{VERSION 3 0 "IBM INTEL LINUX" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "
" -1 262 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 305 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 0 0 
1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 
1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "
Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 
1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 3 0 0 0 0 
1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times
" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 
2 2 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Normal" -1 256 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 1 0 0 0 0 
1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 257 1 {CSTYLE "" -1 -1 "Times
" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 }3 1 0 0 8 2 1 0 1 0 2 2 0 1 }
{PSTYLE "" 256 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 18 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" 
{TEXT -1 12 "Posloupnosti" }}{EXCHG {PARA 258 "" 0 "" {TEXT -1 5 "Napr
." }}{PARA 256 "" 0 "" {TEXT -1 24 "1, 2, 3, 4, 5, 6, 7, ..." }}{PARA 
256 "" 0 "" {TEXT -1 38 "1, -1/3, 1/9, -1/27, 1/81, -1/243, ..." }}
{PARA 256 "" 0 "" {TEXT -1 33 "1/2, 2/3, 3/4, 4/5, 5/6, 6/7, ..." }}
{PARA 0 "" 0 "" {XPPEDIT 18 0 "a_1 = 1/2;" "6#/%$a_1G*&\"\"\"\"\"\"\"
\"#!\"\"" }{TEXT -1 4 " ,  " }{XPPEDIT 18 0 "a_2 = 2/3;" "6#/%$a_2G*&
\"\"#\"\"\"\"\"$!\"\"" }{TEXT -1 4 " ,  " }{XPPEDIT 18 0 "a_3 = 3/4;" 
"6#/%$a_3G*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT -1 4 "  , " }{XPPEDIT 18 0 "
a_n = n/(n+1);" "6#/%$a_nG*&%\"nG\"\"\",&F&F'\"\"\"F'!\"\"" }{TEXT -1 
2 " ." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "Cviceni 1" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 53 "Urcete n-ty clen druhe z vyse uvedenych p
osloupnosti." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }{TEXT 273 7 "Reseni." }{TEXT -1 2 "  " }{XPPEDIT 18 0 "(-1/3)
^(n+1);" "6#),$*&\"\"\"\"\"\"\"\"$!\"\"F),&%\"nGF'\"\"\"F'" }{TEXT -1 
22 " .  (Proc je exponent " }{XPPEDIT 18 0 "n+1;" "6#,&%\"nG\"\"\"\"\"
\"F%" }{TEXT -1 10 " a ne jen " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT 
-1 2 "?)" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Vytvoreni posloupnos
ti v Maplu (pomoci " }{TEXT 262 1 "$" }{TEXT -1 16 " a prikazu seq)." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "n^2 $n=1..10;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6,\"\"\"\"\"%\"\"*\"#;\"#D\"#O\"#\\\"#k\"#\")
\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "seq(n^2, n=1..10)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"\"\"\"%\"\"*\"#;\"#D\"#O\"#\\
\"#k\"#\")\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "n/(n+1)
 $n=3..7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'#\"\"$\"\"%#F%\"\"&#F'\"
\"'#F)\"\"(#F+\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "seq(
n/(n+1), n=3..7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'#\"\"$\"\"%#F%\"
\"&#F'\"\"'#F)\"\"(#F+\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "a := [[n, n^2] $n=1..10];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"a
G7,7$\"\"\"F'7$\"\"#\"\"%7$\"\"$\"\"*7$F*\"#;7$\"\"&\"#D7$\"\"'\"#O7$
\"\"(\"#\\7$\"\")\"#k7$F-\"#\")7$\"#5\"$+\"" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 30 "plot(a, x=0..12, style=point);" }}{PARA 13 "" 1 "
" {INLPLOT "6&-%'CURVESG6$7,7$$\"\"\"\"\"!F(7$$\"\"#F*$\"\"%F*7$$\"\"$
F*$\"\"*F*7$F.$\"#;F*7$$\"\"&F*$\"#DF*7$$\"\"'F*$\"#OF*7$$\"\"(F*$\"#
\\F*7$$\"\")F*$\"#kF*7$F3$\"#\")F*7$$\"#5F*$\"$+\"F*-%'COLOURG6&%$RGBG
$FQ!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!G-%&STYLEG6#%&POINTG-%%VIEWG6$;F*
$\"#7F*%(DEFAULTG" 2 400 300 300 5 0 1 0 2 9 0 4 2 1.000000 45.000000 
45.000000 10020 10061 10056 10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 
1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "b
 := [[n, n/(n+1)] $n=1..10];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG
7,7$\"\"\"#F'\"\"#7$F)#F)\"\"$7$F,#F,\"\"%7$F/#F/\"\"&7$F2#F2\"\"'7$F5
#F5\"\"(7$F8#F8\"\")7$F;#F;\"\"*7$F>#F>\"#57$FA#FA\"#6" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(b, x=0..12, style=point);" }}
{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7,7$$\"\"\"\"\"!$\"1+++++++]!
