Ninn P1) 'D 21c3M Pinso Sir -I/iya D So Nido 13199 & Jed Sho Ma helgil & 13191) DS (14) Mox31y)d 11134) No 31096 akug 1151) > "&1 Ma N51 Nido · "Yogil apido SYN(1)491421219) 1317) D Mo D3lp) (f) 131911 naide If * Andi 7317/7/1319)571913 DRIO DEIYS /g) So Melgi Moldo i no DBITD Big X29) & (2 b) Jog 25X5b * D Sidodkid D -don /D & 7) 01 Olde 431(/33)/K" & D131/)6 & 33810 0130 Si X a ,b Jos -ieo , acxb 7513991 " b 2 )3X C -"5 % 013195/4 /iPad b 2 D 13139D ngiY Melco of Sidd &1) + 3) > "(01) +f MINIOn Bly DER2 d) (DERP) igion c 13149D ngI/D ) Dr109 6 D & ISng 41301948 PhS legh Nok 4 Syll sly) Trigg MBIPS Digi (f) a 110 , : Jakm e"ged kithnood 68 God Maldit kn (kX , ky] f(kX , ky) lim 5 (x , y] - "I (x , y) = (0 6) , p'd'piligod lim 5(x , 3) = 0 iSK (x , y) = (0 , b) en , KO isk displ polko lim DOR / 5(x , 3) (x , y) = (0 , b) lim 18 8830 F(x , 3) & As f(x y) EDS = , Mo God M3 Pagl 13k (X y) EDS P + xd(X , Y) EDS G8D , MiddID iO Sidd VISidin God &34 Mis Sized Mao f(x,y) Addin God F(xY] Myaldin day ik 0-8119 Siddi Play jo1k Sial ofa Sigdo engin da 1366 ↑ "488102-15)N4 ↑ "TK8 Sidde "918 Si22 MYNSrids CONS p3 Sida TJM/P" Sidad hysapijida sil e'lla piedad Mijns ji) Midd Sied piadai So pingon is night 2 13 /106 So : eSki uljadin ↑ &C e visso D & ok Pl prors (x , y) = (0 , b) Pgkb siad displa 1219) kmf(x y) su disaldin Displa , 40199 If so G & add eci Doc picond porghi Iain 1 Mi a XY x + yu lim (X (X , &+ y y) => (o , x) y = a (X , x2 + yY y) => (o , x) X = = lim + = D (1x) eiffodi 179d13 a Sid (o x) , = 1 -MDSIK = R In6 X- 0 &36 117d 01951 Pod O-87110 &19 did 112 kX XY lim y) => x(kX a XY lim , = kyk ky2y2 K =m -If ~ JNO 300 P")19 1141 Span ps La ONOD K = 12 + 1 So SIPCD + o = L- 04 P" , k6 Pond cood by f(m) lim f (Mo) = 4) gasic MoME/gSi 1000 : D 50 . I & - 5(r) 112 lim 00Nf N M- Mo 018 Gods lim g(m) viradid limg(r) 'SK M Le = g(r) f(M) + D (a((2 + e) vipan , **, log Nobel , 231934 -old = limf (m) · 2 13 limq(t) +y / 110 t - lim5(m) = A ! M Mo = ! ) to to = (1130 t = to Mo-6 . + Relyin Sik000) + = 131 / 40 . 12/g Nexox lim (5(4) M- Mo . g(M) limg(m) = 0 = 0 - is Mo 64 MPIDOD 1 15(471/5 ( g(M) . indian +"N M- Me Mo O g(m) D poof Se (3 Sidd g(t) ak said = - Lola Dizg11on limg(f(m)) limg(t) M - Mo D 3- g(t)p@ Ndld Mo = hizgsid Nixo M- Mo Le disgllodo dialys disgildi , viradia : limg(f (m)) g(t) Sk = Let a = f(M)g(r) lim Y +211368034864 375/9) M = My lim f(M) I f(M) + g(m) M = Ms lanca - (2 M = My lim M = Mo all0 La M = Ma 8 <Let' (Les0 B 5(e) = Sidd (1 disigalipan ok Mo = Diff 00 disg10 M- Ms [Mo-f SIG00) Sied Plains Disguid 8 = D f(M) L'Sk t = ts Good Mississ 'Dillsjoin Sad 1K'8 + 3 : , 10/ =(M) lim = Nod 0 (n pil M = Mo (Cood", a D Mely) 60 4x1000C lim f(m) = L 13 I M = Me Mo-o piphani pigigod 2000k . piSigoN NON &" , Yik Orin Gioand SiPadron i Letha posted limef(m) f(Mo) = Ma N 151116 Rela 310 f(M) +13910-meg 10131 M = Mc limef(M) = f (Mc) + "gon Si Nigh N & : op Mel &Mo did su Pine Machi M = Mc Yiksid So 13g11017 Mod ENC figed el Mo Ch1301E1g10 &InSiSi' Ndid + . Nd6] 31)10 & - S Y Ga ok neido valg) (9) Mo-y Noise 110130-111 1'0130 BBIg i Mizp lon x003214K6f(M) limf(M) P 18 / Sk M = Mo /P (2 [3 '010y'k Mlimf(M) Mo = I 13110 Credid o Mission - (Mo) = f(Mo) il pos disgslo lim5(M)121 / 34 113 , M = Ma pl O Alld S y1d 10 % NEE 11391104 & Sk , Sky PINd nelgo 1Slago 131) Y On Melf) Nadine 20130 KisdOd : Ping Y delf) NgaSil Mizgll0 Nigh Disgsl0 MBglon o of 11 G , kin No de 1314/ (c)(4) 113 , 10 Nrga/f(M) Sk /131) . rested Ya GCPf 10130 So N10 30 M = Mo 1 closen -an &g limf(m) (4 KI3NS ididoal y 1) Plc-Godd 13/1811 13131 Mdion Rizkidnisk Middl misglo Mo-p Mind 1013) 131494 : Adiyidil i yu fayh missldil 110 / 1317 / Kn G Playing d) poi Rig ve ils Missio e'dise 101sof(M) dis/10 Leadi Odiogdi yogi a GRI Jago on kin & poo 10 30 . 00 & N f(r) Pl Boise pigi ↑ 110 e 131994 gi Man Goddid jol) Mojafic o Ok0& : " ↳ close spa Good F(M) PL Si pij elegan f(x Y0) , lim X · &NO 113d78 - and 101 118 Min (X1146) D3gRD Pigmen Naga Mine P'dige aird -x"n16 -"M Mosagi 1314 Nigh sigot it's 100 Moses & /P Pl > Mesas Medi 18101 vid"9 f(x , y) f(x0 yo) f(x(xx Yc)(X xx) - - , , lim (x -0. - Sipki3013 01318131/ Kind 14 0 1 R13] Y phy : KIDP2 & 321/16/2013018 GK1360013 1131/10) - &13GRY ~ SpK3j03 18 48 3) . 18 Migdin "20121367013 NOBB KO MyORD Nusagd1319) (0 12 Oek norfind Mo-110 301 . vid"IRI -lgon 110130 cosa) kba Odend pigged 1132 100 da "yet ol &'Di932013 poodl ilee &Ne -100llk1010n8 ading ind 063 106 Cr3P RISE Clay of Pind (3 131969 Mizplod diy 131998 11494 - / oodil . 113/1097/10N in 60 1318 PLOIND Pl 11506 Mission & 1319) Ki3N8 venok di Giga Nissan /gor Br 6x Ngh Meas eigond ? P -18101C13/1013 S31SP 1139/18 Pl 11gei Nigip1230138inechis Page -180k13600 38 iSK ank Mosasind 10130 PINNOd Pl 113/1101 111 "OPD 1131/101 D Disas . 