST Imam) : [4 FUNCTIONS m1 13m:- mo'r amE-To—omE on “me”? ENTIRE Dormws OFTEN BEconE ONE-Ta—ONE wHEm THEIR Donmros HIRE RESTRICTED 50 mEy fiflVE INVERSES ON THESE RESTRICTED DODHINS, EXfinPLES : 3, y: smx am [—315] 4 y : 5w x = arcsw x on [1:] I! THE "moms ' no [-15 .E wHoSE same as X ( no 5mm? FORDULH FOR conPuTms Tms one ) H. y:cvs X on) [0,173 -l y = cos x = Arccosx on) i-UJJ - THE "mums" m [0,173 wHosE caSmE 13 x 5. y=¥n~x mo (—7"? III) 1.0:. -I y: 759“) Y =fircz'mo X 0N C'wam) = THE “31%;.ow (-51%) wHOSE 779N65NT '5 X (N0 smns Fonnum FDR ConPumua 771/5 one ) ONE on» Do sonETmNG 81mm)? FDR cor X , 55c x BM) c5c x BUT WE WILL HfivE PELHTIDEL)’ LITTLE USE FOR THESE ...
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This note was uploaded on 10/23/2011 for the course MATHEMATIC 221 taught by Professor Staff during the Fall '09 term at East West University, Chicago.

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Review of Functions - Lt, 1.31 Lil] 1.5, La 8mm .0: m Tm;...

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