#;7$$\"\"#F*$\"1mmmmmmmmF-7$$\"\"$F*$\"1+++++++vF-7$$\"\"%F*$\"1++++++
+!)F-7$$\"\"&F*$\"1MLLLLLL$)F-7$$\"\"'F*$\"1r&G9dG9d)F-7$$\"\"(F*$\"1+
+++++]()F-7$$\"\")F*$\"1))))))))))))))))F-7$$\"\"*F*$\"1+++++++!*F-7$$
\"#5F*$\"1\"4444444*F--%'COLOURG6&%$RGBG$FX!\"\"F*F*-%+AXESLABELSG6$Q
\"x6\"%!G-%&STYLEG6#%&POINTG-%%VIEWG6$;F*$\"#7F*%(DEFAULTG" 2 400 300 
300 5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10020 10061 10056 
10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([[n, n/(n+1)] $n=1..100
], x=0..100, y=0..2, style=point);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'
CURVESG6$7`q7$$\"\"\"\"\"!$\"1+++++++]!#;7$$\"\"#F*$\"1mmmmmmmmF-7$$\"
\"$F*$\"1+++++++vF-7$$\"\"%F*$\"1+++++++!)F-7$$\"\"&F*$\"1MLLLLLL$)F-7
$$\"\"'F*$\"1r&G9dG9d)F-7$$\"\"(F*$\"1++++++]()F-7$$\"\")F*$\"1)))))))
)))))))))F-7$$\"\"*F*$\"1+++++++!*F-7$$\"#5F*$\"1\"4444444*F-7$$\"#6F*
$\"1mmmmmmm\"*F-7$$\"#7F*$\"1J#p2Bp2B*F-7$$\"#8F*$\"1'G9dG9dG*F-7$$\"#
9F*$\"1LLLLLLL$*F-7$$\"#:F*$\"1++++++v$*F-7$$\"#;F*$\"1`B)eqk<T*F-7$$
\"#<F*$\"1WWWWWWW%*F-7$$\"#=F*$\"1:j_5Uot%*F-7$$\"#>F*$\"1+++++++&*F-7
$$\"#?F*$\"1B&4Q_4Q_*F-7$$\"#@F*$\"1YXXXXXX&*F-7$$\"#AF*$\"1[VI\"R<_c*
F-7$$\"#BF*$\"1MLLLLL$e*F-7$$\"#CF*$\"1+++++++'*F-7$$\"#DF*$\"1;YQ:YQ:
'*F-7$$\"#EF*$\"1H'H'H'H'H'*F-7$$\"#FF*$\"1Vr&G9dGk*F-7$$\"#GF*$\"1/Jz
8C<b'*F-7$$\"#HF*$\"1nmmmmmm'*F-7$$\"#IF*$\"15(Q[N>un*F-7$$\"#JF*$\"1+
++++](o*F-7$$\"#KF*$\"1(ppppppp*F-7$$\"#LF*$\"1w6%HN#)eq*F-7$$\"#MF*$
\"19dG9dG9(*F-7$$\"#NF*$\"1AAAAAAA(*F-7$$\"#OF*$\"1I(H(H(H(H(*F-7$$\"#
PF*$\"1eJE0@%ot*F-7$$\"#QF*$\"1V(*eV(*eV(*F-7$$\"#RF*$\"1++++++](*F-7$
$\"#SF*$\"15c(4c(4c(*F-7$$\"#TF*$\"1iZ!>w/>w*F-7$$\"#UF*$\"1;^Yg=Wn(*F
-7$$\"#VF*$\"1tssssss(*F-7$$\"#WF*$\"1xxxxxxx(*F-7$$\"#XF*$\"1u@l&p3Ey
*F-7$$\"#YF*$\"1\">`D/Msy*F-7$$\"#ZF*$\"1mmmmmm\"z*F-7$$\"#[F*$\"1RpMn
$=fz*F-7$$\"#\\F*$\"1+++++++)*F-7$$\"#]F*$\"1^uio:#R!)*F-7$$\"#^F*$\"1
2Bp2Bp2)*F-7$$\"#_F*$\"1\")pra2K6)*F-7$$\"#`F*$\"1:[\"[\"[\"[\")*F-7$$
\"#aF*$\"1=======)*F-7$$\"#bF*$\"1r&G9dG9#)*F-7$$\"#cF*$\"1r(3NShX#)*F
-7$$\"#dF*$\"1^l*o?'eF)*F-7$$\"#eF*$\"1sidu%30$)*F-7$$\"#fF*$\"1LLLLLL
L)*F-7$$\"#gF*$\"1#\\qPdlg$)*F-7$$\"#hF*$\"1b$>un4(Q)*F-7$$\"#iF*$\"1T
)p7%)p7%)*F-7$$\"#jF*$\"1+++++vV)*F-7$$\"#kF*$\"1ZQ:YQ:Y)*F-7$$\"#lF*$
\"1\\[[[[[[)*F-7$$\"#mF*$\"1;nloiu])*F-7$$\"#nF*$\"1*eqk<TH&)*F-7$$\"#
oF*$\"1;\"oPYs]&)*F-7$$\"#pF*$\"1eG9dG9d)*F-7$$\"#qF*$\"1ludH\\:f)*F-7
