emeronti GnuKmn_BiCKNitnigminBiCKNit Algebric function nd non lgebric function >nimn½ nig lkçn³ GnuKmn_ f KWCGnuKmn_BiCKNitluHRtEtmnGnuKmn_ n CBhuFdWeRkTI n ( n ) mnemkunccmnynsnitn Edl epþógpþt;tmnk;tmng; n n + +... + + + 0. n n 0 ]ThrN_³GnuKmn_,, + KWCGnuKmn_BiCKNit. lkçn³ f & g( CGnuKmn_BiCKNitBIrenHeK)n³ ) ( f + g) f + g ( fg ) f. g ( λ f ) λ f, λ ( f g) f ( g ) smkl;³crms;éngnukmn_bicknitcgnukmn_bicknit. bnþk;énbirgnukmn_bicknitcgnukmn_bicknit. > crms;éngnukmn_ ekeggnukmn_ f : D I EdlD CEdnkMNt;énGnuKmn_ f ekf f mncrms;elicenøh [ b, ] DluHRtEt f Cb;nwgekIndc;tcenøH[, b] rw f Cb;nwgcuHdc;tcenøH[, ] ebi 0 [ b, ] 0 f( 0) Edl f ( ) 0 f ( b).tmnk;tmng 0 f( 0 ) KWCGnuKmn_BI cenøh f ( ), f ( b) etacenøh [ bedlehafgnukn_rcs;éngnukmn_, ] f.kmnt;sresr f rw f smkl;³ f f IEdl I. 3>GnuKmn_elkrItnigGics,ÚNg;Esül 3>>GnuKmn_elkrIt. b.
* GnuKmn_elkrItKWCGnuKmn_ f kmnt;bi + eta Edl én nwg > 0,. ebi lkçn³ eenhekeha log 0, log log log + logb log log log log log b b < b, > log < log b > b,0 < < rubmnþsmn;²³ f log GnfelkrIteKl f fgnukmn_elkritenebén rw Lin kmnt;sresred ln log & log b log b b, > 0, log b.logb c log c bc,, > 0,, b log b ( b, > 0,, b ) logb logc b log b ( b, > 0,, c ) log c ]ThrN_³ edhrssmikrnigvismikrgerkm³ 3 ).log 5 3 b).log 3+ 3 c).log log + log 4 4 d).log > log6 3 + 3>>RkbGnuKmn_elkrIt * -ebi > ek)nrkb log ekinbieqvgetasþmekfgnukmn_ekineli + krni 0< < témø log < 0 > témø log > 0 -ebi 0< < ek)nrkb log. * cuhbieqvgetasþmekfgnukmn_cuheli. + f.
krni 0< < témø log > 0 > témø log < 0 - RkbGnuKmn_ log kt;gks½gb;siusrtg; (,0) Cnic. - EdnkMNt;GnuKmn_ log KW > 0. ]ThrN_³ sg;rkbéngnukmn_ log & log. - ebi 0 elkritekl0én kmnt;sresred log. CTUeTA³ - edim,isg;rkbgnukmn_ log q + ekrtuvsg;rkbgnukmn_ log rycefvibemøgkil RsbGkS½( o) cmnyn q Ékt eligeliebi q > 0 cuherkmebi 0 - edim,isg;rkbgnukmn_ log ( p) ekrtuvsg;rkbgnukmn_ log rycefvibemøg kilrsbgks½ ( o) cmnyn p Ékt etagsþmebi p > 0eTAgeqVgebI p < 0. - edim,isg;rkbgnukmn_ log ekrtuvsg;rkbgnukmn_ log rycefvibemøgqøúh efobgks½( o ). q <. ]ThrN_³ sg;rkbéngnukmn_ 3>3> GnuKmn_Gics,ÚNg;Esül GnuKmn_Gics,ÚNg;EsülCGnuKmn_kMNt;ed usbi. 3>3>> RkbGnuKmn_elkrIt - ebi > ek)nrkb log +, log & log. 3 Edl ehi CcMnYnBitviC mn ekinbieqvgetasþmekfgnukmn_ekineli. - ebi 0< < ek)nrkb cuhbieqvgetasþmekfgnukmn_cuheli. - RkbGnuKmn_ kt;gks½gredenrtg; ( 0,) Cnic. - GnuKmn_ CcMnYnBitviC mnrkb;témø. CTUeTA³ - edim,isg;rkbgnukmn_ + qekrtuvsg;rkbgnukmn_ GkS½ ( o) cmnyn q Ékt eligeliebi q > 0 cuherkmebi 0 q <. rycefvibemøgkilrsb 3
