eroberogeday lwm pl:ú bribaøabr&tknitvitüa ig BaNiC kmµ f( si ebi ebi rkßasitiæ 8
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emeroti cmykmupøic -iym&y cmyedlmatrmg ehafacmykmupøic TRmg a i b Edl aigbcacmybit ehafatrmg BICKNitécMYkMupøic a i b a ehafaepñkbitedlekkmt sresr b ehafaepñkbitedlekkmt sresr Re( a Im( b ehafaéktaimµitedl rw i i i ektagsmnmucmykmupøiceday -RbmaNviFIelIcMYkMupøic ½ sµtfaekmacmykmupøic Edl CacMYBit a ; b ; a' ; b' -plbuk ' (a a' i(b b' -pldk ' (a a' i(b b' ig a i b ' a' ib' -plkun ' (aa' bb' i(ab' a'b
-cmras a ib a b ' aa' bb' ab' a'b i a b a b -pleck -ÉklkçN¼PaBKYrkt smkal ebi ig CaBIrcMYkMupøicea¼eKma ½ ' ( ' ' ( ' ' ' ( '( ' k -cmykmupøicqøas k-ebiekmacmykmupøic CacMYBit ( ' k k k C ' ; IN * cmykmupøicqøas é tageday -lkçn¼ ; ;, IN * ' ' Edl ig a i b a b a i b ebi ig CaBIrcMYkMupøicea¼eKma ½ ' ' ' ' ' ; ; ' ' ' '
K-sMKal ebi ea¼ a i b a i b eká ig Re( Im( i -sv&ykuné i cmeba¼rkb IN * k ekma ½ i k ; i k i ; i k 6-dMeNa¼RsaysmIkardWeRkTIBIr ek[smikardwerktibir ; i k i a b c ; a, a;b;c IR -ebi ac b smikarma sbirepßgkñacacmybitkmt eday b b ; a a -ebi ac b smikarma sdubmyycacmybitkmt eday b a -ebi ac b smikarma BIrCacMYkMupøicqøas KñakMt eday b i b i ; a a
7-kartagcMYkMupøictamEbbFrNImaRt k- cmuc ébøg RbkbedaytRmuyGrtUrm al M (O, i, j Edlma kugredae ehafacmucrubpabé ( a ; b cmykmupøic cmykmupøic a i b ehafagahvikécmuc a i b M (a; b y M -viuctr& W ébøg RbkbedaytRmuyGrtUrm al (O, i, j Edlma kugredae ehafavictr&rubpabé ( a ; b cmykmupøic cmykmupøic a i b ehafagahvikéviuctr& a i b W (a; b
y M 8-m UDulécMYkMupøicmYy y b M a k-ebiekmacmykmupøic Edl ig a i b a b CacMYBitm UDulécMYkMupøice¼KWCacm ayomkmt eday ½ OM a b
-lkçn¼ ; ' ' ; ' ' K-vismPaBRtIekaN cmeba¼rkb cmykmupøic ig ekma ½ ' ' ' X-cm ayrvagbircmuckñúgbøg ebi ig CaBIrcMucmaGahVikerogKña A B A ig ébøg RbkbedaytRmuyGrtUrm al B (O, i, j eká d(ab B 9-TRmg RtIekaNmaRtécMYkMupøicmYy y A b M a 6
ekmacmykmupøic a i b Edl ig a b CaBIrcMYBit TRmg RtIekaNmaRté kmt eday r (cos isi Edl ig a b r a b cos ; si r r -RbmaNviFIelIcMYkMupøicTRmg RtIekaNmaRt sµtfaekmacmykmupøicrtiekanmartbir ½ ig r (cos isi ' r' (cos' isi ' -plkun ' rr' cos( ' isi( ' ' r r' -pleck cos( ' isi( ' -sv&ykunti sµtfaekmacmykmupøicrtiekanmart r (cos isi sv&ykunti écmykmupøice¼kmt eday ½ r (cos isi r cos( isi( RKb Z -rubmþdwm&r cmeba¼rkb ekma ½ IR ; Z cos isi cos( isi( ( ehafarubmþdwmr& 7
- sti écmykmupøicmyy ebiekma r (cos isi CacMYkMupøicmisUü ig sti écmykmupøice¼kmnt eday ½ IN W k r k k cos( isi( ; k -TRmg Giucs, ÚNg EsülécMYkMupøicmYy,,,,( ebi CacMYkMupøicmam UDúl r iggakuym g ea¼trmg Giucs, ÚNg Esülé kmt eday -rubmþgwel cmeba¼rkb cmybit ekmatmak TMg ½ cos e i e i i i e e si ig i 6-TMak TMgrvagTRmg BICKNit-RtIekaNmaRt ig Giucs, ÚNg Esül ½ re i a Edl ib r(cos isi re a b r a b ; cos ; si r r i 8
lmhat;ti ek[cmykmupøic a i ; b i ig c i k-cursresr ig CaTRmg BICKNit a b c a b c -curepþógpþat faekgackmt cmybit k edim,i[ a b c ka bc dmenahrsay k sresr ig CaTRmg BICKNit ½ a b c a b c eyigma eyigá duce¼ a a a b c ( i ( i ( i b c 8 6i 7i 6 9i 7 7i 9 i 8 6i i 8 6i 7 i 6 9i 8 6i 7 i b c 87i eyigma a b c ( i( i( i duce¼ ( 6 i 9i ( i ( 9 7i( i 9 6i 7i 8 7 9i a b c 7 9i 87i 9
kmtćmybit k eyigma a b c k a bc ektaj a b c 87i k duce¼ lmhat;ti k abc 7 9i ek[cmykmupøic ig a i ; u ( i(y b 6i Edl ig y CaBIrcMYBit curkmt témø ig edim,i[ y au b dmenahrsay kmt témøé ig y eyigá au b u b a eday ig a i ; u ( i(y b 6i eká 6i ( i(y i
( 8i( i ( i(y i ( i i 8 ( i(y ( i ( i(y ( i(y i ; y ; y ektajá duce¼ am[ y
lmhat;ti ek[cmykmupøic y log ( i log log y ig W i i Z Edl * IR ; y IR k-cursresr W CaTRmg BICKNit -kmt ig y edim,i[ * Z W dmenahrsay k-sresr W CaTRmg BICKNit eyigá duce¼ i ( i( i W i W i -kmt ig y edim,i[ eyigá log log am[ smmul Z W y ( (y ektaj ; y Z W log log y y i i y ( log y Ca ssmikar u u eday ektaj s ' 6 u u 6 6 8 i duce¼ ; y 8 8 ; y
lmhat;ti ek[smikar (E: a b Edl a;b IR curkmt témø ig edim,i[cmykmupøic a b i Ca srbs smikar ryctajrk s myyyetot ( E rbs smikar etigñkbiitüexijducemþccmeba¼cmykmupøic ig? dmenahrsay kmt témø a ig b edim,i[cmykmupøic Ca srbs smikarlu¼rtaet i vaepþógpþat smikar eká ( i a( i b i ektajá a ai b ( a b i( a a a b a ; b duce¼ 7 KNa smyyyetotrbs smikar ½ a b 7 ebi Ca srbs smikarea¼tamrtwsþibtevüteká ; a eday i
ektaj ( i i duce¼ i eyigbiitüexijfa ig i i CacMYkMupøicBIrqøas Kña lmhat;ti ek[cmykmupøic Edlma CacMYkMupøicqøas rbs va eda¼rsaysmikar dmenahrsay eda¼rsaysmikar ½ i log 7 tag i i log 7 am[ i y iy smikargacsresr ½ i Edl ; y IR ( iy i( iy log iy i 7 iy i y log y i 7 y y ( log y i i 7 7
y 7 y 7 y log log y 7 y 7 eday y ( y y y y 7 ektajá ekárbb&æ y ektajcemøiy, y duce¼ lmhat;ti6 y am[ y, y CacemøIyrbsśmIkar i ; i ek[cmykmupøicbir ½ ig log ( i ( y W y i [ ] Edl ig y CacMYBit kmt ig y edim,i[ W dmenahrsay kmt ig y edim,i[ W lu¼rtaet Re( W Re( Im(W Im(
ektajá y log ( y tam ektaj ( y ( eká log ( ( ( ykcyskñúgsmikar ( lk&ç&nð log ( tag am[ t t log ( ekásmikar t t t t t edaygg:ageqvgésmikarcagukm_eki ig Gg:ageqVg CaGuKm_efrea¼eyIgásmIkarma setmyykt KW t cmeba¼ eká ig t y ( 7 duce¼ ; y 7 6
lmhat;ti7 eda¼rsaysmikar 9 7i i Edl CacMYkMupøic dmenahrsay eda¼rsaysmikar ½ 9 7i i tag iy, ;yir eká (9 7i( ( iy iy ( i( i iy ( y ektaj y 8 y i 9 9i 7i 7 iy 8i y ( ( tam ektaj yketacyskñúg eká ( y ( 6 ( 6 6 6 ;, ' 7 ektaj s 7 7 (miyk ; eká ; y duce¼ CacemøIyrbs smikar i 7
lmhat;ti8 ek[cmykmupøicbir ig Edl Z Z currsaybba ak;fa Z Z Z Z dmenahrsay Z RsaybBa ak;fa Z Z Z Z eyigtag ig Edl CacMYBit a i b c i d a,b,c, d eyiga Z a ib (a ib(c id ac iad ibc i bd Et Z Z c id Z (c id(c id c i eka Z (ac bd i(bc ad ac bd bc ad i am[ Z Z Z ac c c d bd d (ac bd a (a a c c (c c a c d d c d bc c b d d (b (c c d ad d (bc ad abcd b d b c c d c b d ektaj Z a b edayekma Z duecñh Z Z Z Z c d d c (c d d abcd a Z Z d c a c (a d d b d b i 8