3108 py + (3 - xo] (y y0)2 Old" , & & visa) , - %1713/2013 16 K6 DiPK13/2013 - (1 (2 5'y(x0 ye)(y ye) E (X , Y)s(0 , b) - - 199t Disson vigon - 81) &7/1352013 "didki3j00138'neyin & Moupidod lik od , &18 33N P - - of 113110 -18 Alld %01306 113/181 ↑ 813) Gak did "n , ? Mosai'of Provigtindo Csa) virsay f(x0 Y0) X- Xo >Xs Itizidi 600k) Meli - 112 6411 : " L(x) = f(x , 30 , zo) + 5x(Ma)(x - xo) + . 5'y(M )(y . df ~ P1xON (131930 (X0 Yo) , - 84131 7101948 14 6 /131Sng) Ok - y0) + 61c13/10 : ibk didipisj0 3 D13/10 i 3k f'z(Mo)(z z0) - 3 Mission " py 80 mad year 147 14 07310196411997804399107 . vly'f ploy 300 , 7713 , 107 61c3j2013 ↓ (o Ye) , = 5'xdX + flydy - af180")'sk Mo -a1160/13/1013113 / 1107 ok gen-10 = (X , Y)n694n60 / &67 z = -didi Kn ((X) = t Ja didipiiss0is 60 f(mm) + 5' (Mo)(X Xo) + f 'y(Mo)(y ye) , (f(x(Ma) fy(Ma) 1) - - - = , , Mand 4-41883 ~ 11781013) dipk 3/ 013 , - 132176 didgd do -gran v137 19 disallon Mid you 1993) pya (2 dispion 1198/C f(x y) f(u(x) v(y))a , , f(x = = , 5'x fu 4(x 55 5x = + - , fly fu 4'y f(x , y) f(x = f(t) 5t = u = fly , u(x , y) = = , fi yy 1 = 1(x y) , t f(t(x , y))a = f(u , 5)(0 , f(u 5) = t(x y) , , f(t)(3 5 tx , f'y ft ty = = f(u(t) , +(t)) < u = u(t) , 5 = +(t) f(u , 5) , 8193019) +334 , 5 fu 4t 5 'j v't (m , n) G5 (Mo) = LIGD YOSRIRP) - (x + mt y + nt) , = G 10 10 = G5(MO) t - 1252) f(X0 Yo) , Of ResD m2 + na so 4 117 & F(Mo) . diad "Ody -Sl Sayid/iGugogi de disas M'n'ndgu /11 = lim t f(Mo) Gladi G (4 + - 9/1131 D15 / /10) (2 , , fj v'y + . v(y) = , 5'y u,x , u(x) 1 = . f(x y) f(u(x y) , v(x y))a , u = IP /1131 dislod Ok din'Yan visipkisidia posit -180 1800d DiDK130013 18 'Sidkjid Micha ~ 1139/101 SK ↑"god 10 16 nislon /Illin /I'll PK P"gen Pl 1131 ,0 · 21 2009 - 131) = ) 11318 vision , = 0 fx(x y) = 0 f'y(x 3) = e , 1131 ,1 -1319)20n/ - - 1001249 - 1232/77883 -(d) Nigh fxx a (Mi) = a , Sy = b , fjy 11316 &Gigi = 10 disa visis) , f(x y) Ni 131/64 2 b D C all - 14 12 = b = bC 10/1406377yof open) 4004131)030146 as o min a so max ↑ = c ? < 3 &k 30s a ~ : piph pipdi Podrid Nu + 3) Min Max -1 peop & nd uddy 9 , 694 113' Missio losit DPdi/pinaa , Niviy de Ris1/107 916 17 eicing . 1319] P 9 18 , 2786 /13187 17 /91 Giky (y131/773147 /k +13/1 /Sik 1131104 Orid Max Min COMIN I'n' N'x 17. 