ML}  X c0C)HCCH Mhhݩh `eCDiCD`  RyHP   * 1H0芢@) Y0.Ș`i`#(PMRR\ \b Pgi 0  % @ / ՠ`d   0DDԝL @L}5 _$% l0$)$$Hȱ$ UhL" `e$$%`$%`  R@}W!( L(1   Y I`  d  Ld M * @  $ % C}C$$)ǥ%1 Udߥ$9%: !0 S$% DD˙`  }J})Lr S@A+EQUATIONNFTOTRYEQUATIOFFFADFBRUNPRINCOUNAS@WY`lSe`A3p}Seu1uSe}Wc@ =0Seu1u #$ +, 34 ;? 6FCG&KO=4SW6F[\cdklst{@}KW=(5HAVE YOU PL }ACED THE EQUATION AT LINE 1000? (0=N,1=Y)AM"QWW A [ll**THIS PROGRAM WILL FIND A S}&OLUTION TO F(X)=0 GIVE }N THE CONTINUOUS* hFUNCTION F ON THE INTERVAL [A,B]WITH F(A)F(B)<0# A lt6-@x# A}+0(PLEASE E }NTER A 6-* A/[06-0(PLEASE ENTER B 6-* A_p06-H$!v8("TH },ERE IS NO ROOT IN THI }S INTERVAL.;(>(H @0&"(PLEASE ENTER THE TOLERANCE&1-(%PLEASE ENTER MAX NUMBER OF ITER };ATIONS1 5'( }DO YOU HAVE A PRINTER?(0=N,1=Y)+5 A?j /(WORKING ON ITERATION %!/ An / 6- A }6-6-}) A4/6-/6-%++&,'@8E,6-) AIX/6-"^d @0h,,3a=b }2=f}(p)= 3p=3+!"8C)++&,'@GP, + ATa(6-%@ep2!$!v6- }! @ < 6- }@Nd;,(METHOD FAILED AFTER  ITERATIONS8"T;e/,3METHOD FAILED AFTER  ITER}ATIONS/(ROOT}="$3ROOT=pp(hPLEASE ENTER THE EQUATION USING THE FORMAT: 1000 EQUATI}AON=YOUR EQUATION. }RERUN THE PROGRAM WHEN DONE.&''6-+@EL$+#@PX,,%%@\$hh(`PLEASE ENTER YOUR E}QUATION USING THE } FORMAT:1000 EQUATION=X. TYPE 'RUN' WHEN FINISHEDD:BISEC$hh(`PLEASE ENTER YOUR E](^}PNTOGPASPRIN@ -8See@=>EXSeeSee@]`@eSeeO5(-HAVE YOU E}C-NTERED THE EQUATION?} (0=NO, 1=YES).9E"39O A0=/+(#DO YOU HAVE A PRINTER? (0=NO,1=YES)/ ddIF G IS CON}sTINUOUS ON THE IN}TERVAL [A,B] AND G(X) IS WITHIN [A,B] FOR ALL X WITHIN [A,B], THEN **G HAS A FIXED POINT WITHINx [A,B]}F (ENTER }TOLERANCE (ENTER MAX ITERATIONS 6-@Jnn(fENTER YOUR APPROXIMATION OF THE FIXED POINT} (USE THE }BISECTION METHOD TO! QOBTAIN THE APPROXIMATION).(2 ! AUg3 6-7 A@k< 6-K''(N})OW WORKI}NG ON ITERATION .L,"@-^,3P=G(P)=NO:&,  A boP6-%@sZ 6-}d }@P D--(METHOD FAILED AFTER  ITERATIONS.9"@H93METHOD FAILED AFTER  ITERATIONS.