lmhat;ti9 ek[cmykmupøicbir Z ig Z currsaybba ak;fa Z Z Z Z dmenahrsay RsaybBa ak;fa Z Z Z Z eyigtag ig Edl CacMYBit a i b c i d a,b,c, d eyigma Et Z Z (a ib(c id ac iad ibc i bd Z Z am[ Z (ac bd i(ad bc eka Z Z (ac bd (ad bc Z a (a c c abcd b b c (a d d a b d d i abcd b c c (a b d (a b (a b (c ektaj d edayekma Z Z a b c d Z Z a c b d duceh Z Z Z Z 9
lmhat;ti ek[cmykmupøicbir Z ig Z k> currsaybba ak;fa Z Z Z Z > Taj[afa ( a c (b d a b c d cmebahrkb; a,b,c, d CacMYBit dmenahrsay k> RsaybBa ak;fa Z Z Z Z kñúgbøg;kmupøic eyigerciserisviuctr½bir ( XOY ig am[viuctr½ Z Z V U ig Z Z U magahvik tamlkçn³rcugrbs;rtiekaneka U V U V eday ³ U Z U V Z, V Z Z duceh Z Z Z Z V magahvikerogkña > Taj[afa ( a c (b d a b c d eyigtag ig Edl CacMYBit a i b c i d a,b,c, d ma am[ Z (a c i(b d Z Z (a c (b d Z Z Z
ehiy Z a b, Z c tamsrmayageliekma Z Z Z Z duceh ( a c (b d a b c d lmhat;ti ek[cmykmupøic ³ d Z i, Z i, Z 8 i k> curkna Z, Z, Z ig Z Z Z > Tajbgðajfa Z Z Z Z Z Z ig Z Z Z Z Z Z dmenahrsay k> KNa Z, Z, Z ig Z Z Z eyiga Z 9 6 ehiy Z Z ( 8 Z Z Z ( 6 69 89 7 ( i ( i ( 8 i eka Z Z Z 7 9 76 6 duceh Z, Z, Z 7 ig Z Z Z 7 i
> Tajbgðajfa ³ Z Z Z Z Z Z ig Z Z Z Z Z Z eyigma Z Z Z ehiy Z Z Z 7 duceh Z Z Z Z Z Z mü:agetot Z Z Z Z ig Z Z 7 duceh Z Z Z Z Z Z lmhat;ti ek[smikar (E: a b, a, b IR curkmt;cmybit a ig bedim,i[cmykmupøic i Cab srbs; smikarrycknab smyyetotrbs;smikar dmenahrsay kmt;cmybit ig ³ a b edim,i[cmykmupøic Cab srbs;smikarlu³rtaetvaepþógpþat;wg i smikar
eyiga ( i a ( i b 9 i i a ia b, i 9 i a ia b ( a b i( a a a 6 a b a 6, b ektaja am[, b duceh KNab smyyetotrbs;smikar ³ cmebah smikarkøayca a 6, b 6Z Z tamrtwsþibtevüteyigma edayeksáal; Z 6 i eka 6 Z 6 ( i i ducehb smyyetotésmikarkw i Z Z lmhat;ti ek[cmykmupøic i k>cursresr CaTMrg;BiCKNit >cursresr ig CaTMrg;RtIekaNmaRt K>TajrktMélRakdé dmenahrsay Z cos ig 8 si 8 k-sresr CaTMrg;BiCKNit eyiga ( i Z
duceh ( ( (i (i i i i -cursresr ig CaTMrg;RtIekaNmaRt ekma duceh i cos isi i cos isi cos isi 8 8 ig K-TajrktMélRakdé cos ig si 8 8 cos isi 8 8 i tamsmrayageliektaj duceh cos 8 ig si 8 8
lmhat;ti ekegaycmykmupøic ³ 6 i ig i k>cursresr ig CaragRtIekaNmaRt, Z >cursresr K>TajeGayafa dmenahrsay k>sresr, ekma duceh ekma duceh ekma Z CaragBiCKNit ig 6 cos ig Z CaragRtIekaNmaRt³ 6 si 6 i i cos isi 6 6 cos( isi( 6 6 i i cos isi cos( isi( Z cos( isi( 6 6 Z cos isi CaragBiCKNit Z duceh > sresr eka 6 i ( 6 i ( i 6 i 6 Z ( i ( i( i i
duceh 6 6 Z i K> TajeGayafa ³ 6 ig 6 cos si tamsrmayageliekma ³ Z cos isi ( ig 6 6 Z i ( pþwmtmak;tmg! ig @ eka ³ 6 6 cos isi i duceh 6 ig 6 cos si 6
lmhat;ti ek[cmykmupøic i k-curbgðajfa (cos isi -cursresr Z K-cUrKNatémøé dmenahrsay CaGuKm_é S CaTRmg;RtIekaNmaRt k-bgðajfa (cos isi ekma i tag ig a b eyiga a cos ( cos 6 6 cos cos cos cos mü:agetot b eka duceh cos si si cos isi (cos isi cos isi 7
-sresr Z CaTRmg;RtIekaNmaRt ³ eyigma isi (cos eyiga isi (cos ] isi [(cos Z 6 isi 6 cos 8 cos 8 isi 8 cos 8 cos 8 isi( 8 cos( 8 cos 8 isi 8 (cos 8 cos isi (cos 8 cos 8 isi 8 cos isi (cos isi cos ( isi (cos duceh 6 isi 6 cos 8 cos Z K-KNatémøé S tamrubmþdwmr½eyigma ³ isi cos ig isi cos eyiga isi cos isi cos S duceh cos S 8
lmhat;ti6 ek[cmykmupøic Z cos isi currsaybba ak;fa 6 6 ( Z 8cos (cos isi dmenahrsay RsaybBa ak;fa ³ ( Z 6 6 8cos (cos isi Z cos isi eyigma tamrubmþ cos cos ig si si cos eyiga Z cos isi cos b Z cos (cos isi tamrubmþdwmr½eyiga ³ ( Z cos (cos isi 6 6 8cos (cos isi 6 6 ( Z 8cos (cos isi duceh 9
lmhat;ti7 ek[cmykmupøic Z ( i k-cursresr Z CaTRmg;RtIekaNmaRt -KNab sti# é Z dmenahrsay k-sresr CaTRmg;RtIekaNmaRt ³ Z eyiga Z ( i 8( i 8( cos isi 8 cos( isi( 8(cos Z 8 (cos isi duceh -KNab sti# é Z eyigtag Cab sti# é W Z 8 (cos isi isi k k k W r cos( isi( k k k W k 8 cos( isi( : W (cos isi : W (cos isi : W 9 9 (cos isi tamrubmþb sti : eyiga -ebi k -ebi k -ebi k
lmhat;ti8 curknab sti écmykmupøic Z cmebah,,,, 6 dmenahrsay KNab sti écmykmupøic Z cmebah,,,, 6 eyigma Z cos( k isi( k tag Cab sti é eyiga ³ Wk Z W k ( k ( k cos isi eka ( k ( k W k cos isi k : W cos isi i k : W cos isi i eka (k (k W k cos isi k : W cos isi i k> cmebah -ebi -ebi > cmebah -ebi -ebi k : W cos isi -ebi k : W cos isi i K> cmebah eka (k (k cos isi -ebi k : W cos isi i W k
-ebi k : W cos isi i -ebi k : W cos isi i -ebi 7 k : W cos isi i X> cmebah eka ( k ( cos isi -ebi : W cos isi -ebi : W cos isi -ebi k : W cos isi -ebi : W 7 7 cos isi -ebi : W 9 9 cos isi g> cmebah eka 6 ( k ( cos isi 6 6 -ebi k : W cos isi i 6 6 -ebi k : W cos isi i k k k k W k W k k : W cos isi i 6 6 7 7 k : W cos isi i 6 6 k : W cos isi i k : W cos isi i 6 6 -ebi -ebi -ebi -ebi k k
lmhat;ti9 KNab sti écmykmupøic cmebah,,,, 6 Z i dmenahrsay KNab sti écmykmupøic Z i cmebah,,,, 6 eyigma³ Z i cos( k isi( k tag k ( k ( k W k cos isi eka ( k ( k W k cos isi k : W cos isi i k : W cos isi i Cab sti é W Z i cos( k isi( k tamrubmþeka k> cmebah -ebi -ebi > cmebah eka (k (k cos isi 6 6 -ebi k : W cos isi i 6 6 -ebi k : W cos isi i 6 6 W k
-ebi k : W cos isi i eka (k (k W k cos isi 8 8 k : W cos isi 8 k : W cos isi 8 9 9 k : W cos isi 8 k : W cos isi 8 eka ( k ( k W k cos isi k W cos isi k W cos isi i k 9 9 W cos isi k W cos isi k 7 7 W cos isi eka ( k ( k W k cos isi k W cos isi k W cos isi k W cos isi i k W cos isi K> cmebah -ebi 8 -ebi 8 -ebi 8 -ebi 8 X> cmebah -ebi -ebi -ebi -ebi -ebi g> cmebah 6 -ebi -ebi -ebi -ebi
-ebi 7 7 W cos isi -ebi 7 7 k W cos isi i k
lmhat;guvtþ_!> cursresrcmykmupøicagerkamcatrmg;bicknit Z a i b k> a / Z ( i( i b / Z ( i( > a / Z ( i ( i b / Z ( i ( ³ i( i K> a / Z ( i ( i b / Z X> a / Z 7i i b / Z g> i a / Z ( i( i b / Z @> curkmt;bircmybit ig edim,i[cmykmupøic a b Cab smyyrbs;smikar (E: a b i ( i ( i 9 7i i i i i #> curkmt;bircmybit ig edim,i[cmykmupøic a b i Cab smyyrbs;smikar (E: a b $> ekmasmikar (E: 6i k-kmt;cmybit edim,i[ Cab srbs;smikar b b i E -curedahrsaysmikar kñúgsmnmukmupøic ( E %> ekmasmikar (E: ( i ( i ( k-curepþógpþat;fa 8 i (7 i -curedahrsaysmikar kñúgsmnmukmupøic ( E 6
