lmhat; lmhat; PaBCab;énGnuKmn_ CONTINUITY OF FUNCTION ³ k> curkmnt;témø a edim,i[ f Cab;Rtg; 2 RblgqmaselIkTI

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Jázmin Lídia Magyarné
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1 PaBCab;énGnuKmn_ CONTINUITY OF FUNCTION I>sikSaPaBCab;énGnuKmn_xageRkamRtg;cMNuc x ³ k> ( x ) x x 6 () nig x x> x 1, x1, K> ( x) x 7, x,3 () nig x X> x x x 1 nig x ( x) ( x) 1 3x, x,1 x sin x, x 1, nig 1 x g> ( x) ( x 1) x x nig x RblgRKUbzm x 1 II>1>eK[GnuKmn_ ( x) x siksapabcab;éngnukmn_ Rtg;cMNuc x > ek[gnukmn_ 1 x ln x, x ( x) x 1, x siksapabcab;éngnukmn_ Rtg;cMNuc ( x) ax; x x 3> CaGnuKmn_kMNt;elI eday ( x) x 1 etignukmn_ Cab;elI Edrb et 1 cosx III>1>eK[GnuKmn_ ( x), x ehiy ( ) ln( m 1) KNna lim ( x) x x kmnt;témø m edim,i[ Cab;Rtg; x qmaselikti ( x) ( ax 1) ; x > CaGnuKmn_kMNt;eday curkmnt;témø a edim,i[ Cab;Rtg; RblgqmaselIkTI1 5-- ( x) ax 1; x,1 3> CaGnuKmn_kMNt;eday Edl a, bcacmnynbit ( x) x b, x 1, k>kmnt;tmnak;tmngrvag a nig b edim,i[ Cab;elI x>curkusrkapicén kalna a 1, b x

2 PaBCab;énGnuKmn_ CONTINUITY OF FUNCTION 3 x x 1>GnuKmn_ kmnt;day ( x) cmebah x 1ehIy (1) a a 8 Edl a CacMnYn Bit k>knnalimit lim ( x) x 1 sin( x 1) x>kmnt;témø a edim,i[ CaGnuKmn_Cab;Rtg; 1 x 1 cos x >ek[gnukmn_ kmnt;elicenøah, Edl ( x) sin x cmebah x nig sin x ( x) cmebah x etignukmn_ CaGnuKmn_Cab;Rtg; x Edrb et 3> CaGnuKmn_kMNt;eday x 1 y ( x) cmebah x 1 nig ( x) x 1 x1 e etignukmn_ CaGnuKmn_Cab;Rtg; x 1 Edrb et sin x ( x) a > GnuKmn_ kmnt;day ³ x kmnt;témø a edim,i[gnukmn_ Cab;Rtg; x x 5> g CaGnuKmn_kMNt;eday g( x), x ehiy h CaGnuKmn_mYyeTotEdlkMNt;eday³ sin x h( x) g( x), x kmnt;témø m edim,i[ h CaGnuKmn_bnøaytamPaBCab;énGnuKmn_ g Rtg; x h() m RblgqmaselIkTI > CaGnuKmn_kMNt;eday x e ( x) x, x & x 1 ln x () m k>knnalimit lim ( x) x x>kmnt;témø m edim,i[ CaGnuKmn_Cab;xagsþaMRtg; RblgsBaØabRtTutiyPUmi -7- x

3 PaBCab;énGnuKmn_ CONTINUITY OF FUNCTION x 1>eK[GnuKmn_ kmnt;)aneli x IReday x x kx 1 x rkcmnynbit k edim,i[gnukmn_ Cab;Rtg; x >ek[gnukmn_ EdlkMNt;elIcenøaH ; \ eday x k > KNnalImIt lim x x 1 tan x cos x cos x x > kmnt;gnukmn_ g CabnøaytamPaBCab;énGnuKmn_ Rtg; x 1 x 1 3>eK[GnuKmn_ kmnt;eli eday ³ x x ln x ln3 e m x KNna lim x Tajrktémø m edim,i[gnukmn_ Cab;xagsaþ MRtg; x >ek[gnukmn_ EdlkMNt;eday x 3 x x x k > bgðaja GnuKmn_ Cab;Rtg; 1 x > etignukmn_ Cab;Rtg; x rwet 5> CaGnuKmn_kMNt;eday ( x) k>knnalimit lim ( x) x cos x x 6 x x x 1 x x cmebah x x1 x x>kmnt;gnukmn_ g edim,i[edlcabnøaytampabcab;éngnukmn_ Rtg; RblgqmaselIkTI x x

4 PaBCab;énGnuKmn_ CONTINUITY OF FUNCTION 1>kMNt;témø a nig b edim,i[gnukmn_xagerkamcab;eli IR ³ ax 3 k> x x a, x 1 ( x) x> ( x) 3 x x x log 3 x, x 1 x, x x sin, x x K> ( x) 1 X> ax 5x 9, x 1 ( x) b, x 1 (3 x)( a x), x 1 >erbirtwsþibtcmnucknþalbgðajagnukmn_xagerkammancmnuc c kñúgcenøahedl[ ³ k> ( x) x x 1,,5, ( c) 11 x> ( x) x 6x 8,,3, ( c) 3>eRbIRTwsþIbTcMNuckNþal rktémø c sáal; k k> ( x) x x,,3, k 1 x> ( x) 5 x, 5,3, k 3 x 7, 1 x 1 >ek[gnukmn_ kmnt;eday ³ x) ( x,1 x 3 k>eti 8 k 9 man c EdleFVI[ ( c) k Edrb et x>etirkb; 8 k 9 man c EdleFVI[ ( c) k Edrb et 5>RsaybBa ak;asmikarxagerkammanb sy:agticmyyencenøahedl[³ k> sin x 1,, x x> log 1 x x, 1,1 6>eK[GnuKmn_ kmnt;eday x x ( x), x x 1, x k>etignukmn_ Cab;Rtg; x Edrb et x>cursg;rkabéntag[nukmn_ 7>eK[smIkar ax bx c,( a ) Edl a, b, cbmebjlkçxnð 3b 6c ;bgðajasmikarenahmanb sy:agticmyyenacenøahbit, 3 a

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