p - edim,isg;rkbgnukmn_ ekrtuvsg;rkbgnukmn_ rycefvibemøg kilrsb GkS½ ( o) cmnyn p Ékt etagsþmebi p > 0eTAgeqVgebI p < 0. - edim,isg;rkbgnukmn_ ekrtuvsg;rkbgnukmn_ rycefvibemøgqøúh efobgks½( o ). lkçn³ 0 + b b <, > < >,0 < < ]ThrN_³ edhrssmikrnigvismikrgerkm³ ).3 9 7 b)..4 + 3.6 5.9 c + + ).3 34.5 5 0 4 d). > 3 9 e). ( 5) 5 5 ]ThrN_³ edhrssmikrrbbnæ½smikr ). 3 9 3+ 4 8 0 b). 5 3> GnuKmn_RtIekNmRtRcs; k>gnukmn_ Arcsin GnuKmn_ sin kmnt ;nwgcb;ehiekindc;telicenøh, edekinbi +. 4
ekgckmnt;elicenøh[, + ] nuvgnukmn_rcs;mycb;nigekindc;téngnukmn_ sin kmnt; sresred lkçn³ - ebi >GnuKmn_ GnuKmn_ Arcsin ehafgk;siunusén. sin Arcsin Arcsin ( ) Arcsin Arcsin sin sin Arcsin Arc cos cos kmnt;nwgcb;ehicuhdc;telicenøh[ ] 0, edcuhbi +. kmnt; ekgckmnt;elicenøh[, + ] nuvgnukmn_rcs;mycb;nigcuhdc;téngnukmn_ cos sresred Arc cos ehafgk;kusiunusén. cos lkçn³ - ebi Arc cos 0 Arc cos cos cos Arc cos Arcsin + Arc cos ed³ sin cos : & cos Arcsin + Arcsin Arc cos + Arcsin Arc tn tn kmnt ;nwgcb;ehiekindc;telicenøh, ed tn + + nwg tn ebi. tn K>GnuKmn_ GnuKmn_ ebi ekgckmnt;)ngnukmn_rcs;mycb;nigekindc;téngnukmn_ kmnt;sresred Arc tn ehafgk;tg;én. eli. 5
lkçn³ - ebi tn Arc tn Arc tn ( tn ) tn ( Arc tn ) Arc tn ( ) Arc tn + 4> GnuKmn_GIuEBrbUlIk k> GnuKmn_ ch & sh GnuKmn_ ch ehafkusiunusgiuebrlikehi GnuKmn_ lkçn³ sh ehafsiunusgiuebrlikehi ch + sh e ch sh e ch sh ch( + b) ch. chb + sh. shb ch( b) ch. chb sh. shb sh( + b) sh. chb + ch. shb sh( b) sh. chb ch. shb ch ch + sh sh sh. ch ch ch + &sh ch ch sh & sh ch sh sh & ch ch > GnuKmn_ th GnuKmn_ e + e ch. e e sh. th ehaftg;sg;giuebrlikehi th kmnt;cmebh RKb;. sh e e e th ch e + e e + lkçn³ th( ) th th ch 6
th + thb th thb th( + b) & th( b) + th. thb th. thb th th + th th ch 5> GnuKmn_GIuEBrbUlIkRcs; k>gnukmn_ Arg s h GnuKmn_ s h kmnt ;nwgcb;ehiekindc;telicenøh ], + [ nwgkrkb;témøkñúgcenøh. ekgckmnt;)ngnukmn_rcs;mycb;nigekindc;téngnukmn_ s h eli. kmnt;sresred Argsh ehafgk;kum:g;suingiuebrbulikén. sh lkçn³ - ebi Argsh 0 Argsh( sh) sh( Argsh) + Argsh ln + + edtg 0& e e e t > sh t t t t t. t 0 t e + + ln + + >GnuKmn_ Argch GnuKmn_ s h kmnt;nwgcb;ehiekindc;telicenøh ] 0,+ [ nwgkrkb;témø ekgckmnt;)ngnukmn_rcs;mycb;nigekindc;téngnukmn_ ch eli. kmnt;sresred Argch ehafgk;kum:g;kusiunusgiuebrbulikén. ch lkçn³ - ebi Argch 0 Argch( ch) ch( Argch). 7
Argch ln + edtg 0& K>GnuKmn_ GnuKmn_ ], [ +. e + e e t > ch t + t t + t t. t+ 0 + t e ln + Argth th kmnt;nwgcb;ehiekindc;telicenøh ] 0,+ [ nwgkrkb;témøkñúgcenøh ekgckmnt;)ngnukmn_rcs;mycb;nigekindc;téngnukmn_ th elicenøh], [ kmnt;sresred Argth ehafgk;kum:g;tg;giuebrbulikén. lkçn³ - ebi Argth th + ], [ Argth th th Argth Argth Argth + Argth ln ed e th, < < e + + + ln e +. 8