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Hat\303 \241r\303\251rt\303\251k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "limit(sin(x)/x,x=0); limit((cos(x)- 1)/x^2,x=0); limit((exp(x)-1)/x,x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "#!\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "l imit(sin(x)/x,x=0,complex); limit((cos(x)-1)/x^2,x=0,complex);\n" } {MPLTEXT 1 0 32 "limit((exp(x)-1)/x,x=0,complex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "#!\"\"\"\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "3.1. 25. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }} }}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "3.1.26. T\303\251tel." }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 21 "3.1.27. P\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "limit(limit((x-y)/(x+ y),y=0),x=0); limit(limit((x-y)/(x+y),x=0),y=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 66 "3.1.28. Jobb \303\251s bal oldali hat\303\241r\303\251rt \303\251k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 54 "limit(floor(x),x=2,right); limit(floor(x),x=2,left) ;\n" }{MPLTEXT 1 0 46 "limit(floor(x),x=2); limit(floor(x),x=2,real);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I*undefinedG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 "I*undefinedG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 26 "3.1.29. Szakad\303\241sok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "discont(1/(sin(x)-1/2 ),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "<#,(*&#\"\"\"\"\"'F&I#PiG%*prot ectedGF&F&*(#\"\"#\"\"$F&F(F&I%_B1|irG6\"F&F&*(F,F&F(F&I%_Z6|irGF/F&F& " }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 29 "3.1.30. P\303\251ld\303\241k." }}{PARA 0 "" 0 "" {TEXT 201 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "limit(signum(x),x=0,righ t); limit(signum(x),x=0,left);\n" }{MPLTEXT 1 0 53 "limit(signum(x),x= 0); limit(signum(x),x=0,complex);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 61 "limit(abs(signum(x)),x=0); limit(abs(signum(x)),x=0,complex);" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I*undefinedG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 "I*undefinedG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "3.1.31. P\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 129 "3.1 .32. A b\305\221v\303\255tett val\303\263s \303\251s a b\305\221v\303 \255tett komplex sz\303\241mok topol\303\263gi\303\241ja." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 21 "3.1.33. P\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "limit(1/x,x=0); limit(1/x, x=0,complex);\n" }{MPLTEXT 1 0 44 "limit(1/x,x=0,right); limit(1/x,x=0 ,left);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 48 "limit(1/x,x=infinity ); limit(1/x,x=-infinity);\n" }{MPLTEXT 1 0 30 "limit(1/x,x=infinity,c omplex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I*undefinedG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&I)infinityG%*protectedG\"\"\"*&,$F#F%F %^#F%F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I)infinityG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$I)infinityG%*protectedG!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 " " {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 96 "3. 1.34. M\305\261veletek b\305\221v\303\255tett val\303\263s \303\251s k omplex sz\303\241mokkal." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "infinity+infinity; infinity-infinit y; 1/(infinity+I*infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I)infinit yG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I*undefinedG%*protecte dG" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "3.1. 35. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }} }}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 26 "3.1.36. Megjegyz\303\251s." }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "3.1.37. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 40 "3.1. 38. T\303\251tel: rend\305\221r-elv." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "3.1. 39. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }} }}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 35 "3.1.40. K\303\266vetkezm\303\2 51ny." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "3.1.41. P\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 30 "3.2. Sorozatok \+ \303\251s sorok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {SECT 0 {PARA 5 "" 0 "" {TEXT 207 17 "3.2.1. Sorozatok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "limit( 1/n,n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "3.2.2. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "3.2.3. T\303 \251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "3.2.4. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "3.2.5. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%# %?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 28 "3.2.6. P\303\251ld\303 \241k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "limit(a0+n*d,n=infinity) assuming(d=0);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 40 "limit(a0+n*d,n=infinity) assuming d>0;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 38 "limit(a0+n*d,n=infinity) assum ing d<0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I)infinityG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 " ,$I)infinityG%*protectedG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "limit(n^2,n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I)infi nityG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "limit( 1/n,n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "limit(1+(-1)^n/n,n=infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "limit(1+I^n,n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 ";,$^#\"\"\"!\"\",&\"\"#F%F$F%" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 73 "3.2.7 Fels\305\221 \303\251s als\303\263 hat\303\241r\3 03\251rt\303\251k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "limit((-1)^n-1/n+1/n^2,n=infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 ";!\"\"\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "3.2. 8. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}} }{SECT 1 {PARA 5 "" 0 "" {TEXT 207 36 "3.2.9. \303\201ll\303\255t\303 \241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 25 "3.2.10. Cauchy-sorozatok." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 57 "3.2.11. Cauchy-f\303\251le konvergencia-krit\303\251rium ." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 29 "* 3.2.12. Megjegyz\303\251s. " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "i:='i': \+ x:=0:\n" }{MPLTEXT 1 0 71 "for i from 0 do while (x+1)^2<2*10^(2*i) do x:=x+1: od; x; x:=x*10: od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$S\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$T\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%59" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&ST\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'?99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'@99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(5UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(8UT\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\")I@99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\")N@99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*]8UT\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "\"*c8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"+gN@99" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"+iN@99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\",?c8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\",Bc8UT\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"-IiN@99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-PiN@ 99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\".qBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\".tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"/IPiN@99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"/IPiN@99" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"0+tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"04tBc8UT \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"1!4tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"1&4tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"2]4tBc8U T\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"2]4tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"3+&4tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"3/&4tB c8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"4S]4tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"4[]4tBc8UT\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"5! 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Nevezetes sorozatok hat\303\241r\303\251rt\303\251ke." }}{PARA 0 " " 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "limi t(1/n^(1/p),n=infinity) assuming p>0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "limit(a^(1/n),n=i nfinity) assuming a>0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "limit(n^(1/n),n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "assume(a>0); assume(k>=0); limit(n^k/(1+a)^n,n=infini ty);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "limit(a^n,n=infinity) assuming abs(a)<1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&limitG6$%*protectedGI(_syslibG6\"6$)I#a|irG F'I\"nGF'/F+I)infinityGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "limit(a^n/n!,n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 14 "3.2.14. Sorok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "sum(1/k^2,k=1..infinity); " }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"\"\"\"\"'F%)I#PiG%*protectedG \"\"#F%F%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 56 "3.2.15. Cauchy-f\303\251le konve rgenciakrit\303\251rium." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%# %?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 35 "3.2.16. K\303\266vetkez m\303\251ny." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 37 "3.2.17. \303\201ll\303\255t\303 \241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 61 "3.2.18. \303\226sszehasonl\303\255t\303 \263 krit\303\251rium." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%? G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 35 "3.2.19. K\303\266vetkezm \303\251ny." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT 207 43 "3.2.20. 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