2017 L(x , 3 , z) = (1 1134 /2 / 1319)(134)(3 9 1 6 , 77(3134117314x 6 pigin /1319) 361448 - -1418 diayi Din Mod Posi 13/gsi /Ggi in 1969 posi 31g f(x y) + xD (4 /2 y13) 6) 1316i 1937 - : K 28 110d do side Ge , pind/nsi D 13179 - 140130 f(x Y) Godd'od Olde"I , , : 5/ 1626 and pref edega poi piyisis - (5'yx Exy)/8171 · : de &115414Mo Mesa , y) 001 SK13600 3 18 " G apidoy elid , gi Niger d ISK Me-D is sas 110130 n dy 5'x(x0 30)(x Xo) + f'y(x0 Ys)(y Yo) - = No visa) Sic13,00 13 dX df(x 3) 304 Clyd , mido minion : - , , pe 130N jn -33 - df(x y) Sxx (x0 30) (dx+ 25 xy (X0 Ye)dxdy Jyy (X0 3)(dy)2 + = , , df(x y z) , , = , : , f(xx(M)(dx( 25xy(m)dxdy 25xz(m)dx(z f yy(4)(by) 2fyz(m)dydz fz(m)(dz) + + + + + diy Ge cific · S12Mo11634 => (M) = Mo 113058 f(Mx) + df(Mx) + Opidod 2(4f(Mx) Ngon Noise +... + des as nd f(x) + 1869 f(x , y) pla Pic -& Rx(r) -k 446641(161c Mo : sir f(m)e(me) -1 f(M) Nig NId & Tidio P160 f(m) do 60 (11546 Eigh vigig , &1319) Kin Mo Sir d5(Mole &Elys (214 Mo S12df(Moke PIN'd nx92"80)53/1 kin 11314 Tk(M) py 010 . 113218 Mo Mo isk (1444131)py10 & >KI : 6 69 : Me 1519)k1 (dx dy) + (0 3) 6360k(0 , , , , (dx , dy) + ( , 0766012 +10 Spy d5(Ma) e'dgodiyln adjoga Old 13 dx , by (i) 10 Patt - & Sin D - COS & 3T 2 US = S 49' 948na 113790'k : 11 - Exo ) 618 didis 18 19 didis Miz/lo pinda ↑ 4 31] fixdx 2xx 2 = 1 Missio X 113 SSf(X Y]dxdy , = 0 '08 IGNIO Sky pind gen n(x) = PIC 119108a'dis Plund b(X) D 64 1310 : portl 000d Sf(t)dts a(X) 10 1 35 n'(t) f(b(x))b'(x) f((x)x'(x) = - t 8> 8 · imm eu right /do Gigod e , So -N & N dir(x0tF) no + Not o Gicizjcio (g 10 en"9 134147 + adj) = xf D - = 0 : pire Seextady F Sk (x) = cigo 0160 N & ND30 F : 18 = 0 Good D PIC -p up) TMONPNON13 & 8103 SSodxdy-S(D) ping SSf(x 3]dxdy - m() Ping &od12 , SSz2(x 3) ze(X 3)dxdy - +(5) = , , 636/ 'I + Co nso 1210)(3 - 1934 (5aw)x* y2 p + Xo X'R I y'r 2059 Y'a RSInG - = "Sing = acose X R Y RCOSO = RSing = R = 5 axdyJdRd 94 % 9061k y 1kx86 nday1(myp +k 0503277416 18k 2 (400 (c) : X y j ↑ 5- Oleg 1100s9 displod Pine Nic uxu'y is 5 1x v'y + a = . - eyea notiM % P3) Dining , '06) j ga X 06 = G(x 3)/25x , 106 Y SKI Da = des [(x 3)1 , < = = D , y- , Nicid (1 pine (x)5y5g2(x)] Mizak y5d Ra b R 4 Coy19 De = ya bRCS8 = sjand/ axdy - pa Y aRCOS = Ideas Isisigy 2 X May 119) enk fe(3) = x = f2(37] 300314x106(y9)413736k834/ PIPIDM - (xx) 334504'11) ODID 1 - 1194'of R &S = 2 S COSD O Co SinDa (2 31N 61778 (y70 & OIp'n & - PININ NISiPadOn , 4 P Pho po 8 Vididad 01 RP3M 3504π NKINN-R D do in 'R-Gold (OliN8&n 186) On (3 Ping Gaon Coldi &, ok SaOND dy esied dy 5 Sf(X 3 z)dxdydz-m(f) 22 nod(2 SSSeaxdydz , - 10317 810762610 uzs10 110 82 pindy X Y Nic pin1x(13)01 -01 Nd 14 > 4 8 82 4437 4 13) 7434 . z = R = dXdydz = JdRdodz -18 D5652T x +y 2 R = 2 x+ ya+ z = x+ y + z 1 ma = P18 X y RsinE + & Moj RSin5 = 5 Mis in : +a n0S(0 +2 RCOS * = z -(2) - , tracj & 110) =052Th X 0895T y = RCostSin9 = RSing Sing z = J = RCoS9 = R2 sing : s good ! OIC 86 & 14370 & 13) & 0821P3R4 p13/Sil E good 2301k750 NIND & 1682010n + 886 + -123 31180 + PJ- & E Lesidadesileyed modi Y 4) T 120 7 . 0 33 . 3 of My 1x Vyvz W'x Why stigh n MO & -113) MOS - 8 6270) . 60 Didid) J 01M Rose sind VRSInG Sin W = = &O Mi Wiz Grac = +133 Uz u'X 3 3 TIR T 12 5 13) -juddw exdydz = + RCOSC R & sing Metha Cond linked (d) - m()(310680nod(2(() Sod = x'(t)dt = (x(t)) (y'(t))* (z'(t))2dt + = + dh 1+ (4'x)2dx O /Xyldy &L RISGNO dL = = + : c = : C= y CX : RYz + (R'()(2d0 B c = & f(n(t) Y(t)bt (f(M)d) (f(x) = = * It) (1(e) Cese , de Red = dL is in (t)0164 + (0 Y(x) olgon Pic (2 X(3) 198 o (3 eyen al 4 +(0) 66 1324410 B . = . - kid t)dt >(16) 30k1x7day,3) , - - - - - = - & (t)) Cplyi 60 X- S & 131) 80 B , yl0 -120(y(n)in)(0 to -pisd (t)1131610 ak-gion C4131187 &disk , (t) to , * Xo y Y0z 20 (t) (t) 1 Ma 0160/1134(16/kin / 847 Y'(to) X'(ts) z'(ts) - . RVf + (r(b))2de (e) Sine) yog10n)))Y(t) 410 7 d) -1819 & 110 G Go 13100y01k( - 2 di 14 & - x led (2 / 01-0194 t Ping is (3 (630K1yMIID) PNO 1319) -IPY Migh t K3Nj/ X : 80gG1 aloid 19 Y &D B w = S eas move 15 is 6) 26k6 Dind ylgi dyd MabinI 11321 & &x ukpi 116igg Ci 1396119 = = ulB74(f) nizadayt yaydl 131390 K SJE((d) ply /OCINS + 1301 Collye) 134kX ply (30 & , 000 = 131y9 ded F & 130 Fix Y) , = disoda boy 130 Nad pind (2 jec enk) pinged , / dri -zo is Glad of 497 Sa e(x , y) All Ned Din01313 / 1391 o y = X : Xo = X 2 B Sd & = Xs Y : Ye sX = u(B) - n(f) : , , G dojk (2 vizdigris (3 Y SdX = (x , y) · X 1 99 13 Sissio La Le , (Xo Yo) Day ex , Say yosdy u(x(x y)(1 9/1396'nei : didis/dizio Kit Siizacio Scyx + Pic u'y(x y] = "19 1301 ( C ]) See = 6 130 pilgen a(x y) alond (1 D plgo 180 u(x y)a Usk73089 80 Pion Papi-B py POINd pind Sibody 180 30d6") 210 80cos Nkd Godd led giorpigon (2 Y & , 9 Nido / Szygon Se Sjksodil [X , y) u(x , BRO , , D &x D iM"goal (dx dy dz)73196p1 & in = Fec (3 = ~ c , 60 36: /14 (4 gigogine O, D SE SSoxx -pydxdy pdx + 2dy + Rdt de yaj6 dio) ) & alod 19 Pr & = (x ye) , > X 3 sy 613/ 0017-3414C618063B - 6 & 7731964131463187 -1919'd10 (O Y Sgz - 28t + 3 - )dt L & · E t B S : E = 05 a = + St : (E E E) = = 1 = 1 R15gD , , L T I - - D E 0 t ↑ (t) Ndit2K13d it -'(t) = dXdY dZ 2t 3+ (1 , 13196 