$$\"#rF*$\"1766666h)*F-7$$\"#sF*$\"1O,j)p8I')*F-7$$\"#tF*$\"1l['['['['
)*F-7$$\"#uF*$\"1nmmmmmm)*F-7$$\"#vF*$\"1z:j_5Uo)*F-7$$\"#wF*$\"1q)H,(
)H,()*F-7$$\"#xF*$\"1s[zr[zr)*F-7$$\"#yF*$\"1))*=:s<M()*F-7$$\"#zF*$\"
1++++++v)*F-7$$\"#!)F*$\"1Vl()4Kaw)*F-7$$\"#\")F*$\"10y[!y[!y)*F-7$$\"
##)F*$\"1c\"*Gs!=&z)*F-7$$\"#$)F*$\"1\"Q_4Q_4))*F-7$$\"#%)F*$\"1rk<THN
#))*F-7$$\"#&)F*$\"1eDBI4s$))*F-7$$\"#')F*$\"1oVEru0&))*F-7$$\"#()F*$
\"1OOOOOO'))*F-7$$\"#))F*$\"1-#Q%\\/k())*F-7$$\"#*)F*$\"1*))))))))))))
))*F-7$$\"#!*F*$\"1\"*)4,*)4,*)*F-7$$\"#\"*F*$\"1'3EyM/8*)*F-7$$\"##*F
*$\"1q&z#=JZ#*)*F-7$$\"#$*F*$\"1'fw7-<O*)*F-7$$\"#%*F*$\"1j_5Uot%*)*F-
7$$\"#&*F*$\"1MLLLL$e*)*F-7$$\"#'*F*$\"1Y[\\;s!p*)*F-7$$\"#(*F*$\"1pMn
$=fz*)*F-7$$\"#)*F*$\"1**)*)*)*)*)*)*)*F-7$$\"#**F*$\"1+++++++**F-7$$
\"$+\"F*$\"1,*4!*4!*4!**F--%'COLOURG6&%$RGBG$FX!\"\"F*F*-%+AXESLABELSG
6$Q\"x6\"Q\"yFa[m-%&STYLEG6#%&POINTG-%%VIEWG6$;F*Fcjl;F*F/" 2 400 300 
300 5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10020 10061 10056 
10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}
{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "Cviceni 2" }}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 77 "Nakreslete grafy nasledujicich posloupnosti. Pokuste se
 podle grafu odhadnout" }}{PARA 0 "" 0 "" {TEXT -1 29 "zda konverguji \+
ci diverguji. " }}{PARA 0 "" 0 "" {TEXT -1 5 "(a)  " }{XPPEDIT 18 0 "(
-1)^n;" "6#),$\"\"\"!\"\"%\"nG" }{TEXT -1 21 "                 (b) " }
{XPPEDIT 18 0 "(1+1/n)^n;" "6#),&\"\"\"\"\"\"*&\"\"\"F&%\"nG!\"\"F&F)
" }{TEXT -1 18 "              (c) " }{XPPEDIT 18 0 "(1+2/n)^n;" "6#),&
\"\"\"\"\"\"*&\"\"#F&%\"nG!\"\"F&F)" }{TEXT -1 22 "                 (d
)  " }{XPPEDIT 18 0 "(1-1/n)^n;" "6#),&\"\"\"\"\"\"*&\"\"\"F&%\"nG!\"
\"F*F)" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "(e) " }{XPPEDIT 
18 0 "sqrt(n+1)-sqrt(n);" "6#,&-%%sqrtG6#,&%\"nG\"\"\"\"\"\"F)F)-F%6#F
(!\"\"" }{TEXT -1 11 "       (f) " }{XPPEDIT 18 0 "sqrt(n^2+n)-n;" "6#
,&-%%sqrtG6#,&*$%\"nG\"\"#\"\"\"F)F+F+F)!\"\"" }{TEXT -1 13 "         \+
(g) " }{XPPEDIT 18 0 "sin(n);" "6#-%$sinG6#%\"nG" }{TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
274 7 "Reseni." }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 51 "plot([[n, (-1)^n] $n=1..20], x=0..20, style=point);" }}{PARA 13 
"" 1 "" {INLPLOT "6&-%'CURVESG6$767$$\"\"\"\"\"!$!\"\"F*7$$\"\"#F*F(7$
$\"\"$F*F+7$$\"\"%F*F(7$$\"\"&F*F+7$$\"\"'F*F(7$$\"\"(F*F+7$$\"\")F*F(
