(Oa Ne UE CoG i Corag Gamay CALCULUS) (F Ora 'UNCTIONS) qos (Functions) ? ayer, x0 y AR HC WEES ge TERETE AIT CH, Ta xe SOS AICAS SY ye TES eS AT Ne ret y BM XT SAB SATE aot y = fx), ORICA yn BR xa TCT Boia PrSaAher eaita Ba (dependent variable) <4 x-ce 8 bat (inde- nt variable) 311 21 aya $ A OH, x Soy GAA ates Det, y = f(x) = x3 + oy — dk As AC TA a | TART, 34 3x2 + 2x — 4 BT oe COE SH xt aft Tt EA y = f(x)-6 Ge ARPS 9 area AA seat BAT [Raya i432 421 -4=2,x=2 eyed 4 = 20 Fen) | acerca, x aA ve a y GEA BAT! al aE, OC FANG CH woo Lx Zoo OA St AAT 1 ata Ugyel @ etd 7a (Domain of finition and Range) ¢ = f(x) Ca area rote aa, Sed xs IAA Bera oe ARCATA SGT ET ied Gar y at frSaAe veraiha WA eA TT Sara 2 HT coll g By ues (Even and Odd Functions)? coereeeas ym acta AA BI, TAF M(x) = fx) BARK Abeer erceree emt eT, UAH M(—x) = — f(x) BL Fe care UTE (Explicit and Implicit tions) ares uf wa Bet a feria “sera oreM 3 erepe eeeee ET BL GIy = f(x) = 2x? — errata, seorreee UA aA cera a Roa ores CHa] ARIS, OLA UI ACATE GUEST TT! GRR —ax? + Qhxy + by? = 0. GAN y-GE xg ca SUT ma 1.5 *tffrge wees (Periodic Functions) ¢ mm ge ACT Yee ALT AR fx + m) = £0) BA fhe) ea ona qTS See ae m-Ce oHiNTS ETerECER AAT (period) ‘at SAI GAR— ssin (x + 2n) = sinx ; ABAR sinx Ge oniaqe carota a ea HBT PART 21 1.6 BLISTER PHAITASS testa (Parametric form of A Functions) & caren crete TAA GAA Bow va aft GE aa ve weer Ria Sere eH, Old CoH CR FER SEM OR ‘sptatcatt eats (Parametric form) <1 A Wat, TOA va x 6 GAA OF y, Bea Ge Ge vat GF TORE ; SAE x =H) GR y = (HI GB AHR y = (00) SOMA HAAS STATA! SE var -Ge sbtatfeore (Param- eter) i Lar itera ay to.g A (B) 3 (a) -1 2413. oR (=> “ Ercan] @ Leg eF OO) {feet Co SL ay rast: 00) HY? Ler a?) 1 gg er EEA CH ATH SEN a 1G) =F wer (c) aioe eo wT worm: + (x)= 087 t(-x)= log = fog(1~x)-log(1+%) e-fun(ien}-testt=x)) =-lontZ2 (tx) -talt- xd} slong =~ 1981) ceeelt Feo Ans. (8) 1 - SE TH my, (0) 4 veel EO, ore FCT CF ART E (00 eee ia oe! pox afer r or ges) Fg OT! (0) 1 sx 2 ret ee mE RST a pyar cz errs, 1S * SAM ae w <2 Ans. (0) afin) + 1 St. (ARTE ( feat Om pea ins = 2m! =fn+D , t naa aCe Ge A 2osin 3x y -+ Ww $s¥s1@) 52» cava 1S sind SEACH AAS sin 4S pel W142 2-sin I-42 Ans. (8) ° et MIEN BENE eB es (8) Sus eee (Sot eae (0) cerca ax = wor i- panty ae (0 fogs Ree CE ae ® e (©) loge (O) log,* fig) = x2 — bh] SOR A yas sore ows 8) (8) Sa cers (0) corer ara i (y) = SS H AUEO) = wt @+ @2 OF x 1 opatl Brent avee s)+4(4) aa aR (Ay3 (8)2 (cyt (DK)0 f(x)=log(x+ Vx +1) eres xa (A) Sas eer (B) at Sores (C) (A) Bear ®) (0) corearta aa (x)= 222, (2 a fx + 9) + fhe y se W)2foty) (B) F f(x) (2) f2p08 BR eee footy) (C) Pa (0) xy) royer(4) BH aR 1G) = 28 TTA x Wes Bos OSD (x)= a, exe Ft(toon] wo x O~x oO ie 1 20, (a) Sos G4) sDeceweta fois enews ea 1 ) 5 8. om) 2 Hf 26¢(x)-3. (t}-¥ Or x 60-0, OR (VER ER x nw ws @-j; or Mf , F(x) =log(x-+ Ve? +1) exe wa was ey sae (c) entra (0) ceranta ani 0 may Rg GAS of; wn oftshuree nT TE ERYD EL ANGE Tak aay CONTR y = firgeen ART aa x= OR ay HA soere Ba Gh (y= 2x45 B)y = 348 (C)y=aned Oa eys3 af orca Rngeera gH Tr x OAR er comTUN A Rofo 5A AGT SOE SET STAT wa-Be (@) A=> oa-Be Mas 20 Rm aie Ganera wARee x Sm Set ATH Set UR CREE y THAT IM y-ce ak SONS Sort al (A) y = 4x? — 80x (C) y = 4x? + 20 XSGH WSS AAR CY TET f(x) = 3 + 2x — OT RS oF ws es (C) caren qxea a GR (0) corona ani fx) = log, sR G(x) = x2 RT (4(3) ) 01 aR we @3 9 (0) caren au af f(x)= log a, a = + sat wa wet (A) to) (8) 2%) (©) -2F)_— (0) 3) . UF fla + b) = fla) + Mb) RCRA fix) eB — (8) era eres (8) ya sores (0) sea (0) corcaft = afi (x)= xed BH, IIT [f(x)] 98 FR “ 4(x’)31(4) (8) fw) +200 © e(w)or{2) (0) cerca =H(A) 35 3a 23 OF ox OF 3H 604) = wt rah) = log-sinx seat W(x)" = tog cost OS 20) ae at 1 We @)0 @-1 oF 7A) 15.8) , 200) 2340) 14) 248) 3a) aay 5:0) OY (8) 10(8) 1148) 1246) 1914) 174A) 18(8) 19.(A) 204A) 21.0) 2. Hf y = log, =f) x=ty) x=er=f71Q) fluo =e" ade *(#+4)-( gan fx) <=? 8.0) 16:8) et ve (ar) - ble ae wre) cae ail 2) bar) “ p72 © oe wet extmayeny ABs pene) ryex)=toa(-x + 4148?) Jes VEH +) & (=x) ==log( THF +x) = =F(x) ihe) —f00) TEAR, Fe eS ery ee 16. 342x- x2 =342x-8-141 2341-8 - 2x4) =4-G-1F (x=? GR err Cet RT POR A WR (x — 1) aA AT EA (x = Daa eRe ST Gx 18) 2 SereraBa qZEN aR = 4-0=4 ‘Ans. (B) 1. 9G)= ; £{6(3)} =f (9) = tog, 9 = log, 3* =2 log,3=2 ‘Ans. (A) 1 20, = F(x)=xtE f(w)=” +s ones, [£00] -(x+4} =x adaaedl x4) sfx +4) =f e}s3(4) ~ Aw 22. sin(3x + 2a) = sin 3x TET sin 3x8 ates econ onfareart 2 73, eB 4 cE) = PPE logsn? x 4, glogcoss = eles el intx + cos*x = 1