XN3NKY Z , 2) (2 Plain & Q 700'Sic 2 A: E 3 SinD A 1 = B: 3 = & CJSD a = = 3 Sin - , b = 3 41437534 = RCoSp = 3rSing X-ARCOSOX y D = (106 1 : brSinf = 3 (0) - = + sidi92 13d : CoSD = -y Y X = (RCOSO 3RSins) , The = dX 2 dy (0) -Sine 3 cose) = , I S by (Cos + 3sinf)(sing) + (S0-3Sing)(3cs8) de X Y = Y X Reggi Y A 2 X P iiin day led godde +1968 it voit ⑪ & ③ · Ca 28 Ca ↳ 33 91 ⑭ SSd S = 3 00041149 pid"sen ind S 11138 Org 3164131 - - SSoxx -pydxdy = - SS2dxdy = 3π 2 San Jeax = y = X : + yay 0 -dy 4 Sa = 0 = x2 2y + 32x = 23ax = 6 (3 11011 SSeds-5(b) 5) g(X yids-m(6)101cod/2 , ds X ds = x(y z)8048 , 1 + = duds xX y = 100snced FX dudt = (zx(+ (zy)+ 1dxdy = aloid : : Sodajk e pilide no G = (4 , ) si 30 infed z(x , y) = 3dS iSRd noOmn d(P P (2 MSNND (x(y) (xz)dXdy + 68k5 Plit Guia re & f(x zdS ↑uxudisk 5) (x(u x) y , , (u SSf(x 3 , , z)ds = SS f(x , y , z(x , y)) = , , 1) 3(4 , 1) , z(u , , (zx( (zy) 1dxby + . + : Sk 6 z(X 37180m1 = , 1135' Once ~I Oriod 5 (8 , 9) D = = (a cessing a sing sing accsq) , 5(0 9) 10 5052 0595T]N , , - ↑ 10 9) = = Mex sk6 = = E(X 3 z)lXy2 z 22: , + , no (0 asing 3 100 . G2 : , (2 , , , E(0 9) 10 50 = 2T 0595TY , ↑ ( m) , 1Sk 6 = E(X 3 z)(x y2 227 , , (aceso a sing my = , D = [(x y z)1 + - = s 6 (a cost sing bsino sing a cesa) = , D - , D >k , , E(0 , n)/ = = 2π , Sh50] * - + = J = = , 71768d(3 Xin = 2 2 - ↑ (u x) , D Juxfo + (40 , ) = = is , , , E(u , 1)10 us2π = , Ggl] , 24713130 con Carcesu asinu 4) +xid(u )(2 - 65(x 3 z)la + + 0 = + = 14 x] 15(4 5) 1311080 , infoydis nik didino Takin Sayi 6-6 , 04 Gn691 vid Ply P isk SSvdsSSaxdys dS N = = = , Sands, sen n axdy , GodGj'k inded aloid you ese nezen N 11361'08 pigpul -1Giddl SNja 100Ni Se Sk ric I = 13ina N ujk3edi - T zy 1) T (z(x)2+ (z'y2+ 1 T (zx + -- T - = , - G Sk SG = ok (1 (u , 1) = In z(X , 3) o 82 [2 Pl & M PuXi , Ends *S SSENds SS(p(zx) x( z(y) = 100Mid >6 m 1)dxxy + + 13111 &1) YIRD - So in * 13 conNo o (2 Fas SSdirFaxdydz 3 - 773080713691710 11) 82261) 60 120 1 = Not Plain MOOd TRONY d FEC = ↑ - v XF = 0001-1101 T j1g Of Bipo (3 Plan (a Nexdy 319i7 i j K 2 2 2 GX by Ot & Q R = (R'y-Gz) i - SSpotF Naxay = - DIld (R'x -P'z)j (ax P'y)19 + - J J J '06 R 60 (d) 106 Q 60 154) -(a) nin0 -sa) nin0 X -sa) nin0X z08960 y08960 Y a 60 -Sk Y'ynD 106 R 60 134) z08 : / : Sund ROOM cido pige/111 01 dist 80170123 = D 130 Sc ))net Fies (SnotF Not Etc(t)(0 16 pD80csp) Sk (PMONX led 80Nd] opico & = - 188/12 - good = Itin/111) (4 121521 /11 , J 210d Origin Bacpisi) du POR p(2 dir ex + 2'y + Rz * 16. 