^> ekmasmikar Edl (E: (a ib a i a,b IR kmt;témø ig edim,i[ Cab smyyrbs;smikar a b i ( E ryccurkmt;rkb s myyetotcmebahtémø ig EdlarkeXIj a b &> ekmasmikar (E : ( i ( 9i ( 8i k-kmt;cmybit edim,i[ Cab srbs;smikar b b i ( E -cursresrsmikar Carag Edl ig ( E ( ( p q p q CacMYkMupøiucBIrEdleKRtUvrk K-cUrepÞógpÞat;fa 8 6i ( i rycedahrsay smikar kñúgsmnmukmupøic ( E *> curedahrsaysmikaragerkamkñúgsmnmukmupøic ³ a / b / c / i ( i ( i ( i ( i ( i ( i ( 7i ( i (> curbegáitsmikardwerktibiredlma ig Cab skñúgkrniimyy² agerkam ³ k> a / i, i > a / i, i K> a / i, i b / i, i b / i, i b / i, i!> ekmacmykmupøic ig i i cursresrsmikardwerktibirmyyedlma Z 7
ig Cab s> Z!!> curkmt;rkcmykmupøicedlmam:udúlesµi ehiykaerrbs;va 8 CacMYimµitsuTæ!@> curkmt;bircmybit ig y ebiekdwgfa ³ 8 9i ( i( iy ( i( iy i!#> curkmt;bircmybit ig y ebiekdwgfa ³ i ( i( y ( i( y i!$> ekmasmikar (E : a b c, a, a,b,cir curbgðajfaebi Cab ssmikar eah k¾cab srbs; Edr ( E ( E!%> ekmacmykmupøic i ig i k-curbegáitsmikardwerktibirmyyedlma ig Cab s -ektag cmebahrkb; IN currsaybba ak;tmak;tmg S S S S K-edaymiac;BøatcUrKNa? N i i!^> ekmasmikar (E : ( i,, IR * curbgðajfasmikar b sbirsutæetcacmyimµitsutæedlekwgbba ak; ( E!&> ekmasmikardwerktibir (E : A B C Edl ehiy CacMYkMupøic 8 A A,B, C
k> bgðajfaebi eahsmikar mab sbirkmt;eday ³ A C i B ( E C i, i A > bgðajfaebi eahsmikar mab sbirkmt;eday ³ A C i B ( E C i, i A K> Guvtþ_ ³ curedahrsaysmikaragerkamkñúgsmnmukmupøic ³ a / ( i b / ( i ( i i ( i ( i!*> ek[cmykmupøic ig i i curkmt;rkepñkbit igepñkimµitécmykmupøic W ebiekdwgfa W Z Z Z!(> ekmacmykmupøic ig Edl ig i ( i curkmt;epñkbit ig Epñkimµité Z Z @> ekmasmikar (E:iZ ( i Z ( i k> kmt;cmybit edim,i[ a Cab smyyrbs;smikar a i ( E rycknab s myyetotrbs;smikar Z > curkmt;cmybit ig edim,i[ p q q p q Z @!> ekmacmykmupøicbir ig Z k> curbgðajfa (Z (Z Z Edl p Z Z Z Z ig Z i Z i Z > curkmt;rkepñkbit ig Epñkimµit é Z Z Z Z 9
K> curepþógpþat;fa ryckmt;rk ig Z Z Z Z (Z Z Z @@> ekmacmykmupøic ig Edl Z i y Z y iy,y IR curkmt; ig edim,i[ y Z Z ( 6 i 7 @#> ek[cmykmupøic ³ ig (a b i(b c, Z (b c i(c a (c a i(a b Z Edl, b, c a CabIcMYBitusKña curbgðajfa Z Z Z Z Z @$> curknab skaerécmykmupøicagerkam ³ k> a / Z 8 i b / Z > a / Z i b / Z K> a / Z 8i b / Z Z i 77 6i i 6 @%> cursresrcmykmupøicagerkamcatrmg;rtiekanmart ³ k> a / Z i b / Z i > i a / Z b / Z i K> a / Z 6 X> a / Z i i b / Z i b / Z i g> a / Z i b / Z i Z Z
@^> cursresrcatrmg;rtiekanmartécmykmupøicagerkam ³ k> a / Z cos isi b / Z si 9 9 > a / Z si i( cos b / Z cos icos isi 7 7 K> a / Z cos i cos b / Z i ta 7 X> a / Z si icos b / Z ( (cos isi 8 8 g> Z cos i cos @&> curedahrsaysmikaragerkamrycsresrb simyy² CaragRtIekaNmaRt ³ k> a / b / > a / b / @*> cursresr Z i CaragRtIekaNmaRt @(> cursresr Z i CaragRtIekaNmaRt #> k-knatémørakdé ig si, cos ta -TajrkTRmg;RtIekaNmaRté Z i #!> ek[cmykmupøic i 6 ig i k> cursresr > cursresr ig, CaTRmg; Z b i a Z CaTRmg;RtIekaNmaRt
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$(-edahrsaysmikar i i i %-ek[sivútécmykmupøic ( Z kmt;eday ³ Z ig Z ( Z Z KNa Edl IN edaysresrltæplerkamtrmg;rtiekanmart Z 6
emeroti limitégukm_ -iym&y GuKm_ malimitesµi kalna f ( L itcit ma&yfacmeba¼rkb cmy ekmacmy Edl eká ekkmt sresr ½ -RTwsþIbTlImIt / / / / / f ( g( kf ( f ( g( f ( g( f ( L f ( ; IN * f ( k f ( f ( f ( f ( g( ; ; f ( L g( k IR g( g( -RTwsþIbTlImItGuKm_RtIekaNmaRt / / si ta si ta 7
-limiteqvg-sþam ebiekma f ( L & ea¼ Edl tagerogkñacalimiteqvgigsþam f ( & f ( -PaBCab égukm_ k-pabcab Rtg cmucmyy f ( L f ( L GuKm_ Cab Rtg cmuc lu¼rtaet y f ( f bmebjl&kç&nðbiducagerkam ½ ma&ylimit f ( ( CacMYBit f (a ma ( limitcacmybit f ( f ( f ( ( limitesµiwgtémøégukm_rtg cmuc -PaBCab eliceøa¼myy -GuKm_ eliceøa¼ebik lu¼rtaet f ( ] a;b [ Cab cmeba¼rkb cmyeakñúgceøa¼ebikea¼ f ( -GuKm_ eliceøa¼ebik f ( a ; b lu¼rtaet f ( Cab eli igma ] a; b [ f ( f (a ; f ( f (b a b 8
6-RTwsþIbTtémøkNþal ebigukm_ Cab eliceøa¼ f ( a ; b ehiy ea¼y agehacnas macmy f (af (b myyeaceøa¼ ig Edl a b ( y f y a b a b 7-lImItRtg Gþ ebi CaGuKm_mYy ig CacMYBit f ( L f ( L ma&yfacmeba¼rkb Edl M f ( L f ( L ma&yfacmeba¼rkb Edl N f ( L ekmacmy kalna M ekmacmy kalna N 9
8-lkçN¼lImItRtg Gþ / k f ( k f ( ; / f ( g( g( f ( g( f ( g( / f ( / f (g( f ( / g( f ( g( ; g( (lkçn¼limitrtg 9-GasIumtUtéEßekag k GasIumtUtQr GuKm_ f ( f ( g( duckñawglimitrtg Edr ebi y f ( f ( a ea¼ekfabþat masmikar érkabtag ( y f a a CaGasIumtUtQr (C : y = f( = a GasIumtUtedk GuKm_ ebi y f ( f ( b ea¼ekfabþat masmikar f ( b CaGasIumtUtedk y b
érkabtag ( f y y = b (C : y = f( K GasIumtUteRTt GuKm_ ebiekgacsresr y f ( f ( a b g( EdllImIt ea¼ekfabþat masmikar g( CaGasIumtUteRTtéRkabtag y a b f ( y (C : y = f( y = a + b
lmhat;ti curknalimitagerkam ³ k> > * IN, dmenahrsay KNalImItageRkam ³ k> 6 ( ( ( ( ( ( ( ( ( ( ( duceh > 6 > * IN, ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( duceh (
lmhat;ti curknalimitagerkam ³ k> > * IN, ( K> * IN m,, m m dmenahrsay KNalImItageRkam ³ k> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( duceh > * IN, (
( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( duceh ( K> * IN m,, m m m m m m m m m m m duceh m m m
lmhat;ti curknalimitagerkam ³ k> ( ( ( > IN *, ( ( ( ( dmenahrsay KNalImItageRkam k> ( ( ( 6 ( ( ( ( ( ( ( ] ( [ ( ( ] ( [ ( ( duceh 6 ( ( ( > IN *, ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ] ( [ ( ( ( ( ] ( [ ( ( duceh ( ( ( ( (
lmhat;ti curknalimitagerkam ³ k> ( ( > * IN, ( ( dmenahrsay KNalImItageRkam ³ k> ( ( duceh ( ( > * IN, ( ( tamrubmþetvfajútu C C C C C ( ( C C ( C C ( C C ( duceh ( ( ( 6
lmhat;ti curknalimitagerkam ³ k> ( > * IN, ( ( dmenahrsay KNalImItageRkam ³ k> ( 6 ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( duceh 6 ( > * IN, ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 7
lmhat;ti6 curknalimitagerkam ³ k> > * IN,p, ( p p dmenahrsay KNalImItageRkam ³ k> 6 ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( duceh > * IN,p, ( p p p ( p ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( p p p p p p duceh p ( ( p p 8
lmhat;ti7 curknalimitagerkam ³ k> a ( > b ( a ( p K> IR IN *,a,b,p, b ( a ( p dmenahrsay KNalImItageRkam ³ k> a ( a a a ( a ( a a ( a ( a ( duceh a a ( > b ( a ( p bp a b ( a ( b ( a ( p p duceh bp a b ( a ( p K> IR IN *,a,b,p, b ( a ( p a bp a ( b ( a ( a ( b ( a ( p p 9
