485960975.taller i - 2011 - clase teórica nº6(1)

7/26/2019 485960975.Taller i - 2011 - Clase Terica N6(1)

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Asignatura: TALLER DE LENGUAJES I 2011Carrera: PROGRAMADOR UNIVERSITARIO / Lic. EN INFORMATICADictado: Ing. Juan Manuel Conti.

Graficacin de funciones matemticas.

La graficaci ! "# f$!ci%!#& 'a(#')(ica& i'*+ica g#!#ra+'#!(# "%& *r%,+#'a&-

La # i&(#!cia explcita "# ejes de graficacin "if#r#!(#& "# +%& *r%*i%& "# *a!(. La !#c#&i"a" "# $!a escala *ara c%'*a(i,i+i ar +a& '#"i"a&.

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Si !% #&(a,+#c# $! c%+%r *ara #+ f%!"%5 #+ c%'*i+a"%r a"%*(a #+ +ac *%r "#f#c(%.L%& c%+%r#& *$#"#! #&cri,ir "ir#c(a'#!(#5 +% c$a+ r#&$+(a '$= *r)c(ic%5 *%r # #'*+%-

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La& + !#a& #! */ / &%! +%& # #& "# *a!(a++a.E& a+(a'#!(# c%!4#!i#!(# # *+ici(ar ca"a + !#a "# # #& a (ra4?& "# +a& c%%r"#!a"a&*#cifica"a& =a :$# a& *%"r#'%& r#"i'#!&i%!ar % r#$,icar +%& 'i&'%& c%! &$'ac%'%"i"a". A"#')& 4#r#'%& #! ,r#4# :$# (a',i?! faci+i(a! +a graficaci ! "# +a&f$!ci%!#& 'a(#')(ica&.

A3%ra *a'%& a+ c "ig% *ara g#!#rar #&(%& # #& c%%r"#!a"%&-

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*#r% #&% +% "# a'%& *ara +#c(%r.

Ca+i,raci ! "# # #&.

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// --- RA ADO DE

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La &ig$i#!(# i!&(r$cci ! '#r#c# !$#&(ra a(#!ci !-

Xp 3 Xi89 je = (#ng?#ng&ni)> sc ;

=a :$# "#,# i'*+icar :$# *ara ./ /% +%& 4a+%r#& "# +a 4aria,+# "# graficaci ! 6A!g75+%&Xp "#,#! 3a++ar &%,r# #+ # # 3%ri %!(a+. S%'#(a'%& a *r$#,a #&(a # *r#&i !*ara a',%& 4a+%r#& # (r#'%&-

#ng 3 #ng&ni Xp 3 Xi89 je = (#ng&ni 7 #ng&ni)> sc3 Xi89 je

#ng 3 #ngFin Xp 3 Xi89 je =(#ngFin 7 #ng&ni)>

(Xder je ?Xi89 je ):(#ngFin 7 #ng&ni) 3 Xder je

C%! +% c$a+ %,($4i'%& +% c%rr#c(%.

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A"#')& 8Fa *$#"# (#!#r c$a+:$i#r 4a+%r. Para #+ ac($a+5 > 5 #! r#a+i"a" 3#'%&r#*r#!(a"% '#!%& "# $! cic+% c%'*+#(% *$#&(% :$# +a c$r4a "# > a @B0 5 *#r% &i3$,i?'%& (%'a"% Fa 0 3a,r a'%& r#c%rri"% ')& "# $! cic+% c%'*+#(%5 ') ac(a'#!(# >0 .

Si! #',arg% !% #& ?&(a +a !ica f%r'a "# r#&%+4#r #&(# *r%,+#'a5 c%'% 4#r#'%& #! #+*r i'% # #rcici%.

C%! $!(% "# %!"a& !%i"a+#& "# "i&(i!(a& carac(#r &(ica&.