3714) z(x , y) D : - = (1) O3did /lis Olky 10016 (u , +)p(1 = CS N = - ° R Not X u(x 3 , z) , = (9dx + y = z B &Fai - Y = 67 22y +Smdz X= X X = ta t y = = to * + c Siscio u(b) u(e) - 1313, (2 Ping kin , find (,3, 5) : X 3 3 (Xo , Ye te) 14314631014 : = 0 (3-0 , 6100 -NeN y , x (x 30 , > , ze) (x , Y , to) 02 300 , 130 JEC(R3)(1 Z ya - = - /13/ &G -1849 Sison pin(130 & Fat X = 0 - = u(B) - u(8)yny4)83,00 2408 vigi Mich sil S Face CO Nien (2 60 + "3 / 110(91)13 jec +, 600 17 yinan ↑ 18N16 - X, 3 , z 180747 - Play - yog6) +184-180d"O63/113d /1344 Saya Dipisd , 1 PMID-Rond Mo 1319149 (4 , 5) 1k Piksi y + 3601yri /1 80 mng & NoM PMID-MONG T >end) nggal - /kN213 SN) Of ONLY 60 GNr] X 3 2006731939 , , + Gux's > Crys cap) - Nowad ( ,5) 113131k7 + Had 88 ok Dogan On virio do Gary mind/1447(11) 32] Cry MAYOsided 11 19 7130(12)) 400 - (n(10)(13) x + y + z2 Ra MOND - O 4/137 z = Ord = x + 2x + y = 0 Sidd 5 > in z89413 , /109 Gadi de SNet orid Bird -110 /1 d 81828 * pilGed (a , 1 0) , da x2 + ya 80 1 R 2 * P1D13 2 X X - E 1 Z = & 2 ZX n GP20 in P 1418 = 809 1 n GP20 in SX X 809 113p1x0 SX 113p1x0 D 00 z = u - x2- ya 4,1 x y2 pa + PYCON NOSMMY p13) =G =Paud - 71805052Th JCRdD I X j 05752T (x + y (x Y8696k4178) , - (3) 095Th It 66 X 96 13108) y . nOSDRY PYNN J R = + + -18 6 Sedojci) z JdRd7dZ · J : R2-N & N -N&N 1906 eigige Se = (x y) #slpSicis3618y"3 , 10 "f p(x , y) SE = , - 296x 92 u(x(x , y] = = = RES c + n'y(x y) , : a sing z = N = a Sicijgig S FT s = cost 0852π : & , 100 = s - 120 ! 3C) ↑ 107/11 7 · - I DOOPInS - good + - sing &N pind (2 jec 1 Geds E * + z'y2+ 1 dxdy iSkeNON150 &13 / 010 &Six , 1101 glod 3 , z7ds 19 u(x , 3 , z) P God Sex +SaySRc y = Yo X= X z = Zo z = zs - good Gogok nggd SENdS FS)F ( z(x - - - , Po z'y , 1)dxdy P(p(-z(x) G( z'y) R 1) - , Z = od noed -x dudy 15 & -"3 / 18 DC nond & " clod ·10 & & d dojc " R3 - 80 gGj je S 2x-Pydxdy j2000 Not = = 0(3 - pri dod 31 / 62d 3 , z7d) 119 dS 0595T , * 13516 Nee Sing exig , + = ecossing = 'I19 GrdGjila SF Sydx ady Rdz1313) 80 fo 4100 Xy MI30D 7301 SS(x Ply 2011 pilye X u(x , 2) yxdX RE & u(x , y) = a(x , y) u(B) u(e)32n8 + pind(25(1 400 di2 esied Ge goj'l 201 RYE) + R'()2dE & p'y(38 / 3 , z)di , Sear XE+ Y'EzEdt & (413118s1 = S Six Z = no R Sing = 13216y 2x 1335 . RCoS9 = Sea * - 6103 Gr dGjik , Rsing) X y z= Ra dios no end SS(x 37dxdyeing e RSING = Rsinsing = E Idudud w = 13437 RCOS-Sing = = 1937 RCOSI = Y Seaxdy = - , dS X= X < Y= Y Sines = s 4 = () P ↑ Sin GNIS ↑ /)15in Sean T s s 14 I'm , 'I'y = s d =S dirFd divF = P(x + 01138092713 2'y Rz + Snetf was Snot F N Exdy( 101)0 , + = - Si PRIN piged 3166675146318 7 p(x ,71791906c 1) ' , j K G 2 2 2 X by Z i NotF = & Q R no & Ni 80 78 . 