}( }FIXED POINT=""@ "3 FIXED POINT= ll(dPLEASE ENTER YOUR EQUATION IN TERMS OF X, WHERE GP0=X. FOR }}INSTANCE,IF THE EQUATION WAS X=5X+3, YOU ee(]WOULD WRITE 4000 GP0=5X+3. THIS WILL BE LINE #4000, SO DO NOT FORGET TO I}}KNCLUDE THE 4000. ((( RERUN THE PROGRAM WHEN FINISHED. ((6-+6@OU,&+@Y`$+#@d,,$ D:FIXED}PT}KCLUDE THE 4000. ((( RERUN THE PROGRAM WHEN FINISHED. ((6-+6@OU,&+@Y`$+#@d,,$ D:FIX}EDPTd M * @  $ % CC$$)%1 Udߥ$9%: !0 S$% }} DD˙`  }J)Lr J  ((  p L () !}  J}NjL= ( L 0q A    IB JC;?"} D W } LL  ` W )LA!  ߰"#})-݆ p"  } $G@LL 08`Q")<2Q0 -G$Ș݆ UL# ; p8$}(()(0ʥ)NQ`!}$GȘ݆LU )L ݆ L GȘ ݆LL )W>%}Z   HH)H "}p h  hyhy D L> L JJ    &}! LA*` BF#}7'8  M HN H` 8 Z  \LdJJ!"! GF'}E@F (!L$}GEE !E^ ^ E E7EȩE(}dE/EȩE  D%}% .L }  ;F d  ;?F7F? ( )}.   Z D LL d &} . D  L    p  E` , d) *} D L) 0BM݊L݉'} ML  N݆ L NLML+} [ TEqEHȱEqEh 0Gȹ G(} HLL GɛL  LFREE SECTORS,} G) *Gȩ GȽG GȌ*jj >G)}Ǡ LSYSBiNEWTONQ \BxSECANTa mBSTEFFENq BINTERVA6}GL C C*(> C8jJ3j29}CD( C202C ԠBX` N 1? l LlD:RAMDISK7}7,.COMLu L1 L ;L:}HL1  T`  `1  ɐ     `TU 8} L ? .  t`;}GBJ ~DEHI B V0dV9}QDEHI VF<}9 ,0 ,0 s0hhL  L` H hDHEh:}ǢDEL=}8HI4 0 HI,0 0  9 .G VLO;},0 L4*IJ`>}llD1:AUTORUN.SYSNEED MEM.SAV TO LOAD THIS FILE.D1:MEM.SAV J y08 B|DEHI<} V0 0`B?};DEL`?<0LV`@ʆ v s? F0Ξ05: [ BDEHI=} VY8@} B V  @  /DE `E:D1:DUP.SYSERROR-SAVING USER MEMORY ON DISKTYPE Y TO >}STILL RUN DA}OS B;DE J  (` 9 V⪍ ઍ  - } 3EB}:}DISK OPERATING SYSTEM II VERSION COPYRIGHT 1984 ATARI CORP.A. DISK DIRECTORY I. FORMAT DISKB. RUN CARTRIDG @}"E C} J. DUPLICATE DISKC. COPY FILE) hK. BINARY SAVED. DELETE FILE(S) L. BINARY LOADE. RENAME FILEm M. RUN AT ADDRES A}SFD}. LOCK FILE 5N. CREATE MEM.SAVG. UNLOCK FILE: pO. DUPLICATE FILEH. WRITE DOS FILES P. FORMAT SINGLEuL !N' B}#"&)E})9(&*)/h)''-&؆莟R'S  vL/ˢ L }Insert DOS 2.0s, type Y Λx  C}ǍDF}EfHI 1莏#q! @ y0ɛ8A0,' ȅ 1 1ild! 1L!NO SUCH ITEMSELECT D}G} ITEM OR FOR MENU! 0 .z:*{}.|{ 1 0 0JB 18L%|DLH} E}%DIRECTORY--SEARCH SPEC,LIST FILE?[# 0 0 &|D3" 1L!NOT A DISK FILEN !B 1L!E# 1 !BI}D F}ǝED:}:1BJ|DE 1DEBHI 1 h0ߢ J}0. G}ǝ  0?