7$$\"\"*F*F+7$$\"#5F*F(7$$\"#6F*F+7$$\"#7F*F(7$$\"#8F*F+7$$\"#9F*F(7$$
\"#:F*F+7$$\"#;F*F(7$$\"#<F*F+7$$\"#=F*F(7$$\"#>F*F+7$$\"#?F*F(-%'COLO
URG6&%$RGBG$FGF,F*F*-%+AXESLABELSG6$Q\"x6\"%!G-%&STYLEG6#%&POINTG-%%VI
EWG6$;F*F^o%(DEFAULTG" 2 400 300 300 5 0 1 0 2 9 0 4 2 1.000000 
45.000000 45.000000 10020 10061 10056 10074 0 0 0 20530 0 12020 0 0 0 
0 0 0 0 1 1 0 0 0 2181 3584 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "plot([[n, (1 + 1/n)^n] $n=1..30], x=0..30, style=poin
t);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7@7$$\"\"\"\"\"!$\"\"#
F*7$F+$\"1++++++]A!#:7$$\"\"$F*$\"1q.Pq.PqBF07$$\"\"%F*$\"1+++]iSTCF07
$$\"\"&F*$\"1+++++K)[#F07$$\"\"'F*$\"18@urji@DF07$$\"\"(F*$\"182/(p*\\
YDF07$$\"\")F*$\"1[.&R^%ylDF07$$\"\"*F*$\"1(>8<zu6e#F07$$\"#5F*$\"1++5
gCu$f#F07$$\"#6F*$\"1Jv*=,*>/EF07$$\"#7F*$\"1yYA!HNIh#F07$$\"#8F*$\"1K
d)y)3g?EF07$$\"#9F*$\"1p3Ic::FEF07$$\"#:F*$\"1>zs<(yGj#F07$$\"#;F*$\"1
+mO(\\Gzj#F07$$\"#<F*$\"14J=vVTUEF07$$\"#=F*$\"1&o(4@eUYEF07$$\"#>F*$
\"1X/kEV.]EF07$$\"#?F*$\"1?W90xH`EF07$$\"#@F*$\"10h#R@jil#F07$$\"#AF*$
\"1)yP&e)p*eEF07$$\"#BF*$\"1#yQ'=,XhEF07$$\"#CF*$\"1%fo!e7tjEF07$$\"#D
F*$\"1?u[Jj$em#F07$$\"#EF*$\"1SP`m\\ynEF07$$\"#FF*$\"1uD\"y(RfpEF07$$
\"#GF*$\"1S3W`yFrEF07$$\"#HF*$\"1,3)R9\\Gn#F07$$\"#IF*$\"1&Hqex=Vn#F0-
%'COLOURG6&%$RGBG$FV!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!G-%&STYLEG6#%&PO
INTG-%%VIEWG6$;F*Fct%(DEFAULTG" 2 400 300 300 5 0 1 0 2 9 0 4 2 
1.000000 45.000000 45.000000 10020 10061 10056 10074 0 0 0 20530 0 
12020 0 0 0 0 0 0 0 1 1 0 0 0 2164 24640 0 0 0 0 0 0 }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 56 "plot([[n, (1 + 2/n)^n] $n=1..30], x=0..30
, style=point);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7@7$$\"\"
\"\"\"!$\"\"$F*7$$\"\"#F*$\"\"%F*7$F+$\"1I'H'H'H'HY!#:7$F0$\"1+++++]i]
F57$$\"\"&F*$\"1+++++Cy`F57$$\"\"'F*$\"1m(HFpb'=cF57$$\"\"(F*$\"1zA&**
4&z2eF57$$\"\")F*$\"1i!RvZk/'fF57$$\"\"*F*$\"1Rv=S^F'3'F57$$\"#5F*$\"1
++SAkt\">'F57$$\"#6F*$\"1q8-]GT\"G'F57$$\"#7F*$\"1\"Hl'e&*fejF57$$\"#8
F*$\"17cJaYtDkF57$$\"#9F*$\"1W%GqqgY['F57$$\"#:F*$\"1)f'oYgzOlF57$$\"#
;F*$\"1Bu-s,D$e'F57$$\"#<F*$\"1*zQ8W.\\i'F57$$\"#=F*$\"1mcP0LYimF57$$
\"#>F*$\"1?iXfZ]'p'F57$$\"#?F*$\"1+cK\\**\\FnF57$$\"#@F*$\"1c*Hx<Sev'F
57$$\"#AF*$\"1w!oN\\_=y'F57$$\"#BF*$\"1^h*yN7e!oF57$$\"#CF*$\"1o&fzU`z
#oF57$$\"#DF*$\"1;$>i>v%[oF57$$\"#EF*$\"1)[(e8!\\v'oF57$$\"#FF*$\"1\\!
