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RNDr. ODVRKO, O., DrSc.: Matematika pro gymnzia  posloupnosti a Yady, 1. vydn Praha Prometheus, spol. s r. o. 1995. 126 s. ISBN 80-85849-91-7 2) PETKOV, J. , MATEMATIKA  pYprava k maturit a pYijmacm zkouakm na vysok akoly, 1. vydn Praha Prometheus, spol. s r. o. 1998, 303 s. 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U ivo se opr o zskan poznatky, dovednosti a kompetence zskan v minulch hodinch o konvergenci, divergenci a ur ovn limit posloupnost. 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U ivo se opr o zskan poznatky, dovednosti a kompetence zskan v minulch hodinch o konvergenci, divergenci a ur ovn limit posloupnost. Sou st materilu je i uveden nkterch vznamnch limit posloupnost.LqPPh  ) 1 6 /8  9 W O ( (  ( ( <y wW3,$ 0 ONevlastn limita posloupnosti ( <y j3 ,$ 0 8loha: ( <,;y ,$ 0 Pro kter pYirozen sla n v dan posloupnosti plat: an > 100?0A8 7^ ( 6 ( C A ?"? 8 $D 0^  ( 611  ( C A ?"? r 8 $D 0^  ( 6((  ( C A ?"? - 8 $D 0^ ( 611  ( C A ?"?F Q 8 $D  0^ ( 6 ( C A  ?"? w 8 $D  0V ( < ,$  0 XZvr: Pro ka~d pYirozen n e" 7 je 2n > 100B-"*" ( <cy "`}j ,$ 0 @Xeaen:H ( 0޽h ? 33--___PPT10-.V063+ qD,' = @B D>,' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz|}~D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* (Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* (Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* (Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(++0+(y  ++0+(  ++0+(  ++0+( ++0+(  +6   ,. (  , , <my =3 ,$ 0 BUk~eme: H , <y 8,$ 0 Ae zvolme jakkoli velk reln slo K, pak v~dy existuje pYirozen slo n0 takov, ~e pro vaechna pYirozen sla n e" n0 plat 2n > K.zL *"*"*"^ , 611 , C A  ?#" `?"8 $D 0^  , 6 , C A   ?#" `? a 8  $D 0r  , <Խ % qE ,$ 0 xZvr: Za n0 mo~eme vzt jakkoli pYirozen slo vta ne~:>=  0"^  , 6  , C A   ?"? 8  $D 0^  , < ) "/,$ 0 |Xkme:  dan posloupnost m nevlastn limitu plus nekone no &?>" , < Z ,$  0 8Zpis:^ , 6 , C A   ?"?v a8  $D  0H , 0޽h ? 33**___PPT10*.VN+'Dm)' = @B D()' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ,D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ,D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,++0+,k  ++0+,k  ++0+ ,k  ++0+ ,k  ++0+,k  +ZB   0 (  0 0 < wj3 ,$ 0 8loha: 0 < ^ ,$ 0 R Je dna aritmetick posloupnost:!!^ 0 6 0 C A  ?"?,g 8  $D 0 0 <0 ?,$ 0 xUr ete vaechna pYirozen sla, pro kter plat: bn < - 104.J=2  1   0 < "`i ,$ 0 @Xeaen:^  0 6((  0 C A  ?"?"}8  $D 0^  0 6((  0 C A ?"? 8 $D 0^ 0 6 0 C A ?"?z  8 $D  0h 0 <  - ,$  0 Ae zvolme jakkoli mal reln slo L, pak v~dy existuje pYirozen slo n0 takov, ~e pro vaechna pYirozen sla n e" n0 plat bn < L.zK *"*"*"r 0 <ž  +,$  0 xZvr: Za n0 mo~eme vzt jakkoli pYirozen slo vta ne~:>=  0"^ 0 6 0 C A ?"? j 8 $D  0H 0 0޽h ? 33 44___PPT103.Vǐo+!Df2' = @B D!2' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0+P+0+0m  ++0+0m  ++0+0m  ++0+ 0m  ++0+0m  ++0+0m  +3 n f  4 (  4` 4 <C",$ 0 ~Xkme:  dan posloupnost m nevlastn limitu mnus nekone no &@?" 4 <( j ,$ 0 8Zpis: 4 S A ??"?<*V8 $D 0 4 <d dB,$ 0 dXkme, ~e dan posloupnost m nevlastn limitu plus nekone no, prv kdy~ pro ka~d reln slo K existuje n0 pYirozen takov, ~e pro vaechna pYirozen sla n e" n0 je an > K.|n 4"*"*" 4 <xy g ,$ 0 8Zpis:^  4 6  4 C A ?"?j f 8 $D 0  4 <F ',$ 0 dXkme, ~e dan posloupnost m nevlastn limitu plus nekone no, prv kdy~ pro ka~d reln slo K existuje n0 pYirozen takov, ~e pro vaechna pYirozen sla n e" n0 je an > K.|n 4"*"*"  4 <h ,$  0 8Zpis: 4 S A ??"