A c%!(i!$aci ! 4a'%& a *+a!(#ar!%& $! *r%,+#'a '$c3% ')& g#!#ra+ #! c$a!(% agraficaci ! "# %!"a& !%i"a+#&5 "# (a+ &$#r(# :$# $! ca&% *ar(ic$+ar "# ?&(#5

#!g+%,ar a a+ *r%,+#'a :$# aca,a'%& "# a!a+i ar.

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N (# :$# #+ (#'a "# +%& "#&fa&a #& a*ar#c# a:$ -

#ng1 3 Frec1>#ng = Fase1; #ng2 3 Frec2>#ng = Fase2; #ng@ 3 Frec@>#ng = Fase@;

O,4ia'#!(# (%"%& #! ra"ia!#&.

Ta',i?! "#,# %,r4ar :$# #! r#a+i"a" ;*15 ;*2 = ;*@ &%! +%& 'i&'%& "a"% :$# A!g = E&cH #& c%' ! a (%"% a (%"%& #++%&5 *#r% +%& *$&i'%& *%r *ara"% *ara "ar'a=%r c+ari"a".

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A'*+1 A'*+2 A'*+@ 20Fr#c1 Fr#c2 Fr#c@ 1

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% %F#%# /% .

U! ca&% ')& c%'*+ica"% *ara +a& #&ca+a&- +a circ$!f#r#!cia.

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Si! #',arg% c%! +a circ$!f#r#!cia +a 3i&(%ria #& "if#r#!(#- &i &$ ra"i% = #'*+a a'i#!(%#& (a+ :$# a'#ri(#! +a "#(#r'i!aci ! "# #&ca+a&5 !#c#&aria'#!(# "#,#r#'%&"#ci"ir!%& *%r $!a #&ca+a !ica5 ca&% c%!(rari% a*ar#c#r a $!a "i&(%r&i ! #! +a f%r'a"# +a f$!ci ! :$# !%& ++#4ar a a *#!&ar :$# #&(a'%& grafica!"% $!a #+i*.

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Y je 3 Yinf je = /ffs je ;X je 3 Xi89 je = /ffs je ;

(%"% #! * #+#&.E! c$a!(% a+ +a % "# graficaci ! "# +a f$!ci ! #! & 5 #& #+ &ig$i#!(#-

for(#ng3#ng#ngJ#ngFin;#ng=36aso#ng) K

Xp3X je = sc raf>(Xo=*adio>cos(#ng)); Yp3Y je ? sc raf>(Yo=*adio>sin(#ng)); pXo Y je 7 sc raf>Yo

#& +a $,icaci ! #! * #+#& "#+ c#!(r% "# +a circ$!f#r#!cia. A:$ 3#'%& $(i+i a"% +a #c$aci ! *ara'?(rica "# +a circ$!f#r#!cia5 c%!&i&(#!(# #!(%'ar +a& *r%=#cci%!#& %r(%g%!a+#& "#+ ra"i% 6#! f$!ci ! "#+ )!g$+%5 :$# (%'a

c%'% 4aria,+# !ica7-

sc raf>*adio>cos(#ng) ................ c%%r"#!a"a 8 9 "# *a!(a++a.sc raf>*adio>sin(#ng) ................. c%%r"#!a"a 8=9 "# *a!(a++a.

'n detalle - 3a,r) !%(a"% :$# +a 4aria,+# a!g$+ar r#c%rr# $! ca'i!% #!(r# $! 4a+%r i!icia+ = $! 4a+%r fi!a+5 !% !#c#&aria'#!(# 0 = @B0 . E++% !%& *#r'i(# graficar 8arc%&9 "#circ$!f#r#!cia :$# *$#"# r '$= (i+ *ara a+g$!a& a*+icaci%!#&. A #&(% !%& r#f#ri'%&c$a!"% *i"# (ra,a ar #! f%r'a 8g#!#ra+9.