o>)GK&)oF57$$\"#GF*$\"1\"3u(*HD>!pF57$$\"#HF*$\"1)4e<Pou\"pF57$$\"#IF*
$\"17YEU.0KpF5-%'COLOURG6&%$RGBG$FT!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!G
-%&STYLEG6#%&POINTG-%%VIEWG6$;F*Fat%(DEFAULTG" 2 400 300 300 5 0 1 0 
2 9 0 4 2 1.000000 45.000000 45.000000 10020 10061 10056 10074 0 0 0 
20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 2140 400 0 0 0 0 0 0 }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot([[n, (1 - 1/n)^n] $n=1..30], x
=0..30, style=point);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7@7$
$\"\"\"\"\"!F*7$$\"\"#F*$\"1+++++++D!#;7$$\"\"$F*$\"1jH'H'H'H'HF07$$\"
\"%F*$\"1++++D1kJF07$$\"\"&F*$\"1+++++!oF$F07$$\"\"'F*$\"1TQ!owz*[LF07
$$\"\"(F*$\"1P6*3xm\"*R$F07$$\"\")F*$\"1n\"e!e\"*3OMF07$$\"\"*F*$\"1&=
Y6;%RkMF07$$\"#5F*$\"1+++,Wy'[$F07$$\"#6F*$\"1DR\"[**Q\\]$F07$$\"#7F*$
\"1r89!Gc*>NF07$$\"#8F*$\"11;r%)\\eKNF07$$\"#9F*$\"1*e)>-JNVNF07$$\"#:
F*$\"1U9%\\mVEb$F07$$\"#;F*$\"1Gz^/8ugNF07$$\"#<F*$\"1GHYZ>'yc$F07$$\"
#=F*$\"1Nm%zOsTd$F07$$\"#>F*$\"1OY.AM!)zNF07$$\"#?F*$\"1Ba3C#f[e$F07$$
\"#@F*$\"1J&4kkB%*e$F07$$\"#AF*$\"1hg&4,lNf$F07$$\"#BF*$\"1<9!Q`Rtf$F0
7$$\"#CF*$\"1B_&G*Qz+OF07$$\"#DF*$\"1$=!eor'Rg$F07$$\"#EF*$\"1T]OHB*og
$F07$$\"#FF*$\"1O\"4:Q(f4OF07$$\"#GF*$\"1@%o*oi57OF07$$\"#HF*$\"1\\*pT
eRWh$F07$$\"#IF*$\"10hhM^h;OF0-%'COLOURG6&%$RGBG$FV!\"\"F*F*-%+AXESLAB
ELSG6$Q\"x6\"%!G-%&STYLEG6#%&POINTG-%%VIEWG6$;F*Fct%(DEFAULTG" 2 400 
300 300 5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10020 10061 
10056 10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 2182 400 0 0 
0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "plot([[n, sqrt(n+
1) - sqrt(n)] $n=1..30], x=0..30, style=point);" }}{PARA 13 "" 1 "" 
{INLPLOT "6&-%'CURVESG6$7@7$$\"\"\"\"\"!$\"1^4tBc8UT!#;7$$\"\"#F*$\"1?