lmhat;ti8 KNalImItageRkam ³ k> c> 8 8 > q> K> C> 6 6 X> 6 6 Q> g> KNalImItageRkam ³ k> 8 ( ( ( ( ( ( ( duceh > 6 ( ( ( ( ( ( ( 8 ( ( ( 6
K> ( ( ( ( duceh X> 6 6 6 6 6 ( 6 ( ( 6 ( ( 6 6 6 6 duceh 6 6 g> 6 ( ( ( ( ( ( ( ( duceh 6 6
c> 8 8 8( ( 8 duceh 8 8 q> ( ] ( [ duceh C> 6 6 6 8 8 8 6 6 6 6 6 ( 6 6 6 ( 6 6 6 6 6 duceh 6 6 Q> 6 ( ( ( ( ( 6
lmhat;ti9 curknalimitagerkam ³ A 6 6 dmenahrsay KNalImItageRkam ³ 6 A 6 tag U 6 V 6 6 6 6 6 6 ( ( ( (6 6 6 6 Edl 6 6 W 6 ( 6 ( W ( ( 6 ( ( ( ( 6 tag 6 6 T 6 6 ( W 6 ( 6 U V A 6 T U V 6 T 6 6
duceh 6 6 6 ( (6 (6 ( ( ( ( W 6 6 6 ( ( ( 6 6 6 ( (6 ( 6 ( 6 ( ( 6 ( ( ( W ( 6 78 66 7 6 6 6 A 6 6
lmhat;ti KNalImItéGuKm_ageRkameH A dmenahrsay KNalImIt ³ A 7 8 ( ( ( ( ( ] [ ( ( ( ( ( ( ( ( ( 6
lmhat;ti curknalimitagerkameh k> cos c> si > ta q> si K> si si C> si si X> cos cos Q> cos cos g> cos( j> dmenahrsay KNalImIt ³ k> cos si cos ( cos( cos cos si si ( cos cos si si ( cos cos cos si ta si duceh 6 > eday ta si cos cos cos cos cos cos ta si cos cos cos cos ( cos si cos ta 6 66
ta costa ta ( cos si ta ta si si si si si si si cos si (si si duceh K> si ( cos si si si si si si si ( si duceh si si si si X> cos cos cos cos ( cos ( cos ( cos cos ( cos ta si si si si si si cos si si cos si si si si si cos cos cos cos cos duceh 67
g> cos cos( 8 6 6 ( si (si (si si (si si cos( si duceh 8 cos cos( c> cos cos cos cos si ( si cos ( cossi si cos ( cos cos ( cos cos cos ( cos ( duceh > cos cos q> cos cos cos cos cos cos 68
cos cos si ( si cos cos si si duceh cos cos C> ta cos 8 cos ta ( si cos ta ( si cos ta ( cos cos ta ( cos duceh 8 ta cos Q> cos cos cos si cos si cos cos si si cos si cos cos si si( si cos si cos cos si si cos ( si cos si cos cos cos cos cos si 69
lmhat;ti curknalimitagerkam ³ cos cos cos A coscos coscos B dmenahrsay KNalImItageRkam ³ cos cos cos A 7 9 ( si coscos si cos si coscossi cossi si cos coscos( cos cos( cos ( coscos coscos B ( ( ( si cos coscos( si cos si si cos coscos( cos si si cos ( cos coscos( cos cos( cos ( 7
lmhat;ti KNalImItageRkam ³ cos A cos cos cos cos B dmenahrsay KNalImIt cos A ( cos cos cos ( ( si cos cos cos ( si cos cos cos cos ( ( duceh cos A cos cos cos cos B 7
( ( cos cos cos ( cos ( cos ( cos ( duceh ( cos cos cos cos B lmhat;ti KNalImItageRkam ³ k> ( si c> ta ( > cos q> ta ( K> cos si C> si ta X> cos si Q> si g> ta j> cos 8 7
dmenahrsay KNalImItageRkam ³ si k> tag ( am[ kalna eah si( cos si si 6 8 ( si ( 8 cos am[ kalna cos( si ( si si duceh > tag eah 7
cos si cos am[ si( cos( ( duceh K> tag ( duceh X> cos si si kalna eah si ( cos si cos si cos am[ kalna si( cos si cos ( tag si eah 7
si si cos ( cos si ( si cos si si ( si cos duceh g> tag 8 cos ta am[ ( ta( ( ( cos kalna eah ta ta ta ( ( ta ( ta duceh c> tag am[ kalna eah cos 8 7
( ta ( 6 ( ta( ( ta duceh q> tag ( ( ta 6 ta am[ kalna, eah ta( ta cot ta duceh ( ta C> ta si tag am[ kalna, eah ta ta( ta si( ( cos si ta ( cos si ( ta ( cos ta si ( ta ( ( 76
ta duceh Q> tag si si am[ kalna, ( si( ( cos si duceh si eah cos cos si si 77
lmhat;ti KNalImItageRkam ³ k> > K> X> g> ( ta c> cos ( si cos cos ta si q> ( C> Q> j> si ( ta ( cot dmenahrsay k> ( ta am[ ( ta tag kalna, eah 78
u, u u eah kalna am[ tag u ta u u ( u u cot( u ( u u u ta( u ( u ( u u ( ]ta u u ( [ u u u u duceh ta ( > cos, eah kalna am[ tag cos ( u, u u eah kalna am[ tag u si u ( u ( u ( u cos( u ( u u 79
u si u u ( u u si u ( u u u si u ( u u u 8 u u u 8 u u u duceh cos K> si (, eah kalna am[ tag si ( u, u u eah kalna am[ tag u u u u 8 u si u ( u ( u si u ( u u cos ( u ( u ( u si( u ( duceh 8 si ( 8
X> tag t tag duceh g> tag tag cos t t t cost ( tcos t t t t ( t t u t t u ebi t u ( u cos( u u si u u u ( u u cos cos am[ kalna, eah ( cos ( cos u u ebi u ( u 6u u u ( u cos( u ( usi u 6 u u si u u ebi 8
duceh cos c> ta, eah kalna am[ tag ta ta u, u u eah kalna am[ tag u u ta u u ( u u u ta ( u ( u ( u ta( u ( u u u duceh ta q> ( si, eah kalna am[ tag ( si ( ( si 8
u, u u eah kalna am[ tag u u u 6 u cos ( u ( u ( u] si( [ u ( 6 8 u ( u si u ( 8 6u u si u ( u u duceh ( si C> si, eah kalna am[ tag si si u, u u eah kalna am[ tag u si u u u usi( ( u u u 8
duceh si Q> 8 ta ( j> cot ( 8
lmhat;ti6 ek[gukm_ f ( a b curkmt;cmybit a ig b edim,i[ f ( dmenahrsay kmt;cmybit a ig b ³ eyigma f ( a a(? b 8 b( (8a b ( a( ( b( ( (8a b 8a b a( b( edim,i[ f ( luhrtaet ig RKa;Et 8a b ig a( b( a b b eyigarbb½æ 8 a b a b ( ( dksmikarbirehggáigggáeka a am[ a 6 yktémø a 6 CYskñúgsmIkar! eka 8 b am[ b duceh a 6, b 8
lmhat;ti7 ek[gukm_ f ( a b a, b k> curkna f ( cmebah > kmt;témø a ig b edim,i[ f ( dmenahrsay k> KNa f ( ³ cmebah a, b eyiga ³ f ( ( ( ( ( duceh f ( > kmt;témø a ig b eyigma f ( ( a b a( b( (a b a b a( b edim,i[ f ( luhrtaet a b ig a( b b a b ( b a b 86
am[ a b ( dksmikar! ig @ eka a 8 am[ a 8 ig b a duceh a 8 ; b lmhat;ti8 curknalimitagerkam ³ k> ( 7 ( ( ( ( c> ( > q> ( ( ( ( ( ( K> C> 8 X> 7 8 Q> g> 7 j> dmenahrsay KNalImItageRkam ³ k> ( 7 ( ( [ 6 6 ] 87
( ( ( ( ( ( 7 7 7 duceh ( ( ( 7 > ( ( 8 duceh 8 ( ( K> 8 8 8 ( duceh 8 88
X> 8 7 6 8 7 8 7 duceh 8 7 g> 7 7 7 7 7 duceh 7 c> ( ( ( 89
( ( ( ( ( ( ( duceh ( ( ( q> ( ( ( (! ( ( ( ( ( ( ( ( ( duceh! ( ( ( ( C> ( ( 9
duceh Q> ( ( duceh j> ] 6 6 [ 6 ( 6 ( 6 ( 6 ( ] 6 ( 6 ( 6 ( 6 ( [ 6 ( 6 ( 6 ( 6 ( 6 ( 6 ( 6 ( 6 ( 6 6 6 6 6 duceh ] 6 6 [ 9
lmhat;ti9 KNalImItageRkam ³ k> > dmenahrsay KNalImIt k> ( ( ( duceh > ( ( ( ( ( ( ( 9
lmhat;ti KNalImItageRkam ³ k> > 6 dmenahrsay k> ( ] ( [ ( ( ( ( 6 duceh > 6 ( ( ( ( ( 6 ( ( 9
lmhat;ti KNalImItageRkam ³ k> > K> ( 7 8 X> ( ( 9 9 g> ( ( ( 7 7 7 dmenahrsay KNalImIt k> 6 6 ( ( 6 ( ( 6 ( ( duceh > ( ( 9
duceh K> ( 7 8 ( erbah duceh ( 7 8 X> ( ( 9 9 tag k (k (k ( ( 9 9 S ( 9 ( 9 ( ( k k ( k k ( k k duceh S g> ( ( ( 7 7 7 tag ( ( ( 7 7 S ( ( 6 ( ( ( ( 7 7 ( 7 ( 6 (k (k (k (k 6 (k (k (k k k 9