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Para #+ # #'*+% :$# 4i#!# a c%!(i!$aci ! $(i+i ar#'%& $!a # *%!#!cia+ cr#ci#!(# :$#arra!ca "# $! 4a+%r i!icia+ ini = ++#ga 3a&(a $! 4a+%r fi!a+ fin . S$ # *r#&i !'a(#')(ica #& +a &ig$i#!(#-

F(t) 3 ini = ( fin 7 ini)>(1 7 exp(?t : .o))

.o #& +% :$# "#!%'i!a +a 8c%!&(a!(# "# cr#ci'i#!(%9 = #& $! "a(% "# +a #c$aci !.E& #+ 4a+%r "# +a 4aria,+# i!"#*#!"i#!(# *ara #+ c$a+ +a f$!ci ! a+ca! a #+ B@52 "# &$r#c%rri"% "# a'*+i($". N% !%& *r#%c$*#'%& *%r #&(# "#(a++#.

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+"d"Gra,i!"

// --- RA ADO DE E ES --------------------------------------

e(!"$"r C"$"rEje

$ine 4i56EjeH=9EjeH=4derEjeH=9EjeH $ine 4Eje;=9in,Eje;=4Eje;=9 upEje;

// --- RA ADO DE CA

)e(!& +"d" e1("

>// -----------------------------------------------------------------

A &i'*+# 4i&(a 6= #! f%r'a a*r% i'a"a7 *%"#'%& 4#r :$# +a f$!ci ! c%r(a a+ # # "#+(i#'*% #! ( @5 0 ( 500. $#r#'%& &a+ir "# "$"a& &i! '%"ificar #+ c "ig% "#+*r%gra'a $#!%5 3aga'%& #!(%!c#& .ini @. 0 = 4#a'%& :$? *a&a. La f$!ci !"#,#r a arra!car "#&"# #+ %rig#!. Si !% f$# a& *r%,#'%& c%! a+g$!%& 4a+%r#&c#rca!%& = (#!"r#'%& $!a i"#a ,a&(a!(# ,$#!a "#+ *$!(% "# c%r(#.

Taller de Lenguajes I Clase Terica Nro 6 Pg. (!"#


20/23


O(r% ca&% "# # #& "#&*+a a"%&.

Di,$ ar $!a f$!ci ! !%i"a+ "# 'a!#ra :$# #+ # # 4#r(ica+ 3a++# $,ica"% "# (a+'a!#ra :$# +a f$!ci ! arra!:$# #! 120 gra"%& = # (i#!"a 3a&(a @B0 gra"%&.

----------------------------------------------------------------- */

Para 3a++ar +a c%%r"#!a"a 3%ri %!(a+ X je "#+ # # 4#r(ica+5 #& !#c#&ari% "#(#r'i!ar *ri'#r% +a #&ca+a 3%ri %!(a+ "# graficaci !-

sc raf 3 (doFase

C%! r#&*#c(% a +a graficaci ! #! & "# +a f$!ci !5 (#!#'%& "%& *%&i,i+i"a"#& "#r#a+i ar+a-

for(#ng*ad3#ng&ni*ad;#ng*adJ3#ngFin*ad;#ng*ad=36aso#ng*ad) K :: ??? for5a & ???????????????????????????????????????

Xp 3 X je = ro#ng*ad);

:: ??? for5a && ????????????????????????????????????????????????????????????? :: Xp 3 Xi89 je = ro(#ng*ad?#ng&ni*ad));

Yp 3 Y je ?ro#5pl>sin(#ng*ad));

Taller de Lenguajes I Clase Terica Nro 6 Pg. ")!"#

Fase 3 12MQ

#5pl


21/23


p


22/23


d"ub$e E !U An) d"ub$e : 0/ d"ub$e Ndi H

!&ar E !U A2p$S(r :B !&ar E !U An)S(r :B

+"d"Gra,i!"

// --- RA ADO DE E ES COORDENADOS ------------------------

4Eje; 4i56EjeHL,ab E !Gra,H*An)IniRad

e(!"$"r C"$"rEje e($ine (@$e SO


23/23


// --- GRAFICACION DE

// -----------------------------------------------------------------in( r"und d"ub$e 13 i, 1- in( 1 ' 0.0 re(urn in( 1L re(urn in( 1 >// -----------------------------------------------------------------

485960975.taller i - 2011 - clase teórica nº6(1)

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