10 led God 3144709160 ild GOOMI -3) dis(0tF) Not (x) = (gradf) = xf = = 0 0 T1x17 ~ In) 14 101305(X 5) 1 131/4 = (x y) - , f(x0 yo) : . - - , , = + - D - limf(xo , yo) + 5x(X0 y0)(X Xo) + f'y(Xo Y)(y yo) 6,119 10 - - , - , limf(x 3) 94(91) , (X , y) > (X0 , yo) , (X , y) - lim f(x0 yo) (x , Y) s(Xo , Ys) , f(x0 , 30) of , = , , f(x y) , = F'y (Xe 30) (4-3) lim 0 (x y)s(x0 , ye) (X , y) D13pIODD JP) post -199 F'x(X0 Yol(X-Xo) lim n) , sing -199 lim +& (Xo yo) > - light ~ ad = PK f(x(X0 ye)(x Xo) f 'y(x0 ye)(y Ye) (x Xo)2 (y yj)2 (X , Y) s(X0 , Y0) f(x , 3) Mo-dd didii3600 3 Slu - - , lim / , = , (x , y) > - 0 (X0 yo) , f(x0 ye) + 0 + 0 f(x0 , yo) = , -10 317 1 o Nadi >(Xy , y0] - 40 30 . 113& & 844 16141 ) x (Xx , Ye)(X Xo) + fly(x0 ye)(y yo) = - - , = GMs) = Te im t , y + nt) - S/U f(x(Me)(x + f(y(Me)dy & - (x + mt . u(t) , m2 + na lim t D39/10 60 = t se - 110 i Ok : u(0) - f(x , y) df(m0)6123,00 3189) 010K13D f(X0 Yo) = = didDi0 & ul(0) nosa) 573277510619 1081152) 5754457 11411SK/'fipki303 (0NJOD) /P14kD D1318) Visi pin"gen u'(0) 5'x(Mo)x(x) + f'y(Mo)y'() U(t) - & 0131 needn do f(x y) 110) (2 = Y (M) f(M : X'(t) = CoSx X'(b) = CoSX 34ged 5 5 198 E f(Mo) . = 66 pien S () 3Is f(MS i isk Mo >116 3/13/2013 . is pagen f(Mo) 10 disi K Me , & is Moo ↑ /2 E-Hogsi f(Ma to Pil : f() Sc = - Mini Sk f(Mo) -1 CISE =& f(M) M .) > = 911yd ni pef mini Sk · COSE f(M) E = o k P1N/308 015' 1131/ MOMNIOn D1313/ISK /14") 131y D f(x , y] 10 30 1 P & Ond (1910 : P")113/107430isk * (e) + 0 & ND0160/1131 + to - 34) 1 cy kin lto) 131yi Ondakin sdf(t) Mo 1 - = PIC F(ts) - 3 XXYYtzt z'(to) = ↑ "jed S (D) Mordd yadi D indo Sici3610 13 / /10 M (x,y) Nd y U(x 3) = 2x dad isl , - & (x , y) 2(x , y) -13) Q(x, y) + 139 y gl : p'y = 1381 elc 831) /123d/ & u(x(x y] u'y(X y) = , = , 1 p(x , y)/19)79pgd)Q(x , y)9(2)y106p(x , y)020154) : P'y(x 3) Gypsl (1101300 uxy(X y] = , , x(x(x y) 4yx(X y) = , -111 (Uy Yx) = &10/110 30 disdni . , disayna gizi pilda P'y(x y) xx(x y) = , , Ged ↑ (ec' · NIS-8 , Mo = (e) gen , [DED , vididong Me unis , 10 d Big Sk Fux & Diggin Sno & N Pla Fykin , (a del Road On , Gy 80 141D0 in 2046