詛 1 y0YЛ 1 ;#L" ;#L! BL1TYPE "Y" TO DELETE...DELK}ETE FILE SPEC H}CVCOPY--FROM, TO?OPTION NOT ALLOWED697 FREE SECTORS COPYING---D8:COPY32.COM[l# 0|DL} .L/%# I}I##JB|DE 1BHID#E 1#0: B 1L!#͑### M}B 1#c$0SY J}S1}:## # # .#Ƚ# # 𩛙## 1,#PD#ELJ- <.N}BJD#E K}1 1HH 0hh|DL%1}:̳# L% #D#EL% 1 0 . O}.0O% 1L!WILD CARDS NOT A L}LLOWED IN DESTINATION 0 <.|Kc8(8(METHOD FAILED AFTER &@g ITERATIONS.Ar}"@'A3METHOD FAILv}ED AFTER &@+] ITERATIONS.((ROOT="@a3ROOT= F(F(s}#;PLEASE ENTER YOUR EQw}UATION AS LINE' 4000. USE THE FORMAT: &(&(4000 EQUATION=YOUR EQUATION 1(1($RERUN THE PROGt}(RAM WHEN YOU ARE x}DONE. ''6-+@,3$+#@7?,,%%@C$Q(Q(FENTER THE DERIVATIVE OF YOUR EQUATION INTu}O LINE 5000. USy}E THE FORMAT:"("(5000 DER=THE DERIVATIVE)()(RERUN THE PROGRAM WHEN DONE.%%6-+@ v}$+#@ z},,%@$p1(.(#TURN ON YOUR PRINTER AND TRY AGAIN.1X((((ERROR ENCOUNTERED. TRY AGAIN.w}D:NEWTON{},,%@$p1(.(#TURN ON YOUR PRINTER AND TRY AGAIN.1X((((ERROR ENCOUNTERED. TRY AGAIN. .|} !PRINASPPTONQEQUATIOQ89@AHIPQXY`ahipqxy }y}  A`YB(/($DO YOU W}}ANT A PRINT-OUT(0=NO,1=YES)?3?"@]iB3 Apmb(H(=HAVE z}BYOU ENTERED YOUR EQUATION INTO LINE 4000 (0=~}NO,1=YES)?LX"HNb A0R"((ENTER THE TOLERANCE" 3(*({} -(0(3( 0(},(!ENTER YOUR FIRST APPROXIMATION P00 1(-("ENTER YOUR SECOND APPROX|}AIMATION P11-()(ENTER MAX NUMBER O}F ITERATIONS-%%`*RRTHIS PROGRAM WILL APPRO}}XIMATE A ROOT OF AN EQUATION USING THE SECANT METHOD.mmGIVEN TW}O INITIAL APPROXIMATIONS (P0 & P1), THIS METHOD PROVIDES~}G RAPID CONVERGENCE TO THE ROOT. THIS__METHOD DOES NOT REQU}IRE THE DERIVATIVE OF THE EQUATION AS THE NEWTON-RAPHSON METHO} D DOES.%%,*76-@;D APHW 6- A}@[s! 6-# 6- A@w6-}( ! Ap26-&++$+&,,'+&,,3#(#(NOW WORKING ITERATION 4}((P=5"@t3P}=<O:&,  A *F6-%@.OP+ 6-6-6-6-% A@Sb}+6-Z @1f,,(METHOD FAILED A} FTER  ITERATIONS9"@$n93METHOD FAILED AFTER  ITERATIONS.}(ROOT="@r3ROOT=}I r(r(gENTER YOUR EQUATION INTO LINE 4000 USING THE FORMAT:^ }4000 EQUATION=YOUR EQUATION }>( ( '('(RERUN THE PROGRAM WHEN DONE. ''6-+@BI$+#@MU,,%%@Y}$(( (((Q1-Q0=0: OVERF}LOW ERROR.3"@L3 33Q1-Q0=0: OVERFLOW ERROR.( A Pp0(-(}"TURN ON THE PRINTER AND TRY AGAIN.