y&>Xs$yJF-7$$\"\"$F*$\"1G7JC>\\zEF-7$$\"\"%F*$\"1)*y*\\xz1O#F-7$$\"\"&
F*$\"1\")Q$Gl<U8#F-7$$\"\"'F*$\"1GT\"Go:E'>F-7$$\"\"(F*$\"1'*f\"o8en#=
F-7$$\"\")F*$\"1(4QDvGdr\"F-7$$\"\"*F*$\"1&z$o,mxA;F-7$$\"#5F*$\"1.-(=
IrMa\"F-7$$\"#6F*$\"1YN#yCoZZ\"F-7$$\"#7F*$\"1ZBE.m\\99F-7$$\"#8F*$\"1
A&*4861h8F-7$$\"#9F*$\"1dZL%ffKJ\"F-7$$\"#:F*$\"1Ie#z`m,F\"F-7$$\"#;F*
$\"11m<ci0J7F-7$$\"#<F*$\"1Ui,:1N&>\"F-7$$\"#=F*$\"1#*Q@kDei6F-7$$\"#>
F*$\"1c!*e9,PK6F-7$$\"#?F*$\"1-Ec*R(R/6F-7$$\"#@F*$\"1**en[1Sy5F-7$$\"
#AF*$\"1%*G*[jdT0\"F-7$$\"#BF*$\"1mj`A'z9.\"F-7$$\"#CF*$\"1UkLW^?55F-7
$$\"#DF*$\"1\\%y#f8&>!**!#<7$$\"#EF*$\"1`ZQ64H8(*F`s7$$\"#FF*$\"1T\\DU
*>]`*F`s7$$\"#GF*$\"1JA`+&=iO*F`s7$$\"#HF*$\"1Xdr\"zwg?*F`s7$$\"#IF*$
\"1Lg$yxyQ0*F`s-%'COLOURG6&%$RGBG$FX!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!
G-%&STYLEG6#%&POINTG-%%VIEWG6$;F*Fft%(DEFAULTG" 2 400 300 300 5 0 1 0 
2 9 0 4 2 1.000000 45.000000 45.000000 10020 10061 10056 10074 0 0 0 
20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 16413 400 0 0 0 0 0 0 }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([[n, sqrt(n^2 + n) - n] $n=1..
30], x=0..30, style=point);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG
6$7@7$$\"\"\"\"\"!$\"1^4tBc8UT!#;7$$\"\"#F*$\"1z<$yU(*[\\%F-7$$\"\"$F*
$\"1WvP^h,TYF-7$$\"\"%F*$\"1'z&**\\&f8s%F-7$$\"\"&F*$\"17m^]dDsZF-7$$
\"\"'F*$\"1/'yS)pS2[F-7$$\"\"(F*$\"1F)yatZJ$[F-7$$\"\")F*$\"1&p&QUP\"G
&[F-7$$\"\"*F*$\"1\"Q^]!)H$o[F-7$$\"#5F*$\"1a^,<[)3)[F-7$$\"#6F*$\"1s0
wIHD\"*[F-7$$\"#7F*$\"1mz'z'*f***[F-7$$\"#8F*$\"1</KKcP2\\F-7$$\"#9F*$
\"1\"Q%*=YnP\"\\F-7$$\"#:F*$\"1\"o'H[QL>\\F-7$$\"#;F*$\"1BkqC]AC\\F-7$
$\"#<F*$\"10!f`%obG\\F-7$$\"#=F*$\"1*Gp!*3?C$\\F-7$$\"#>F*$\"1i#zh*o)e
$\\F-7$$\"#?F*$\"1f>>>`,R\\F-7$$\"#@F*$\"1sn/-E&=%\\F-7$$\"#AF*$\"1a)R
SePW%\\F-7$$\"#BF*$\"1,YT*[-o%\\F-7$$\"#CF*$\"11yJyU(*[\\F-7$$\"#DF*$
\"1U#R'zc(4&\\F-7$$\"#EF*$\"1(RN)*)f#G&\\F-7$$\"#FF*$\"13/N(pTX&\\F-7$
$\"#GF*$\"1H,]vp8c\\F-7$$\"#HF*$\"1+D0vSid\\F-7$$\"#IF*$\"1G\"Q&RO,f\\
F--%'COLOURG6&%$RGBG$FX!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!G-%&STYLEG6#%
&POINTG-%%VIEWG6$;F*Fet%(DEFAULTG" 2 400 300 300 5 0 1 0 2 9 0 4 2 
1.000000 45.000000 45.000000 10020 10061 10056 10074 0 0 0 20530 0 
12020 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 51 "plot([[n, sin(n)] $n=1..30], x=0..30, style=poin