? l8 $D  0H 4 0޽h ? 33&&___PPT10&. V/+;eDZ%' = @B D%' = @BA?%,( < +O%,( < +D ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 4D ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 4D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 4D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4+P+0+4t  ++0+4t  ++0+4t  ++0+4t  ++0+ 4t  ++0+ 4t  +>    8j (  8 8 <y wq},$ 0 Pozn.: Budeme-li hovoYit o limit posloupnosti, budeme mt na mysli vlastn limitu ( konkrtn reln slo)."nh  8 < W,$ 0 l:Mohou nastat pouze 4 pYpady:j 8 <T /NO,$ 0 Posloupnost je konvergentn, jej limitou je njak reln . a..A> 8 S A ??"?m 8 $D 0 8 <%,$ 0 c1Posloupnost je divergentn a m nevlastn limitu 22^  8 6CC  8 C A ?"?8 $D 0  8 S A ??"?C 8 $D 0  8 <c  ,$  0 c1Posloupnost je divergentn a m nevlastn limitu 22  8 S A !??"? )1 8 !$D  0 8 S A #??"? 6 < 8 #$D  0` 8 <: ,$  0 Posloupnost je divergentn a pYitom nem ani jednu nevlastn limitu. GGH 8 0޽h ? 3322___PPT102."VYż+}ygD1' = @B D0' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 8Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 8DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 8D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 8Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8+P+0+8t  ++0+8t  ++0+8t  ++0+8t  ++0+ 8z  ++0+8z  +R  @<(  < < <`y w ,$ 0 CSamostatn prce: < <,$ 0 Rozhodnte, kter z uvedench posloupnost jsou konvergentn, divergentn nebo maj nevlastn limitu.gg^ < 6 < S A )??#" `?meQ8 )$@ 0^  < 6 < S A +??#" `?m+M8 +$@ 0^  < 6  < S A -??#" `?  8 -$@ 0  < S A /??#" `? + 8 /$D  0 < S A 5??#" `?m Q8 5$@ 0 < S A 7??#" `?  8 7$@ 0 < <{"` ,$  0 @Xeaen: < < K@"`9  Y,$  0 @Xeaen: < S A 8??#" `?<V 8 8$@  0 < S A 9??#" `?M . 8 9$@  0 < < "`qp ,$ 0 3D < <"`,$ 0 30 < <(Ӹ"` ,$ 0 30 < <LƸ"`qP,$ 0 30H < 0޽h ? 33RCJC___PPT10*C.$V|+\oD>A' = @B D@' = @BA?%,( < +O%,( < +DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*<D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*<DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*<D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*<D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*<D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* <D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* <D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*<D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* <D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* <DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*<D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*<D ' =%(D ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*<D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*<D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*<D! 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U ivo se opr o zskan poznatky, dovednosti a kompetence zskan v minulch hodinch o konvergenci, divergenci a ur ovn limit posloupnost. Sou st materilu je i uveden nkterch vznamnch limit posloupnost.LqPPh  ) 1 6 /8  k z (     <B =p  TPOU}IT ZDROJE:  <J wN H@8___PPT9 ~doc. RNDr. ODVRKO, O., DrSc.: Matematika pro gymnzia  posloupnosti a Yady, 1. vydn Praha Prometheus, spol. s r. o. 1995. 126 s. ISBN 80-85849-91-7 2) PETKOV, J. , MATEMATIKA  pYprava k maturit a pYijmacm zkouakm na vysok akoly, 1. vydn Praha Prometheus, spol. s r. o. 1998, 303 s. ISBN 80-7196-099-3 3) prof. RNDr. REKTORYS, K., DrSc.: PYehled u~it matematiky, 4. vydn SNTL 1981, 1139 s. 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