}L0X)(&(ERROR ENCOUNTED. TRY AGAIN.)D:SECANT( A Pp0}(-("TURN ON THE PRINTER AND TRY AGAIN.=- bsASPRINTONPPEQUATIOP78?@GHOPWX_`ghopwx} }}  A`ob(H(=HAVE YOU ENTERED YOUR EQUATION INTO LINE 4000 (0=NO,1=YES)?LX"ub A0}}>C(0(%DO YOU WANT A PRINT-OUT (0=NO,1=YES)?4@"@BC3"((ENTER THE TOLERANCE"5(1(&ENTER THE} M}TAXIMUN NUMBER OF ITERATIONS5/(+( ENTER YOUR INITIAL APPROXIMATION/ &&t* ***}STEFFENSEN'S METHO}D*** THIS PROGRAM WILL FIND AN TTAPPROXIMATION P0 OF AN EQUATION IN THE FORM P=G(P), WHERE P0 IS A }FIXED POINT.} %%1*: AP>I6-@M\ ! A`o( 6- A@s2 6-}< 6- A@%F 6-P//6-&)+1}&,#@5?,,'+&+@C$,%,,Q#(#(NOW WORKING ITERATION R((P(}>)0=S((P()1=T((}P()2=U"DJ @NV223P()0=P()1=P()2}=ZO:&,  A (d6-%@},>n 6-x @0Bg8(8(METHOD FAILED AFTER &@k ITERATIONS.}CA"@ +A3METHOD FAILED AFTER }&@/g ITERATIONS.((ROOT=("@k33ROOT=}+ B(B(7ENTER YOUR EQUATION} INTO LINE4 USING THE FORMAT: &(&(4000 EQUATION=YOUR EQUATION ((WHERE X}F=EQUATION *(*(RERUN THE PROG}RAM WHEN FINISHED 6-#@JN&@R$:(:(/FLOATING POINT ERROR:P2-2P}1+P0=0 (APPROX.)>"@$}_>3*FLOATING POINT ERROR:P2-2P1+P0=0 (APPROX.)( A cp0(0(%TURN ON YOUR PR}_INTER AND BEGIN AGAIN. D}:STEFFEN*FLOATING POINT ERROR:P2-2P1+P0=0 (APPROX.)( A cp0(0(%TURN ON YOUR PR(;()hzASPRINSTAR}ENPPEQUATIOROOABU@@AHK@PS@XY`ahipqxy}}A 3A 23  "* A`.4 %%S*}RRTHIS PROGRAM WILL FIND INTERVALS FOR}. WHICH ROOTS OF A GIVEN EQUATION EXISTS.%%M*X 9@P\h,!9@Pl,}(L(H(=HAVE }YOU ENTERED THE EQUATION INTO! ELINE 4000? (0=NO,1=YES)L*"KQ A0U,C(0(%DO YOU WANT A }PRINT-OUT (0=NO},1=YES)?4@"@$C31 A(R2E(A(6WHERE DO YOU WISH TO START YOURY INTERVAL SEARCH?E<}3(/($WHERE} DO YOU WISH TO END THE SEARCH?3>h(h(]LEAST VALUE? (I.E., IF YOU WISH TO EXAMINE [1.001,1.002], }.001 WOULD BE THE}$ LEAST VALUE).?F " Ap(\P%(%( LOOKING AT [,%]d 6- A@`n 6-}x 6-%6- }A@ 6-$ !' A+4 @p8 0(0(%ENTER YOUR EQUATION USING THE FORMAT:} &(&(4000 EQUAT}VION=YOUR EQUATION '('(RERUN THE PROGRAM WHEN DONE. ]]6-+$$$$,&+@Zj$+$$$,,}%+@n$+$$,,&+@}$+$,,%+@$,%@$p0(-("TURN ON THE PRINTER AND TRY AGAIN.0X-(-( THER}E WHERE  INTERVALS FO}UND.Z6"@i63 THERE WHERE  INTERVALS FOUND.