t);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7@7$$\"\"\"\"\"!$\"1l*
y![)4ZT)!#;7$$\"\"#F*$\"1<oDoU(H4*F-7$$\"\"$F*$\"1s')f!3+7T\"F-7$$\"\"
%F*$!1#GzI&\\-ovF-7$$\"\"&F*$!1&QJmuU#*e*F-7$$\"\"'F*$!1f#*)>)\\:%z#F-
7$$\"\"(F*$\"1\"*y=()f')plF-7$$\"\")F*$\"1=QBmCe$*)*F-7$$\"\"*F*$\"1mv
T_[=@TF-7$$\"#5F*$!1*p$*)36@SaF-7$$\"#6F*$!1Nq]l?!*****F-7$$\"#7F*$!1
\\V+!=HdO&F-7$$\"#8F*$\"14kEo.n,UF-7$$\"#9F*$\"1/([pbtg!**F-7$$\"#:F*$
\"1p6d,%yG]'F-7$$\"#;F*$!1`1lmJ.zGF-7$$\"#<F*$!1obz=\\(Rh*F-7$$\"#=F*$
!1hnrnC()4vF-7$$\"#>F*$\"1B&Hm4s()\\\"F-7$$\"#?F*$\"1xiF2DXH\"*F-7$$\"
#@F*$\"1h0O&QclO)F-7$$\"#AF*$!1wQS!H48&))!#=7$$\"#BF*$!11<vTS?i%)F-7$$
\"#CF*$!1Ri1?Oyb!*F-7$$\"#DF*$!1Ix(4]<NK\"F-7$$\"#EF*$\"1Ggz/XeDwF-7$$
\"#FF*$\"1I]/%GfPc*F-7$$\"#GF*$\"1!pyI)y04FF-7$$\"#HF*$!1v'H@%)Qjj'F-7
$$\"#IF*$!1='G4C;.))*F--%'COLOURG6&%$RGBG$FX!\"\"F*F*-%+AXESLABELSG6$Q
\"x6\"%!G-%&STYLEG6#%&POINTG-%%VIEWG6$;F*Fft%(DEFAULTG" 2 400 300 300 
5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10020 10061 10056 
10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 0 10791 0 0 0 0 0 0 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot([[n, sin(n)] $n=1..1
00], x=0..100, style=point);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVES
G6$7`q7$$\"\"\"\"\"!$\"1l*y![)4ZT)!#;7$$\"\"#F*$\"1<oDoU(H4*F-7$$\"\"$
F*$\"1s')f!3+7T\"F-7$$\"\"%F*$!1#GzI&\\-ovF-7$$\"\"&F*$!1&QJmuU#*e*F-7
$$\"\"'F*$!1f#*)>)\\:%z#F-7$$\"\"(F*$\"1\"*y=()f')plF-7$$\"\")F*$\"1=Q
BmCe$*)*F-7$$\"\"*F*$\"1mvT_[=@TF-7$$\"#5F*$!1*p$*)36@SaF-7$$\"#6F*$!1
Nq]l?!*****F-7$$\"#7F*$!1\\V+!=HdO&F-7$$\"#8F*$\"14kEo.n,UF-7$$\"#9F*$
\"1/([pbtg!**F-7$$\"#:F*$\"1p6d,%yG]'F-7$$\"#;F*$!1`1lmJ.zGF-7$$\"#<F*
$!1obz=\\(Rh*F-7$$\"#=F*$!1hnrnC()4vF-7$$\"#>F*$\"1B&Hm4s()\\\"F-7$$\"
#?F*$\"1xiF2DXH\"*F-7$$\"#@F*$\"1h0O&QclO)F-7$$\"#AF*$!1wQS!H48&))!#=7
$$\"#BF*$!11<vTS?i%)F-7$$\"#CF*$!1Ri1?Oyb!*F-7$$\"#DF*$!1Ix(4]<NK\"F-7
$$\"#EF*$\"1Ggz/XeDwF-7$$\"#FF*$\"1I]/%GfPc*F-7$$\"#GF*$\"1!pyI)y04FF-
7$$\"#HF*$!1v'H@%)Qjj'F-7$$\"#IF*$!1='G4C;.))*F-7$$\"#JF*$!1]1B`kPSSF-
7$$\"#KF*$\"11pT7oE9bF-7$$\"#LF*$\"1sE2,'=\"****F-7$$\"#MF*$\"1Q-?ho#3
H&F-7$$\"#NF*$!15:'\\pE=G%F-7$$\"#OF*$!1e6VM&)y<**F-7$$\"#PF*$!1%**pNL
\"QNkF-7$$\"#QF*$\"1`Q4(y&ojHF-7$$\"#RF*$\"1y3%G'Q&zj*F-7$$\"#SF*$\"1)
[$z/;8^uF-7$$\"#TF*$!1!4Z!)oEie\"F-7$$\"#UF*$!1Qj:za@l\"*F-7$$\"#VF*$!