duceh S [ ] 6 ( ( lmhat;ti curknalimitagerkam ³ k> ( > K> X> ( ( ( (, g> c> dmenahrsay KNalImItageRkam ³ p p k k(k k> ( eyigtag S ( k (k k k k 96
( ( ( k k k k k k k k ( k k k k k duceh S > eyigtag ³ k k k ( S ( ( 7 ( ( ( k k k k k k k k duceh S K> 97
8 8 9 8 8 9 9 9 ( 9 ( ( ( ( 9 999999 999 99 9 duceh 8 X>, ( ( ( ( (, 8 duceh, ( ( ( ( g> tag k k k (k (k k (k (k k k P ( ( k k k k k k k k k k k k k k k k k k k k 98
duceh ( ( P c> p p k k(k p p p p p ( ( ( ( k k ( p p p p p k duceh k(k p p k lmhat;ti curknalimit ³ ta( dmenahrsay KNalImIt ³ ta( 99
ekma ( 8 (8 ( 8 eka ( 8 ta ta( L ( 8 cot BIeRBaH ( 8 cot ( 8 ta tag ( 8 y kalna eah y eka 8 8 8 8 ta y y 8 ta y y 8 ( ta y y y ( y cot L y y y y duceh 8 8 ta(
lmhat;ti curknalimitagerkam ³ e e k> c> e cos si > a b e e,a,b IR * q> si e e K> e e C> e si e X> e e e Q> (e (e (e g> j> dmenahrsay KNalImItageRkam ³ k> e e si e e e si e si e si e e e si a b e e,a,b IR duceh > * ta ta si e cos cos e cos e cos si
b a b b e a a e (e (e b a b a duceh b a e e b a K> e e e 8 6 e e 6 e (e (e (e duceh 8 e e e X> e e e ( e e e (e (e (e duceh ( e e e g> (e (e (e! e e e
duceh (e c> e e (e (e ( cos ( si e si e si e cos si ta e e si ta (e (e ( duceh q> si ta e si e ta si ta e e e si ta (e cos ta ta duceh si ta C> e ta (cos si e ta duceh e si ta (
Q> cos e cos cos e si 7 9 si e si si si si si si e si (e si si si si e si e si ( si ( e si si si lmhat;ti curknalimitégukm_agerkam ³ k> l( l( c> > 9 l( 6 l( q> K> e 6e C> l(e X> e e 9e e Q> l( l( 6 g> (e ( j> l(e
dmenahrsay KNalImItéGuKm_ageRkam ³ k> l( l( l l l duceh l( l( > 9 l( 6 l( l 9 6 l 9 6 l ( (9 (6 ( l 9 6 l duceh l 9 l( 6 l( K> e 6e 6 e e 6 e ( e e (6 e erbah e duceh e 6e X> e e 9e e
e 9e e e 9e e erbah e duceh e e 9e e g> (e ( tag y ebi eah y y e 6 y e ( y e y ( (e ( y y y y y y y y duceh (e ( c> ( ( ( ( erbah (, ( duceh q> ( ( ( ( erbah duceh 6
C> l(e e l( e ( e l e ( e e e l (e e l l(e l e duceh e l( l(e Q> l( l( 6 l 6 l( ] ( [l( ] ( ( [l ( l l( l( 6 6 6 6 6 6 duceh 6 l l( l( 6 7
lmhat;ti6 ek[gukm_ kmt;rkb;cmybit f Edl f ( k-curbgðajfasmikar mab scacmybitmyysßiteaceøah f ( ig -curbgðafarkb;cmybit ekma f ( ( ( K-KNalImIt dmenahrsay f ( A k-karbgðaj ekma f ( eka f ( ig f ( eday tamrtwsþibttémøknþal eahmacmy f (f ( 6 c myyeaceøahcmy ig Edl f (c duceh smikar mab scacmybitmyysßiteaceøah ig f ( -bgðafa f ( ( ( ekma f ( ( ( ( ( ( ( ( ( ( 8
duceh f ( ( ( f ( K-KNalImIt A eday f ( ( ( eyiga A ( ( ( ( 6 f ( duceh A lmhat;ti7 ek[gukm_ si cos ( f ( ebi ebi cursiksapabcab;égukm_ Rtg;cMuc f? dmenahrsay siksapabcab;égukm_ f Rtg;cMuc ekma si cos f ( ( 9
tag t am[ kalna eah t t eka f ( t si( t cos( t t si cos t t t t cos t cos t t si t t ( t si t cos si t t cos cos t si si t t cos t t (cos t t f ( si t si eday f ( f ( am[ CaGuKm_Cab;Rtg; f ( lmhat;ti8 ek[gukm_ si( kmt;rkb; f ( t t etiekgacbøaygukm_ [Cab;Rtg;cMuc f ab et?ebigac curkmt;rkgukm_bøaytampabcab;égukm_ Rtg;cMuc f ( dmenahrsay kmt;rkgukm_bøaytampabcab;
ekma f ( tag si( am[ t t eka si( f ( t ( t kalna eah t t si( t t t t si( t t t( t t t si( t t t t t f ( eday kmt; eahekgacbøaygukm_ f ( [Cab;Rtg;cMuc ebieyigtag CaGuKm_bøaytamPaBCab;éGuKm_ g( f ( Rtg;cMuc eahekgacsresr ³ duceh si( f ( g( f ( ebi ebi
lmhat;ti9 ek[gukm_ f kmt;eli IR eday k> curkmt;cmybit,b,c, d a edim,i[ ( c d ( a b f f > curtajrksmikargasiumtuterttrbs;esekag ( c taggukm_ f ( dmenahrsay y k> kmt;cmybit a,b,c, d edim,i[ c d f ( a b ekma f ( ( 6 ( 8 ( ( duceh a,b,c,d > TajrksmIkarGasIumtUteRTt ekma f ( eday ducehbþat; CasmIkarGasIumtUteRTtéRkab d : y c tag f
lmhat;ti ek[gukm_ 7 f ( k-curknalimit ryctajrksmikargasiumtutqrrbs; f ( Rkab tag[gukm_ ( c f -kmt;bicmybit edim,i[ C A,B, C f ( A B K-TajrksmIkarGasIumtUteRTtéRkab c dmenahrsay k-knalimit f ( eyiga 7 f ( 7 f ( cmebahrkb; ( tag f ig duceh f ( eday f ( am[ektajfabþat;masmikar GasIumtUtQréRkab -kmt;bicmybit ekma f ( A,B, CedIm,I[ C f ( A B 7 6 duceh A,B,C ( (
K-TajrksmIkarGasIumtUteRTtéRkab tag ( c f ekma f ( eday ducehbþat;smikar CaGasIumtUteRTtéRkab tag y ( c f lmhat;ti p q ek[gukm_ f ( k> curbgðajfagukm_ kmt;acaicþcmebahrkb; f IR > kmt;cmybit ig ebiekdwgfaesekag taggukm_ p q ( c f mabþat; y CaGasIumtUteRTt ehiykat;tamcmuc (, dmenahrsay k> bgðajfagukm_ f kmt;acaicþ ³ ekma f ( p q A eday ( (, IR duceh kmt;acaicþcmebahrkb; GuKm_f IR > kmt;cmybit ig p q edim,i[bþat; CaGasIumtUteRTtéRkab tag luhrtaet ³ y ( c f ( f ( eday p q (p (q f ( ( (
(p (q eka f ( ( p am[ p GuKm_ Gacsresr q f ( müa:getoteday ESekag taggukm_ kat;tamcmuc ( c f eahkugredaeécmuc ARtUvepÞógpÞat;smIkar A(, ( c 8 q q p,q eka f ( am[ duceh q
lmhat;guvtþ_!-edayerbiiym½ycurrsayfa ³!> ( 7 ^> ( @> ( &> ( 7 #> *> ( $> (> ( %>!> (si ( 6 @-erbiiym½ycurrsayfa l( l #-KNalImItageRkameH ³!> 7 ^> @> ( ( &> 7 7 7 #> ( ( *> 6 6 $> (> %>!> $- KNalImItageRkam ³!>, IN ^> ( 6
@> &> m ( m ( ( #> *> ( ( ( $> (> ( ( ( ( ( ( (! %>!> p p ( ( ( p p! %-kmt;témø m IR edim,i[ ³ m? a b 6 a b ^-kmt; aig b edim,i[ &-kmt; aig b edim,i[ 8 *-KNalImItageRkam ³!> $> @> 6 %> 6 #> (- KNalImItageRkam ³!> %> 7 @> ( ^> 8 6 #> &> 6 7
$> *> 6 6!-KNalImIt!!-KNalImIt!@-KNalImItageRkam ³!> ( ( ( ^> ( @> &> #> *> $> ( (> 6 6 ( ( ( %>,!> (!#-KNalImItageRkam ³!> $> ( @> 7 %> #> ( (, * IN 8
!$-KNalImItageRkam ³!> ^> @> &> #> *> ( 8 $> (> %> 8!> 6!%-cUrKNalImItageRkam ³!> %> @> $> 6 #>!^-curknalimitagerkam ³ 8 6 6!> si cos ^> ta si si si cos @> &> si cos cos 9
cos si #> *> cos si 6 cos $> ta cot (> si 8si ta si cos si %>!> cos 6 cos!&-curknalimitagerkam ³!> 6 ^> @> & > #> m * > e ( m ( ( $> ( > e e e e %> e!*-curknalimitagerkam ³ ( m m!> ( m m!> @> ( ( ( #> $> ( m m
!(- curknalimitagerkam ³ si si si 8 si!> ^> 6 si si si (si si[si(si ] @> &> #> si si si *> ta si si si si si si $> si si (> si %> si 6 si(ta ta(si!> @- KNalImItageRkam ³!> cos ^> cos cos cos ta si @> &> cos si cos cos cos cos #> *> si cos si cos cos $> (> %>!> cos cos @!- KNalImItageRkam ³!> si si ^> cos cos cos cos @> &> si cos cos #> *> cos cos coscos