[ (b(( INTERVALS:l(}v-@m(([}*8,,8,] @6-%@.J<<([&,&] IS AN INTERVAL WHERE T}HE EQUATION=0.O (((} TH"@mH3[&,&] IS AN INTERVAL WHERE THE EQUATION=0.^68,-&}h 68,-(# @pq#((((E}CmRROR ENCOUNTERED. TRY AGAIN. D:INTERVALERVAL WHERE THE EQUATION=0.^68,}-&h 68,-(# @pq#((((E/L 䙣ލȎ!"` !"}H h`lDD   }TRATS:D"NUR 䙣ލȎ!"` !"}H h`lDD   S89APRINASBPBQCOUNALPHXDEROOSTREQBBP2}A@X[@`agyA A}$} @  #& +, 34 ;<CDKLSTZ\@bdjl@rt@z} $} A`  &&/* **HORNER'S METHOD** <<THIS PROGRAM WILL EVALUATE A POLYNOMIAL OF TH$}(E FORM: 66PX}=A(n)X^n+A(n-1)X^n-1+ ...3 ...+A1X+A0 qqFOR A CHOSEN X. THE PROGRAM WILL ALSO DETERMINE THE DERIV$}uATIVE P'(X), AND W}ILL ALSO REDUCE THE POLYNOMIAL.\\ALSO, AN APPROXIMATE ROOT WILL BE DETERMINED USING THE NEWTON-| R$}APHSON EQUATION.}%%5*qC(0(%DO YOU WANT A PRINT-OUT (0=NO,1=YES)?4@"@uC3 $} Ap1(-("OF WHAT DEGREE IS YOUR }POLYNOMIAL?19,9,9,+('(WHAT IS THE VALUE OF YOUR X?+1$}5(1(&PLEASE ENTER THE VALUES A0,A1, }... An:-; ((A:"$ 68,-((& ( 6-8,$}68,-* 6-8,68&@!1,-},""-&@59@=B6@F.6-+$,%8,68,-0 6-+$,% 68&@$},-1 2'6-+$,%8"),'}68/U,-4((P()=66-&8[`,'8f,8 ( (P'()=$}8 ^,:!(!(AN APPROXIMATE ROOT=};&(&(THE EQUATION IS REDUCED TO:<-@bg6@k> ( (+8,$} X^&@ @ C"@$7 AR}F A;d3P()=3P'()=8j,3AN APPROXI$}? EG@ NOVW^_fgno}vw},}   A`$* %%I*i llTHIS PROGRAM WILL GENERATEn DIVIDED-DIFFERE,}NNCE COEFFICIENTS OF THE }INTERPOLATORY POLYNOMIAL P GIVEN HHX1,X2 ... XN ANDd F[X(1)],F[X(2)] ... F[X(N,} )].%%(*dC(0(%DO YOU WANT A P}RINT-OUT? (0=NO,1=YES)4@"@htC3 Apx4,}CI(0(%HOW MANY POINTS DO YOU HAVE TO ENTER?49,9<}, -OZ 68,-`i*-o"68<,-,}E& * /(/($YOU WILL NOW ENTER YOUR DATA POINTS:}-KQ&@Uh ((X(%@l)?"$ ,}E68,-&((F(X(%@ 5))?(68<;P,-*} 2-@Ta4-@e7FF68<,-++8<&,}@,,&+8&@<&@D,,,'+8,&8&,,9   d}-JP&@Tki (8, l-qw&@{n,}- &@Vx (8<,  A(>(3FORWARD DIVID}ED-DIFFERENCEb COEFFICIENTS:A(-,} &@) (8<, "@-3 A7@ ADM-SY}&@]t 38, -z&,}@-&@ v 38<,  303(FORWARD DIVIDED-DIFFERE}NCE COEFFICIENTS:3(-|,}&@ " 38<, " A&vp0(-("TURN ON THE PRINTER AND TRY AGAIN.0X}E(B(7FLOATING POINT ERROR:} ,} w(XP(I)-XP(I-J))=0Eb@D(@(5WHAT IS THE VALUE OF YOUR X WHICH YOU WANT EVALU}ATED?DD 6-O:8@{,&,}8 ,,E6-@(J6-+&8.F,,'O 6-T6-8LN<T`,^0-@dj&@}n06-+$+#,,$,}+8<,,h/!