1$)fGEuu<$)F-7$$\"#WF*$\"1e8a5D>q<!#<7$$\"#XF*$\"1%=T`CN!4&)F-7$$\"#YF
*$\"1#4)[wM)y,*F-7$$\"#ZF*$\"1SAXF7tN7F-7$$\"#[F*$!1omB8ma#o(F-7$$\"#
\\F*$!1>ZfFl_P&*F-7$$\"#]F*$!1)GRq`[Pi#F-7$$\"#^F*$\"1ZPVe<H-nF-7$$\"#
_F*$\"1`[S?fFm)*F-7$$\"#`F*$\"1U$==]^#fRF-7$$\"#aF*$!1ih^)[!*ye&F-7$$
\"#bF*$!1*>'eL<b(***F-7$$\"#cF*$!1>\"p3-5b@&F-7$$\"#dF*$\"1\\#yCbZ;O%F
-7$$\"#eF*$\"1r`%3[E(G**F-7$$\"#fF*$\"1z8Rr+QnjF-7$$\"#gF*$!1n@-6i5[IF
-7$$\"#hF*$!1HR3+x<h'*F-7$$\"#iF*$!1HA\\mp!=R(F-7$$\"#jF*$\"1p!GI+dNn
\"F-7$$\"#kF*$\"12z'>Qg-?*F-7$$\"#lF*$\"1N5!\\z'Go#)F-7$$\"#mF*$!1zmR-
a6bEF`y7$$\"#nF*$!1BKv*y*>b&)F-7$$\"#oF*$!18H*o!oFz*)F-7$$\"#pF*$!1s=$
y8[y9\"F-7$$\"#qF*$\"1\"*)yb\"o!*QxF-7$$\"#rF*$\"1ZPaKla5&*F-7$$\"#sF*
$\"1j.iFOBQDF-7$$\"#tF*$!1wI()o&>xw'F-7$$\"#uF*$!1uCo/EY^)*F-7$$\"#vF*
$!1/V4aj\"y(QF-7$$\"#wF*$\"1.=)*oj2hcF-7$$\"#xF*$\"18t!ee,_***F-7$$\"#
yF*$\"1_`()fXyR^F-7$$\"#zF*$!1%3vqoE6W%F-7$$\"#!)F*$!1_PBRl))Q**F-7$$
\"#\")F*$!1RXuU*z))H'F-7$$\"##)F*$\"1_3LCyGKJF-7$$\"#$)F*$\"1a=+6Yk$o*
F-7$$\"#%)F*$\"1@Ht+K!>L(F-7$$\"#&)F*$!1re[*>c2w\"F-7$$\"#')F*$!1)fS+Z
%eM#*F-7$$\"#()F*$!1D#3jOy\"=#)F-7$$\"#))F*$\"1pgOt-$)RNF`y7$$\"#*)F*$
\"1LX7eSp+')F-7$$\"#!*F*$\"1zb+Om'*R*)F-7$$\"#\"*F*$\"1p:^<^()f5F-7$$
\"##*F*$!1Z!ehpgYz(F-7$$\"#$*F*$!1t%*p79#G[*F-7$$\"#%*F*$!1Vlna)>DX#F-
7$$\"#&*F*$\"157OZrhKoF-7$$\"#'*F*$\"1\\MMau(e$)*F-7$$\"#(*F*$\"1<_F!R
xgz$F-7$$\"#)*F*$!1HU!*>(=Qt&F-7$$\"#**F*$!1PN'=Mo?***F-7$$\"$+\"F*$!1
)e(46klj]F--%'COLOURG6&%$RGBG$FX!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!G-%&
STYLEG6#%&POINTG-%%VIEWG6$;F*Fejl%(DEFAULTG" 2 400 300 300 5 0 1 0 2 
9 0 4 2 1.000000 45.000000 45.000000 10020 10061 10056 10074 0 0 0 
20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 12 0 0 0 0 0 0 0 }}}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 14 "Vypocty limit:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 27 "limit(n/(n+1), n=infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "Cviceni 3" }}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 18 "Pouzijte prikazu  " }{TEXT 269 5 "limit" }{TEXT -1 
34 " k overeni vysledku z Cviceni 2.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT 305 7 "Reseni:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "limit((-1)^n, n=infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#;!\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "limit((1 + 1/n)^n, n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%$expG6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "limit((
1 + 2/n)^n, n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#
\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "limit((1 - 1/n)^n,
 n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x := 'x';" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"xGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "limit((1 + x/n)^n, n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%$expG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "limit(sq
rt(n+1) - sqrt(n), n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "limit(sqrt(n^2 + n) \+
- n, n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "limit(sin(n), n=infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#;!\"\"\"\"\"" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }