Partial preview of the text
Download Differentiation topics and more Cheat Sheet Mathematics in PDF only on Docsity!
& oare_O2, OL 23 PAGE. a) ‘a / } xe. Maths 1 i \ Differentiation Exonetse 1 Sotuition( kovision) SP.20].M-201M.2a]5. 20 | 5-229 |W-.20 W-22[M-21|M.a3|¢. af | S-23|W-21 suresh. Goel CEeronor Dirnelar) Alkcanc add. Scbet, Natale, Delhi. VCR INDIA. (+91 9810444 304) Scanned with CamScanner CD) ethatiin tatn — —f tap sil ay. prsucihs % volun 4 f97 enn A poiul: moved along Uhis curve, nia | pasecs A, thy 2%- sscdlinele ds dncreasiong ak. a Atle of 0:15 unit pox serods anol eialieels | am Se eT hl rate ht dciere | Saad d= sy ipa (398) tf ees Oe y= a(-Il3-3aF Pea) | +h 2 Hp ae Wee ay [3-22 “ha Gat | -an)=7 5 3-anek2 | HON H= 30 AE xannpld. re. feloay oil — Ale B $)-CUS, HES) DLN BFI aA L(Y 9) if chapels Ae ael A | BE BE CE DE ‘LP 4 3 = | ERETET] 10) | tone he le bs theo te, podick geeadon Li — W|Shi tal Be valine ta He lilshe sidieale ebb Me valas 9: fai Sebel _ Setudinta) Greduk? cl = F278 4s it Ge zk a-hs “Gudiok J DE=1-0H a7 S| F oe PF 7 ! DD Xa, Grebatai=g | > P79) = nN $4 (a) = 2 q | | | i 1 Scanned with CamScanner i iit spammed a ~ A curve ds duck Lat dix 6 uel A1,=3) biodta, te Curve A point bo (31-4) PBA along te Lune. ud _at A, the y= coocdlinele oy te poi ts cncreasloy ab | if 3 Linidk pea docerd, Evind. fhe Aol af iaedenao. they th a= tadinah: of the Berit 7 =--[3) , : (7-221/12 [Q6(a/ AM -3) (ra) Mt GS Lbet)--O 2 Hos Z dy = dy ee =o TS Gasp 7 [fomOad@) Scanned with CamScanner Ea Se A (a) 719) The. di dasad ” = bin! ye 9 [62 a 4 ; ms 4 % fue fet 4% Phe tune CAtvan X- Gt ak Ke pink A. / Fail Lhe. x- torino 2h. ey) Eid Me ojualion op be iargoul le curve 2 A --L4) 19-21/ 18/47, Solubi ae j= Ue yx?) --D | Aare sulordeclsX- aris => feo S | = 9 (i %— yxe)eo > 9x4[ 1- yx leo Nh, [- Y= BUHL 2. Curve silindock Xeaoue al J yoy (b) apQ dy = 9[-4i b3)i*] asx oe +g1 = rh Pol sela 9 (ty) (Wh) vel > 4l 2 2 Gu y te Lingett fheturve at Al%0) “ye “0-4 (4-4) = yo depend ae Facog tilioary posik maximum) dima d=0 PO = © *[- 47h Jeo =a es 2 aes ot= [2 — Scanned with CamScanner 574 at¢companion - ‘ie eis Bi aaa. oa fi curve, errerg aul a. porist A 2m Furd Me n- a eh ey by _pshick Me en a3 Level owls indent Nae 7 are BS ; [p-23] 283] _ Sulign TS Cu) aan Ory . a 6 And [B244)%3: ‘ (3an)--D = gp ayg-t> dat f iE (satya) fon D_ =F = oa tlalocs 2 Bi : 0. ae acusve, i. Ue ooadien Ao. Cupye 1B %, ae deg n thal d= 26 ak, he. Ab rp" : _ __(B_ Sk had bal kaa" (b) Fd an epialin gf Lhe carve, _LiJel¢). ahs aa =p $tk= =2 9 Posirtsa larm el ser: © ra Beh Degatn df Rationiyfece BMAelermine Le nabite,_— =a FE a ® Soadiet- eb ly) b= = 4 bpej pra) A 7 i i we QR ANE C fart esth roth (f,-j) = ~]=Alp-ary +€ | ae kong £354+f) Li- SRL 707 (©) frrskelimery poiats di — 9 — forO & -4% =e — -2 jugs Buses 9 at fon ted lf — 24 432% L, Slilin hoist C: 42 34). 27 an +0 = I-26 = o=3- frm @ byalin y the C1 WageD. a, ae. Se Pier $i)" ‘Beco tn Mowniin ab Cf 4 my Cuneo, Y¥ =alK—Qat3 aoe a Scanned with CamScanner Le) at L429) fm @ = 24 [a-2nh ) = 48 >: Oo, —|dff_dy = alo-aayae: (2) kay = —6(3-2x)*4ay ——@ Gee < Mtb to = 24 /3-2x%) — (3-ax). tea) | aadetladscas T =-48 <0", fo Shikimary point Ly = a MOK sn Ar@ > —6(3- nSf2y 20 Ge (3-2xJb4> 3-2t2 | => 224 wte Te « Lekiransyporb (4, 20), (24959). | pump The. value y¢ Ae Lallain. 1s tnereesing ab 2 tondleul:2 | 600 Cob foo Setend., Tho baleen. Se eer ere TT ae a ES NT TRE AE wrt? a7 el Lai bie sale of sracrence.uf th aaclins. fic T0-sccodls rasunds ES) [sz oO) 3 ue pala) Valine. of in Seemds = 6oaX30 = 1800 tn? | Ve 247= ovo BGDAZ = 4 29F. + eee Az Sn ase 2 Ab:3.Gy ve 225 db Ta 4 a anaes tans > dg. dv go ‘dv 600 a aL. = Dyke. Rte ce ere (23) as wn ONIBK orm Fins NS (tha ten as7 a 6a) . Scanned with CamScanner _____|arrve sith lal the Leie’ 0h, pthore Ar the moatimum |_/ | poiuk on Me curve, The tsordink i De ry, ere re ee = poiut: at (0, eee dud b en Fa Pa Wa He apare Bae | Sf $20 @halS |e yr Skno tet b2 30. Lee _ Setulion; 9= 2 3— abatsen x : an aY = 3x bathe fe dian 20 Ybytsn—o a £3%-b)(2-b)=0 > X24 wh : | ey G28 —> b=39~ Scanned with CamScanner ae (1 16|| 7 Lpualings a Curve is Y= IJ3x%+4—-X (BD Lui Meo5,9 Lien of Me npcoral b lhe curve at Ls print [4,4) Pip four Quast inl dam Y= mu+e, -~{5] (23 1 Me corn lis +2 fe sbellinarey Porisde --L3)_- (c) beh ee --[2] eid [8-21] 1/811] : la) j= 9 [3x - 2% —-@) W for Abilinany paisl Oy 0 _ fuel fam) 3 2 2Saxty Vay . a ee oe ea ee Ge axty = S3xry 23> 3aty =F GA. = Seah nd ne ae haa; 74% é i O Tease [2B & Grediaty Norm oF (44) = 4. 1 Sblimbouut (Shs 4) + Gustin Lhe normal of lth, (C)_cdif 8) da 4 =bla-y)> f= Y=" Hes “x ed ps (axayy 7 eae (a2 (Btn 3,=-F He SO ty - i, a Scanned with CamScanner a ry ‘ON a | 18,1 Ze. fuaclion fis afiiel by f= bce!) an fel Hed Sti L a ing fue Lee Fgh Fhe sranionue possible values fk tenrtiuk O,___-= S-3f/ 13] 49 bing: Hx) = 4 [2a- 202 fe 4 And x2 by 2 : = (aa-r=2 y for_ fla) ta_b2_clochoadsiiy. Las => (2K-))"= LEo > 2yx-) <2 => ar-/< 4 =5. HSS, Max value x de Sp He as Av —_—_ a | i ae _ 14. Hz chagvam. abgit feat f fe curve yo watKe x 2 ath eguition px 282 K ae bsherek js 1 a Josie aes, | G@ Ceol Ms. cmd nales ¢ te mruvenicnuen. posit | v +! bxans_o¢_k exufg) 9 ake The. biel ab fib a Me be aati, — | | Lrlbodocts Lo y- ani at-, Fiul the \-Cesedlioml of P tn lovond ot k, ---l4] (Ch_on next fage—> a iS : da recat <=) b) bok 2 = Ue OP ay yxh Px @) PO Be (aS ut © te diliney poe ite = (fer fide fe = if = ade om Je Coa aer tg Pe i mh Ses Se pihe sybknrg! [48 5) 2 Kia/34- x Laefo) Ye Sf = ZT *- 7] from Dat a-K, fe (ee ep nyd Y= SK +B k(4-Yk?] = &k fev uslirsacin isith ye ana, | oe Minimum pout (K% 21) ab P tut x=0 a Z : Y= Sk ABE (4k) (Fark Conkinusol On tonk loge] d= ie | Tae dal Scanned with CamScanner zee is bundled by He Curve, he xe eves ok te Urad =] RE At es 24 ra iB morKy y= ot ae phere Kb a positive in a | Come bial --[g} eo Fail Haron ofthe Shaded dy Aapteo oh linms stk, ———— | VEEN ITO! 2 —— Dy = (yde = 1 I =f (ee Day OPT Pet sk ae | Pe One yy yy k | = l $% path [9.42 =f 88kr 4 Ke aK) — fay PRI 2k k) i. - v Ka .& Lf l | | = 49 By Zi Scanned with CamScanner Dat ad. The. cpunlion of & cube ds Y= B01 41324) fear > Ys (65) Lurol A tudo =f 27 (bJ} Euial Bs Prcud inn 2 fo bhilgnazy| bai bee fe CALC. Auth. dlkixrnine tts nalyrr -- [4] 75-251 72199] Aver f= 3rr/— 4(3x+1)--) [0 fo Abana po dy =0 HO an acdxd (aati a pone. pb = Be = 3-6 (24a OI" Vat) Left) dls =bxj HE P| > 3= Seg Pl 334) = 2 Ws 2) Dl gar/=4 > x21 (2h > | forD _y=4-4xa=-4 1 Sli Lonany point (4-4) Nad tach th naleto ¢ dbibinart pond (tg-4)7 fo @ [A¥) = 9 S00 sminmumr IE eae CGPI XAT DE aa th, The diayatan basi the ~" ye wilh us) cule f= 2412, The Line ena, fy 5 sis lisesccle Lo_cusye et dbo E Dasids ALLE) Lull Bl b5) fe ee, 2x. Fucd Lhe 2protin p Lie Longest Ol ke Ko tubye. ot the paid A --L4] _ [§-9(737Q3/ Subd: Ls go O+4 x --@ oA fferesbiadeagD rta: y= LiS tinkd) 7 (ee) AAT 2 Le 8 Wa Ne (Ohta) Op Sm 34 tale Qoodlieal op Lhe Qugetatp 2 Gyyadiy 2 Dy fanatak oF ALRC) g-f= -% (25) AN-l0= — 4749 =— 3X IY= 137 Scanned with CamScanner Date age No, P= Ih 23, The._funedion $4 clo fave by f= (4232) * a> Apbut—ia maaying along Le. cubase ge fla) tn. iiede pb Anay diet. as ct Lasoo tsyh2 poick-hs ck Y= oon iaali ps decheasing at the dale k'unile fire Aacands, Qual. hth w= copccl’omly: LB CW iacsosing ob th vile k_Wails pox Second, Fziscl Lho_ cada nels YA---[6) /5-38[731Q 40). Sts’ iam Y= Wara) "Nad xpd Dabvendinel A Ay. - yxp2) 2x4 Dn-k_. --@ mA =-8 _@| “gw. Wy. vw =1-O TyxF ye Ca def pK Now ak A, Y-cord, b churhraty —— —— => Bak --@ Bl ae Ts (bapa) 8 > VitgeQ> Ha Ow shod y= (wo ty = yw &, Godinaly ¢ ACO Iy)F Scanned with CamScanner ee ay, atfCOMPAMON: _ 25, || The diagram dh He conve: Mls =< on Ta a Auk 4, b(3 A enit, a TO ES We lingual e “TetectenttA me heat ed = AB ad te x-coik, 8(%>1) Festa? Lee lh ae Fa aes Beant = : laa _ Fel dle arene be Laiangle, ---L6 Sdulin; Gorres J= q¥eape----D —__ tip 2) Bay ayaa = =& ~ Tax? = gi 6 he cue al Ble = Be ye a ~/=-2(2-%) ~~ @) Sp Nernst lB; Y-l=4 (4-36) --@ Toph Bickronl x Cain dad) sean se gal ate P a — jormal fBlsinss 5 “ 4 led (y-3)5 x= — leer aan A Blas 4. tae Bn : = =] (2- -th) on ESD) eee a Scanned with CamScanner alQ & ince PAG. Ah palin 8 UO hh a at (0,15) : _1O Baxal Lhe _yralue sf 4. : ---[aj aD y up patil, ---[2) WO 4udel the Lpuelan xf Lt _CUANE, =-£3f (| iid Me tarda of ony ether. shlinary brisk gn le curve _[2) [e231 a ] Stoliontad dy. = bx'-30x+ha---() - les 02> fae Q=0 4192) > $a (Q-h) 0 => G24 ( a>o) aiff DAY 10-30 RL} — = fah-30> 46> 0° | [ier he bein pout inal ta =1s)=9 ab 4,-Is) [es Ge4) ZR. Alelimacy pocuk-ith. a ips a Popetee (O)| Epuokin of Le Curve foo. Ye {eeeser fa)de > ya ET ma burtac [024 => Yo 39%— 10% pobre ES ncn parte tidmyh { 4-/c) Lap} L.O=> = ]E 2 Qe lPH [orb adeahslisl Cae v cat 2 Hoses Pn ® Eyualin yf te Cunet iat Yate 1A babys! BD —_—____—_— (A) dy 6H 3004 6X4 FrD = 62-802 404 = 6(2 5x44) € (2-1) (AR-4) => x=), 224 (abou, bom) 2, houtc anole» dlabhnay poid 0 of 2 =) 24 (Ye rf + ISI baby 4 1, Onder Sokmary pork bat (1.13) 6 = 8 ———_ Scanned with CamScanner 