cos $> (> cos( cos cos cos cos cos %>!> @@- KNalImItageRkam ³ si cos (!> cos ^> ta si ( @> &> si #> *> (si cos $> ( ta (> ( ta %> 8 @#-KNalImItageRkam ³ cos!> ( ta!> cos #> ta $> @$-KNalImItéGuKm_ageRkam ³ si @> si cos!> ^> si si si si
cos si cos cos si @> &> ta #> *> si cos(si cos $> si (> cos ta %> ta si!> cos cos( cos cos @%-KNalImItéGuKm_ageRkam ³ cos si ta!> ^> si si ta @> cos ( cos &> cos cos cos si si cos cos cos #> *> cos cos cos cos $> cos (> cos cos %> cos!> @^-KNalImItéGuKm_ageRkam ³ si!> ( ta ^> a si( a @> cos cosa ta &> si ta cos t si #> *> ( arcta $> ( ta (> arcsi cos arccos
%>!> cos @&-KNalImItéGuKm_ageRkam ³ cos ( cot!> ( ta ^> @> cos si &> cos cos #> *> ( ta 8 si si $> (> %> ( si!> @*-KNalImItéGuKm_ageRkam ³ si arccos!> si ^> cos @> &>> ta ( si #> ( cos $> ( ta *> cot( %> ta 6 (> cos!> cos cos
@(-KNalImItéGuKm_ageRkam ³ ( ( (!> #> @> $> #-curknalimitégukm_agerkam ³!> ( 7 9 @> ( 9 #> ( $> ( %> ( 7 ^> 6 &> ( 9 *> ( 8 8 (> ( #!-curknalimitégukm_ducteta ³!> ( @> ( 8 8 6 #> ( 6 $> ( 6 9 9 8 9
%> ( 8 9 &> *> l( (> (!> ( ( ( 6 #@-curknalimitagerkam ³!> ( @> 7 ( #> $> 8 %> ^> 7 7 ( ( &> ( *> (>!> ( 8 6
##-curknalimitagerkameh!> ( 6 ( ( ( @> cos cos cos cos #>, $> ( ( ( ( %> ( #$-curknalimitagerkameh!> @> 9 #> $> k %> (a cos a cos a cos a cos #%-KNalImItageRkam ³!>! (!!! @>! (!!!! #> 8 C C C C 7
! $> k k k k %> #^- ek[gukm_ f (, k> currsayfa f ( f ( f ( f ( f ( > KNa #&-k> currsayfa l(, > tag 9 l ( ( ( ( P curknalimit P #*-ek[sivútécmybit ig ( U U U V, V U U V V kmt;eday ( V, IN ³ k>curbgðajfa CasIVútFrNImaRt ryckna W U V W CaGuKm_é -curbgðajfa CasIVútefrRtUvkMt; t U V K-Tajrk ig CaGuKm_é rycbba ak;limitvakalna U V 8
#(-ek[sivút ( U kmt;eli IN eday ³ U, U ig IN: U U U k-ektag U IN :V l( curbgðajfa CasIVútFrNImaRt ( V U rycknaty CaGuKm_é V ig V -curbgðajfa U ryctajrk CaGuKm_é V l U U ig U $-ek[sivút kmt;eli eday ³ ( U IN U, U k k ig U U U curkna CaGuKm_é U ig $!> ek[sivút kmt;eli eday ( U IN ig U, U U U U V l(, IN U U k-ektag curbgðajfa CasIVútFrNImaRt ( V rycknaty CaGuKm_é V ig -ektag S V V V V U? V bgðajfa U U e ryctajrk U CaGuKm_é igbba ak;limit U S 9
$@-ek[gukm_ ( f kmt;eday ³ ( 6,f( 6 6,f ( 6 6 6, f f Edl ( 6 6 6 6 6 IN* ( curknalimit L ig L $#-ek[gukm_ kmt;eday ³ f ( f f ( f (, f (, f f (, ( Edl IN* curknalimit f ( ig f ( L L $$-ek[gukm_ kmt;cmebahrkb;cmybit eday ³ f ( f ( f ( ( ( curknalimit f ( $%-ek[gukm_ EdlkMt;eday f ( ( f ( curknalimit f ( ig f ( $^-ek[gukm_ si si f ( f curkmt;témø IN* edim,i[limit f ( CacMYBit $&-ekmagukm_ Edl f ( a b c a,a, b,c IR ig a b c KNalImIt f[f (] f (
$*-ek[gukm_ f ( ta cot Edl IN* curkmt;témørbs; edim,i[limit kmt; f ( $(-KNa si( ta( %-ek[sivút a Edl IN ( * k> KNa S a a a a > KNa LimS
emeroti edrievégukm_ -cmyedrievégukm_rtg cmucmyy ½ sµtfagukm_ f ( kmt eliceøa¼ ehiy I CacMYBiteAkñúg ceøa¼ I ig h CacMYBitmisUü Edl h Carbs I cmyedrievégukm_ f Rtg cmuc ( ebima CalImItrbs GRta kmeniégukm_ f rvag ig h kalna h itetarksuüedlekkmt sresr ½ f '( f ( h h f ( -PaBmaedrIev ig PaBCab ½ h sµtfagukm_ f ( kmt eliceøa¼ I ehiy CacMYBiteAkñúgceøa¼ I ig h CacMYBitmisUü Edl h Carbs I -cmyedrieveqvgrtg cmy égukm_ f ( kmt tageday
f ( h f ( f ' ( h h -cmyedrievsþamrtg cmy égukm_ f ( kmt tageday -edrievégukm_ f ( Rtg kmt tageday ½ f '( makalna f ( h f ( f ' ( h h ( ebima f ( h f ( f ( h f ( ehiy h h h h f ( h f ( f ( h f ( h h h h -GuKm_edrIev ½ k iym&y -ebi f CaGuKm_mYykMt eliceøa¼ I igmaedriev Rtg RKb cmuc eakñúgceøa¼ I ea¼ekfagukm_ f ma edrieveliceøa¼ I -GuKm_EdlRKb Rtg ehafa I pßmácmyedrievé f GuKm_edrIevé f EdleKkMt sresr : f '( f
smikarbþat b ¼ y ( C : y = f ( ( T M cmyedrievégukm_ f ( Rtg cmuc KWCaemKuN Ráb Tisé bþat b ¼wgEßekag c : y f ( ( Rtg cmuc magab sius ehiysmikarbþat b ¼ea¼kMt eday½ T : y y f '( ( ( rubmþégukm_edrievmyycmy GuKm_ edriev!> k @> y y' y y'
#> y y' y y' $> %> e y y' e ^> a &> y y' a la y l y' *> y si y cos (> y cos y' si!> y ta y' ta cos y y' ( cot si y arcsi y' y y' y y'!!> cot!@>!#> arccos!$> arcta K-rUbmþRKwHéedrIevGuKm_ GuKm_!> u @> y edriev y y' u'u u y' u' u #> y u v y' u' v v' u $> u v u' v y y' v v' u
%> u' y lu y' u ^> y si u y' u'cos u &> y cosu y' u'si u *> u e u y y' u'e (> y ta u y' u'( ta u!> u' y arcsiu y' u y y' u' u y arctau u' y' u y V u' y' u v'l u v u!!> arccosu!@>!#> V u -edrievbþbþab ½ «bmafaekma f ( CaGuKm_maedrIevTI eliceøa¼ I ekkmt edrievbþbþab égukm_e¼ducteta½ -GuKm_edrIevTImYykMt tageday f '( -GuKm_edrIevTIBIrkMt tageday f ''( -GuKm_edrIevTIbIkMt tageday f '''( -GuKm_edrIevTIbYkMt tageday ( f ( ------------------------------- -GuKm_edrIevTI kmt tageday f ( ( 6
-vismpabkmeimakmt ½ RTwsþIbT ½ ek[ CaGuKm_maedrIevelIceøa¼ f ( I ebimabircmybit m ig M Edl I m f '( M ea¼rkb cmybit a ig b CaFatuBIrkñúceøa¼ I Edl b a eká ½ m( b a f ( b f ( a M( b a «bmafa ekma ½ a I, I -ebi eká a m( a f ( f ( a M( a -ebi eká a m( a f ( a f ( M( a 7
lmhat;ti ek[gukm_ kmt;eli IReday f f ( k-edayerbiiym½ycurknacmyedriev f '( -cursresrsmikarbþat; Edlb:HwgESekag Rtg;cMuc ( T ( c M magab;sius dmenahrsay k-edayerbiiym½yknacmyedriev f '( tamiym½yeyiggacsresr ³ f '( f ( h f ( eday f ( h h ( h ( h ( h h 8 h 6h h 6 h 8 6 h h h 6h 9h h 6h 9 9 h h h f duceh '( 9 -sresrsmikarbþat; b:hwgesekag Rtg;cMuc ( T ( c M tamrubmþ T : y y y' ( eday eka ig f ( 8 6 ' f '( 9 eka ( T : y 9( ( y 8 y
b ( T : y 9 8 duceh ( T : y 9 am[ ( T : y 9 lmhat;ti ek[gukm_ f kmt;eli IReday si f ( f '( k-edayerbiiym½ycurknacmyedriev -cursresrsmikarbþat; Edlb:HwgESekag Rtg;cMuc ( T ( c M magab;sius dmenahrsay k-edayerbiiym½yknacmyedriev f '( tamiym½yeyiggacsresr ³ f '( f ( h f ( eday si f ( h h si( h si ( h ( h h si h h h h h si h h h si h h h h h h f duceh '( 9
-sresrsmikarbþat; ³ ( T tamrubmþ ( T : y y y' ( eday am[ ig f ( ' f '( y y duceh b ( T : y ( ( T : y lmhat;ti ek[gukm_ kmt;eday ( cmebahrkb; f f ( k-edayerbiiym½ycurknacmyedriev f '( -cursresrsmikarbþat; Edlb:HwgESekag Rtg;cMuc ( T ( c M magab;sius dmenahrsay k-edayerbiiym½yknacmyedriev f '( tamiym½yeyiggacsresr ³ f '( f ( h f ( h h ( h ( ( h h h h h h h h h h h( h f '( duceh h h
-sresrsmikarbþat; ³ ( T tamrubmþ T : y y y' ( eday am[ ( ig f ( ' f '( ( y eka T : y ( duceh T: y lmhat;ti ek[gukm_ kmt; ig maedrievrtg;cmuc f ( c y currsaybba ak;fa f (c h f (c h f '(cf (c dmenahrsay h? h RsaybBa ak;fa f (c h f (c h f '(cf (c tag h h f (c h f (c h L h h f (c h f (c h f (c h f (c h h h f (c h f (c h f (c h f (c h h h h f (c h f (c h f (c h f (c f (c h f (c h h h h f (c h f (c f (c h f (c h h h h f (c h f (c f c ( h f (c h h h ( h eday f '(c f '(c f '(c ig f (c h f (c h f (c f (c f (c
am[ L f '(c f (c f '(cf (c duceh f (c h f (c h f '(cf (c h h lmhat;ti ek[ CaGuKm_kMt;elI IReday f ( k-curknaedriev f '( f -kmt;témø edim,i[ rycknatémøelé f '( f ( cmebah témø Edla K-cUrrksmIkarbÞat; b:hwgesekag tag Rtg;cMuc ( T ( c f dmenahrsay k-knaedriev f '( ekma tamrubmþ u u' v ( ( ' v v eka ( ' ( ( f '( f ( ( ( ( ( ( ( duceh f '( ( ( v' u ' ( 8 6
-kmt;témø edim,i[ f '( eka am[ '( f ( eday ektajb s c a b c, duceh, a KNatémøelé ³ f ( ekma ( cmebah eka ( f f f ( 7 f (,f ( 8 9 9 cmebah eka 7 duceh K-rksmIkarbÞat; b:hwgesekag ( T ( c cmebah am[ 8 f ( y 6 kugredaeécmucb:hkw M (, tamrubmþ T : y y y' ( cmebah eka ' f '( ( y ( eka b ( T : y ( y duceh smikarbþat; b:hwgesekag KW ( T ( c T : y (
lmhat;ti6 ek[ CaGuKm_kMt;elI IReday p f ( ek]bmafamacmybit Edl a f (a curbgðajfa a p? f '(a a dmenahrsay bgðajfa a p f '(a a ekma p q ( eka ( p q' ( ( f '( cmebah f f '( f ' ( ( ( p( ( p q ( (a p(a a(a f '(a (a a ap q f (a a eka a tambmrab;ekma am[ ap q yk @ CYskñúg! eka³ f '(a a (a p(a a( (a (a p(a a p (a a a p f '(a a duceh q p q ap q (
lmhat;ti7 ek[ CaGuKm_kMt;eday f f ( ( Edl ig IR IN * k-curknaedriev rycbgðajfa f '( f '( f ( -currsaybba ak;tmak;tmg ( f ''( f '( f ( dmenahrsay k-knaedriev f '( ekma f ( ( eka f '( ( '( duceh ekma ( ' ( ( ( ( f '( ( eday f '( ( f ( ( am[ f '( f ( f '( f ( eka
duceh f '( f ( -RsaybBa ak;tmak;tmg ³ ( f ''( f '( f ( ekma am[ f ( f '( f ( f '( eka f ' ( ( f ''( ekma f ''( f ''( f '( ( f '( ' f ( f ( f ( f '( f ( ig f '( yk @ ig # CYskñúgTMak;TMg eka ³ f ''( f ( f ' am[ ( f ''( f ( f '( duceh ( f ''( f '( f ( f ( 6
lmhat;ti8 ek[ CaGuKm_kMt;elI IReday f f ( 6 9 currsaybba ak;fa ³ (6 9f ''( 6f '( f ( dmenahrsay RsaybBa ak;fa ³ (6 9f ''( 6f '( f ( ekma f ( 6 9 eka ektaj f '( f '( ( ( f ( 6 6 6 6 6 6 6 9 9' 9 9 9 9 9 6 9 6 6 6 ( 9 9 6 6 erbah f ( 6 9 f '( 6 9 eka ''( 6 9 eday f f '( f ( 6 9 9 f ( ( 6 9f ''( 6 9f '( 6 6 9 f ( 6 6 9f '( f ( 9 am[ yktmak;tmg ig CYskñúg! eka ³ duceh (6 9f ''( 6f '( f ( 9 7
lmhat;ti9 ek[ f CaGuKm_kMt;eday kmt;rkb; IR k-knaedriev f '( -KNatémø f ' ig ' dmenahrsay f ( f si si cos k-knaedriev f '( ekma si eka ³ f ( f '( si cos ( si ' ( si cos ( si cos ' ( si ( si cos cos( si cos (cos si( si ( si cos cos sicos cos cos sicos si si si cos cos si (cos si si cos ( si cos duceh cos si f '( cos si ( si cos ig f ' f ' f ' cos si ( si cos ( cos si f ' ( si cos ( -KNatémø eka ig 9 8
lmhat;ti ekmagukm_ f cos si k-curknaedriev ig f '( f ''( -KNatémø ig f '( f ''( dmenahrsay k-knaedriev ig f '( f ''( ekma cos f si (cos '( si ( si '(cos ( si si si cos si (si cos ( si ( si eka f '( duceh si ( si si f '( si ( si ' f '' ( ' si ( si cos f ''( ( si müa:getot cos duceh ( si -KNatémø ig f '( f ''( eka f ' si cos ( si ( f '' ig ''( f duceh ig f ' 9
lmhat;ti curknaedrievégukm_ ³ f ( si ig si( Edl CacMYKt;FmµCati dmenahrsay KNaedrIevéGuKm_ ³ ekma f ( si eka duceh ekma eka duceh f '( f '( (si g( cos g' ( g( cos cos( si( ( si ( si 'si( (si( 'si ( cossi si( si ( ( si si( (cos g' ( ( cos cos( ( cos si( ( cos( si cos si cos( ( si si( 'cos( (cos( 'cos ( si cos si cos( ( si( cos si( cos ( ( cos si( si cos( ( cos si(
lmhat;ti ek[gukm_ m ( Edl CacMYBit ig Caa:ra:Em:Rt m k-curkmt;témø edim,i[gukm_ matémøbrmartg;cmuc m f ( -curkmt;témø edim,i[gukm_ matémøbrmaetmyykt; m f ( dmenahrsay f k-kmt;témø m edim,i[gukm_ matémøbrmartg;cmuc luhrtaet f ( f '( ekma m ( eka ( m ' ( ( '( m f '( f ( m( ( ( m ( m m m 8 ( m 6 m f '( ( m m m f ' ( m cmebah eka am[
-kmt;témø m edim,i[gukm_ matémøbrmaetmyykt;luhrtaetsmikar f ( smmul mab setmyykt; f '( m 6 m ebalkwrtuv[ lmhat;ti m ek[gukm_ a b ( curkmt;témøécmybit ig bedim,i[gukm_ macmucbrma a f EtmYyKt; ehiyesekagrbs;vamabþat; CaGasIumtUtedk y dmenahrsay f kmt;témøécmybit ig a b ekma a b ( eka (a b( f '( f a b edim,i[gukm_ f ( (a 8a b b a ( (8a 6 b ( b b 6 matémøbrmaetmyykt;luhrtaetsmikar mab letmyykt; f '(
eday ' b 8a 6 f am[ b 8a 6 b b b mab letaletmyykt;luhrtaet müa:getotesekagrbs;vamabþat; CaGasIumtUtedkluHRtaEt y f ( eka a b a f a a, b duceh lmhat;ti ek[gukm_ k-curknaedriev p q Edl CacMYBitusBIsUü f ( ig f '( f '' -curkmt;cmybit pig edim,i[gukm_ matémøgtibrmaesµi q f ( cmebah dmenahrsay k-knaedriev ig f '( f '' ekma f ( p q p q q ( p ' RKb; q eka ig q f '( f '' ( ' q
duceh q q f ',f '' -kmt;cmybit pig q edim,i[gukm_ matémøgtibrmaesµi cmebah f ( luhrtaet ektaja ' f ' f f ' q f ' p q f ( q f '' 8 p, q duceh am[ q p f '' q lmhat;ti ek[gukm_ k-curknaedriev b Edl CacMYBitusBIsUü f ( a ig f '( f '' -curkmt;cmybit ig edim,i[gukm_ a b f ( esµi cmebah dmenahrsay k-knaedriev ig f '( '' matémøgb,brma f
ekma f ( a b eka b b ig b f '( (a ' a f '' (a ' b b a,f '' duceh f ' -kmt;cmybit a ig b edim,i[gukm_ matémøgb,brmaesµi cmebah f ( luhrtaet eka f ' f f ' f ' f f '' a ' a b b b duceh a, b am[ a b a b f '' b b a b f '' b
lmhat;ti6 ek[gukm_ a b markabtmag f ( c kñúgtrmuygrturemmyy k-esekag c kat;gks½gab;sius ' Rtg;cMucmaGab;sIus bgðajfabþat;b:h c Rtg; maemkunrab;tis a k -curkmt;témø ig edim,i[esekag a b c kat;gks½gab;sius abircmuc Mig NEdlbÞat;b:H c Rtg; Mig NEkgwgKña dmenahrsay y bgðajfabþat;b:h c Rtg; ekma eka maemkunrab;tis a k a b ( a b' ( ' a b ( ( a( ( a b ( f f ' ebi CaemKuNRab;Tisé bþat;b:h k c Rtg; eka a( ( a k ( b eka k f ' müa:getotesekag c kat;gks½gab;sius ' Rtg;cMucmaGab;sIus eka a b f am[ a b yksmikar CYskñúg eka ( a( a ( k 6
duceh a k -kmt;témø ig a b smikargab;siuscmucrbsbv Mig NrvagESekag c CamYy a b f b a b E tag ig k ' ³ CaemKuNRab;TisébÞat;b:H k crtg; Mig NeKa a M f ' ig f ' k M M tamsrmayageli edim,i[bþat;b:hehekgkñaluhrtaet a M k k M N N k N a N am[ ( a( a ( ( M a a ( M M M M N N a( a( N N M M N M N ( N N M a a a( M ( M M M N N N N N ( M M M N N a N N a eday ig Cab ssmikar eahekma E M N TMak;TMg Gacsresr ³ a b a b a M N a M N b M N b b b am[ b müa:getotedim,i[ c kat;gks½ ' abircmucmig NluHRtaEt 7
smikar E mab sbirepsgkña ebalkwekrtuv[ b eday ektaja BitCaic RKb;cMYBit b a duceh a IR, b lmhat;ti7 ek[gukm_ f ( (a be a,a, k-curknaedriev f ' ig f '' -kmt;cmybit ig edim,i[gukm_ a b f ( cmebah dmenahrsay a Edl b IR k-knaedriev f ' ig f '' eka f ' (a b'e (e '(a b ae e (a a be (a b ig f ''( (a a b' e (e '(a a b ae e (a a be (a a b duceh f ' (a a be,f '' (a a be a matémøgtibrmaesµi e 8
-kmt;cmybit a ig b edim,i[gukm_ f ( luhrtaet b matémøgtibrmaesµi cmebah e f '( f '( (a be eka f ( e f ( (a be e f ''( f ''( a b a am[ a b b f '' (a be f '' e a, b duceh lmhat;ti8 ek[gukm_ f ( e a b Edl a,a, b IR k-curknaedriev f ' ig f '' -kmt;cmybit ig edim,i[gukm_ a b f ( cmebah dmenahrsay k-knaedriev f ' ig f '' eka (e '(a b f '( e (a (a b (a b ae (a b b' e (a b ae (a b matémøgb,brmaesµi e 9
(a b ae (a b duceh f ' ( f '' duceh [(a b ae ]'(a b [(a b ]'(a b ae (a b [ae e (a b a](a b a(a b(a b ae (a b (a b e a(a b ae (a b f '' (a b (a b a (a b a e (a -kmt;cmybit ig a b edim,i[gukm_ matémøgb,brmaesµi ecmebah f ( luhrtaet lmhat;ti9 f '( f ( e f ''( b a(a b a e (a b bþab;biedahrsayeka a, b ek[ CaGuKm_kMt;elI IReday f f ( ( (e cursresrsmikarbþat; EdlRsbwgbÞat; ( T d : y ehiyb:hwgrkab tmaggukm_ ( c y f ( dmenahrsay sresrsmikarbþat; ³ ( T 6
tag CacMucb:HrvagbÞat; (, y etawgesekag T c tamrubmþ T : y y f ' ( edayekma am[ektaja T // d : y f '( M ( emkunrab;tisesµikña ekma f ( ( (e eka f '( ( ' (e (e ' ( e e ( e ( ( ektaj b am[ '( ( e e f ( cmebah eka f ( ( e e smikarbþat; T Gacsresr b T : y e ( y e duceh ( T : y e y 6
lmhat;ti ek[ CaGuKm_kMt;eday f k-curknaedriev '( f -curkmt;cmybit edim,i[ k f ( IR f ( si 6 cos 6 ksi cos CaGuKm_efrCaic cmebahrkb; dmenahrsay k-knaedriev f '( f '( duceh 6(si 'si 6cos si si (si 6cos si (si cos 6(cos ' cos 6si cos cos si ( cos k si cos k(si (k si (k si ( ksi cos (si k si cos cos si cos ksi cos f '( -kmt;cmybit k ' cos k si cos (cos edim,i[ CaGuKm_efrCaic cmebahrkb; f ( IR RKb; f '( IR eday f '( (k si k(cos k cos si si k si cos luhrtaet ektaj am[ k k 'si 6
lmhat;ti l ek[gukm_ f a b Edl ehiy a ig b CacMYBit k-bgðajfacmebahrkb;cmybit ig bedl ESekag a a C taggukm_ magasiumtuterttmyyedlekwgbba ak;smikar f -kmt;cmybit ig bedim,i[esekag a C taggukm_ f ( b:hetawgbþat; Rtg;cMuc T : y, dmenahrsay A k-bgðajfaesekag C taggukm_ f magasiumtuterttmyy l ekma f a b Edl l eday am[bþat; CaGasIumtUteRTt y a b éesekag C duceh ESekag C taggukm_ f magasiumtutertt y a b -kmt;cmybit a ig b ekma f l a b 6
eka (l ' f ' (a b' ('l l a edim,i[esekag C taggukm_ f b:hetawgbþat; T : y Rtg;cMuc A, luhrtaet f ' a am[ b a b a a b b duceh a, b f A A y T A l a l a b lmhat;ti ek[gukm_ p q Edl f ( k-curknaedriev f '( -curkmt;cmybit pig qedim,i[ ig f '( ( dmenahrsay ( f k-knaedriev f '( ekma p q Edl f ( eka ( p q' ( ( f '( ( ' ( p q 6
( p( ( ( p q p p ( p q p q ( p q ( duceh f ' ( -kmt;cmybit pig q eday ig f '( f '( ( p q ( 9 p q p q ( ektaj am[ p q ( ( ig am[ f ( p q 6 ( buksmikar! ig @ eka p bþab;mk q 6 p 6 9 duceh p,q lmhat;ti ek[gukm_ kmt;eli IReday f f ( si curbgðajfaedrievti égukm_ kmt;eday f f ( si( dmenahrsay? ( bgðajfaedrievti égukm_ kmt;eday f f ( si( 6 (
ekma f ( si eka erbah f '( cos si( si f ''( f '''( ( ' cos( si( ( ' cos( si( si( ]bmafavabitdl;edrievlmdab;ti KW Bit f ( si( eyigwgrsayfavabitdl;edrievlmdab;ti f Bit ( eyigma f ( ( KW ( ( si eday ( ( ( f ( (f (' f ( si( ( ( ( 'cos( si( si ( f ( si( eka ³ ( duceh Bit 66
lmhat;ti ek[gukm_ Edl f ( curbgðajfaedrievti égukm_ kmt;eday f f ( ( dmenahrsay! ( ( bgðajfaedrievti égukm_ kmt;eday! f f ( ( ekma tamrubmþ v' f ( ( ' v v eka ( '! f '( ( f ''( ( [( ( ( ( ( ]' 8! ( ( ( (! f ( ( ( KW ( ( ]bmafavabitdl;edrievlmdab;ti KW Bit eyigwgrsayfavabitdl;edrievlmdab;ti f ( ( ( eyigma f eday ( (! ( Bit eka! [( f ( ( ( (! f ( ( ( ( (f (' ( ]' (! ( (! Bit ( ( ( (! 67 ( ( ( duceh f (
lmhat;ti ekmagukm_ Edl CacMYBit f ( ( e k> curknaedriev f '(, f ''(,f ''' ig f > curbgðajfaedrievti égukm_ matrmg; f f ( (a b e Edl a ig b CasIVútcMYBitepÞógpÞat;TMak;TMg ³ a b a a b K> curkmt; ig a dmenahrsay, IN * CaGuKm_é ryctajrkkesam b f ( k> KNaedrIev f '(, f ''(,f ''' ig f ekma f ( ( e ( ( ( ( f '( ( 'e (e '( duceh e f '( e ( ( e e ( ( e eka f ''( ( 'e (e '( duceh f ''( e e ( e ( 6 ( ( 8e 8e eka f '''( ( 8' e (e '( 8 68
duceh f '''( e e ( 8 e ( 8 6 (8 (8 e e eka f ( (8 'e (e '(8 duceh ( f ( ( 8e e (8 e (8 6 (6 (6 8e >bgðajfaedrievti égukm_ matrmg; f tamsrmayagelieyigma ³ f '( ( e (a b e f ( ( (a b Edl, b a e 8e f ''( ( 8e (a b e Edl, b 8 a f '''( (8 e (a b e Edl 8, b a f ( (6 8e (a b ( a 6, b >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ]bmafavabitdl;edrievlmdab;ti KW ³ ( f ( (a b e e Edl 8 Bit eyigwgrsay[exijfavabitdl;edrievlmdab;ti KW ³ ( f ( ( eyigma eka (a f f f f f eday ( ( ( ( ( b e ( (f ( (a ( a ( e ( e ( (a (' b (a e a ( f ( (a b e ' e a (a (e b b e b '(a b 69
ektaj Bit f ( (a b e Edl ig a a b a b duceh edrievti égukm_ matrmg; f ( f ( ( (a b ig CasIVútFrNImaRtmaersug Edl a ig b CasIVútcMYBitepÞógpÞat;TMak;TMg a a ig b a b K>kMt; ig CaGuKm_é a b tamsrmayageliekma a a b a b cmebahrkb; IN * tamtmak;tmg a a am[ ( a igty a tamrubmþ a a q müa:getotekma b a b am[ektaj b b b a ebiektag c b e q b b eka efr am[ CasIVútBVþmaplsgrYm c c ( c igty b tamrubmþ c ( d ( eday am[ c b b c ( c c duceh a, b ( d 7
TajrkkeSam f ( ekma eday ig f ( (a b e a b ( eka f ( [ ( ]e ( e duceh ( ( f ( ( ³ ( ( e lmhat;ti6 ekmagukm_ f ( e si k> curknaedriev f '(, f ''(,f ''' ig f > curbgðajfaedrievti égukm_ matrmg; ³ f ( f ( ( (a si b cos e Edl a ig b CasIVútcMYBitepÞógpÞat;TMak;TMg ³ a b a a b b, IN * a i b K> ektag curbgðajfa rycsresr ( i CaTRmg;RtIekaNmaRt X> curkmt; ig CaGuKm_é ryctajrkkesam a b f ( ( 7