@$!6-$+&@(3,/6-&@7wj 6-$r 6-%| D(D(THE VALUE} OF F(#) IS} ,} EAPPROXIMATLY=77(/(USING NEWTON'S DIV. DIFF.I ]FORMULA).<"@a<3THE VALUE O}F F() I,}S APPROXIMATLY=@"@ @3,(USING NEWTON'S FORWARD DIV. DIFF. FORMULA). D:DIVDIFF3THE VAL}UE OF F() I,cF89  PRINASADTORFEFAROWVAREDRRDIMSUPS@XY`c@hk@pqx@3}0}4A""?% @uxP ?7D)q) ?7D)q) @ :<@BD@KLRT@Z\@bd@jl@sv@ {@0}#@Y2Va@ }@% A`)46-@8> %%]* hhTHIS PROGRAM WILL APPROXIM0}cATE THE INTEGRAL OF A GIVEN FUNCTION FROM A TO }B USING ROMBERG'S METHOD OF INTEGRATION. %%}*0}*AC(0(%DO YOU WANT A PRINT-OUT (0=NO,1=YES)?4@"@EQ}C3 ApUb(H(=HAVE YOU ENTERED YOUR EQUATIO0}*N INTO LINE 4000 (0=NO,1=YES)?LX"06b A0:I("(}WHAT IS THE VALUE OF A?&)(E(WHAT IS THE VALUE OF 0}C-B?It(O(DHOW MANY ROWS WOULD YOU LIKE7 GENERATED? (NOTE}: A VERY CLOSEt( APPROXIMATION CAN BE ACHIEVED IF0}t+(#YOU SPECIFY A LOT OF ROWS. A LOT OFO(COMPUTER TIME WILL B}E REQUIRED,t( HOWEVER, IF YOU SPECIFY TOO MANYr*("ROWS0}. TRY NO MORE THAN 9 AT FIRST.M(IF THE VALUES YOU GET BEGI}N TOr( CONVERGE IN AN OBVIOUS WAY, THENK*("YOU KNOW THAT Y0}^OU ARE GETTING VERYH(CLOSE TO THE TRUE VALUE.)K(}9<, 6-& V 6- A@bt6-6-) A@x/6-0} V68@ <@$,-+$+%,,'@(@"%(%(R(1,1})=8@DH<@LX,$."@\n.3R(1,1)=8@rv<@z,(0} -@ *%%-@#+@'.#+&@2E,,,)6-}%++&?PIS,$,# A@W)6-- 6-%. /9968@0}<@ ,-?P$+8@!<@%4,%$,06-:E2}-@IV4xx68@Zd<,-+++@ho#+&@s,,$+8@0} <&@ ,,,&8@ <&@$,,,'++@07#+&@;A,,&@EX},6 <-@\>$$(R(,)=8@0}<,@0"@.03R(,)=8@2I<,B F6}-'@MXP-@\iR#68@mv<,-8@z<,0}/# Y Z5(5(APPROXIMATE ANSWER=8@3K<, UNITS.[}A"@Op3A3APPROXIMATE ANSWER=8@t<, UN0}FITS.c l(l(aENTER YOUR EQUATION AS LINE 4000 USINGTHE F}ORMAT:a 4000 EQ=YOUR EQUATION 2(0}/($RERUN THE PROGRAM WHEN YOU ARE DONE.2 6-G:,$p0(-("TURN ON THE }PRINTER AND TRY AGAIN.0X#( (FLOAT0}ING POINT ERROR.# D:ROMBERGNE.2 6-G:,$p0(-("TURN ON }THE PRINTER AND TRY AGAIN.0X#( (FLOAT0%K89\ n PRINXPAHALPHALMZCBDCLEACOUNNUMBEXSPUD@}PS@ WA A< Ax A A 4}.A, Ah A  A  A   @36 @ ;?@PCF@JL@SV}[jWB  A`nt %%}*4}* mmTHIS PROGRAM WILL CONSTRUCT THE CUBIC SPLINE INTERPOLANT S FOR THE FUNCTION }F GIVEN X0,X1, ... 4}8XN AND ,,F(X0),F(X1), ... F(XN), WHERE F(XI)=AI %%W*C(0(%DO YOU WANT A PRINT-OUT (0=4}}NO,1=YES)?4@"@&C3 Ap*4(0(%HOW MANY POINTS DO YOU HAVE TO ENTER?4779,9,9,9,9,4}}C!9,9,9,9,9,k-'2 68,-8A/68,-GP>68,-V_M68,-en\68,-tk68,-4}C}68,-!!68,-'0068,-6??68,-EC ((((YOU WILL NOW ENTER YOUR DATA:-(-4} &@e(-}(X()?68,-((F(X())? 68,- (6-kq&@u268,-4}8%@ ,&8,6 }2-@$*&@.<468,-@@A$E+L8%@PY,$8&@]n,,&+8,$+8%@r,&8&@4},,,%+8&@,$8},$'+8&@(@,$8,,,6 8B68FK,-@OU-68[^,-djB68ps,-y<4}-@ &@$>LL68,-+@(1}$+8%@5>,&8&@BN,,,&+8&@R[,$8&@_,,@68,-8,'8,B22684},-+8,&+8&@,$8&@"?,,,'8},D F068,-@CL!68,-R[068,-anP""-&@rtz64}@#R##68,-8,&+8,$8%@'@,,S666-}++8,$+8%@DJ,%+@NR$8V,Z'@^s,T''68,-++8%@w,&8,4},'8,,&V//68,-+8%@ ,,&8,,'+@0H$+}8,,,W Z-NT&@Xd((A()=8,f((X4}()=8,g"&@ Ah((}B()=8,j((C()=8,l((D()=8,n ( 4} "-!'&@+d3A(})=8,3X()=8,"&@h A3B(4}Ǐ)=8,3C()=8,3D()=}8, 3 +p/(,(!TURN ON THE PRINTER AND TRY AGAIN/X#(4} (FLOATING POINT ERROR.# D:NATCUBIC})=8, 3 +p/(,(!TURN ON THE PRINTER AND TRY AGAIN/X#(4/  2@@COUN!")*129:@}H +@LZAR@^h(@l (@8} DFLU}',@Y]@ag'/@kAP9/A8}AP'/@#AP9/@'+@/:-@>A! "} "  -" "/ AR8}@ "@ A0#X$[(FIGURE 1[(FTHE AREA UNDER THIS }GRAPH IS THE^ INTEGRAL. TO CONTINUE ..8}C.(4F:Ad,"@I*AdAU4 Ap*4F:Ad,"@(M}e*AdAU4 A@i- Ad.8}AdAU/$ii2,10,3,12,4,14,5,18,6,20,7,21,8,22,9,21,10,19},11,17,12,12,13,15,14,20,15,25,16,33,17,44,18,55,19,698}Ǜkk20,74,21,86,22,97,23,90,24,85,25,78,26,73,27,70,28,60,29,50,3}0,45,31,41,32,39,33,36,34,34,35,33,36,32ii37,33,38,36,9}39,39,40,45,41,63,42,69,43,78,44,90,45,115,46,132,47,121,48,103},49,96,50,90,51,83,52,77kk53,73,54,66,55,55,56,43,57,40,589},44,59,48,60,54,61,58,62,62,63,59,64,55,65,52,66,50,67,55,6}8,59,69,64kk70,68,71,71,72,65,73,60,74,55,75,50,76,45,77,40,789},35,79,30,80,26,81,22,82,18,83,15,84,16,85,18,86,22 k}k87,24,88,27,89,31,90,37,91,45,92,49,93,55,94,64,95,73,96,82,97,91,989},100,99,107,100,100,101,96,102,90gg103,88,104,8}6,105,84,106,82,107,80,108,79,109,78,110,77,111,76,112,73,113,70,114,65,119}5,66,116,68 nn117,70,118,72,119,74,120,76,12}1,78,122,80,123,82,124,84,125,86,126,87,127,88,128,90,129,92,130,90,131,88*g9}g132,86,133,84,134,82,135,80,136,78,137,76},138,74,139,72,140,70,141,68,142,66,143,64,144,62,145,604kk146,55,147,50,148,449},149,33,150,24,151,18,152,12,153,9,154,}8,155,9,156,11,157,15,158,20,159,26,160,34>hh161,44,162,58,163,73,164,88,165,99,1669},111,167,120,168,122,169,123,170,12}4,171,125,172,124,173,120Hmm174,117,175,111,176,108,177,107,178,109,179,111,180,120,1819},125,182,127,183,128,184,124,18}5,122,186,111Rhh187,107,188,90,189,87,190,84,191,80,192,70,193,55,194,40,195,35,196,31,197,9 }28,198,25,199,23,200,22\i}i201,23,202,25,203,27,204,29,205,33,206,37,207,42,208,48,209,57,210,67,211,78,212,89,213,125,214,9 }127f 215,128hjj2}16,129,217,130,218,133,219,127,220,126,221,124,222,122,223,120,224,111,225,103,226,95,227,89,228,84j9 } 229,80pjj230, }77,231,73,232,68,233,55,234,45,235,30,236,22,237,18,238,15,239,13,240,10,241,8,242,7,243,6,244,5 # 9 }-@ @` }c " """ " """  ,/AP  ',AD@g'/ADAP :9 }n(FIGURE 2 }:(%RECTANGLES ARE USED TO DETERMINE AREA $$(HIT TO CONTINUE . . . 4F:Ad,"@r*Ad9}%AU }4 A0P 4F:Ad,"@()A*AdAU4 A@Ek A0F "AdAU+q"$##9}C*## }6-)-+39# A=K!( (!(Z  ( ( (((( 1:INSTRUCTI9}ONS +6:INTEGRAL-(-("2:INTERVALS6 S7}:POLYNOMIAL0(0(%3:ROOTc 8:INITIAL VALUE0(0(%9} 4:FIXED POINT s9:INTERPOLATION(( 5:DERIVATIVE# (} (((#( SELECT ITEM.4F:Ad,"@1w*A9}dAU4 A`*9F:Ad,"@0.c*AdAU9%} D:INTERVAL4F:Ad,"@&g*AdAU4 9}AB4F:Ad,"@)N*AdAU4%D:DER8F}:Ad,"@$R*AdAU8% D:STEFFEN8F:A9} d,"@' A*AdAU8% D:ROMBERG7F:Ad,"}@QEx*AdAU7%D:HORNER9F:Ad,"@S|9}4*AdAU9% D:PREDCORR4F:Ad,"@H8P*}AdAU4 AETh7F:Ad,"@5l*AdAU9}"7%D:NEWTON5F:Ad,"@b&W*AdAU5}%D:ZERO8F:Ad,"@[*AdAU8% D:NEVILLE9}8F:Ad,"@XJ*AdAU8% D:DIVDIFF}9F:Ad,"@N*AdAU9% D:NATCUBIC A@ 9}h##ROOT METHODS"*+i+-@/3@7<+(M Vj1}-@Z^@b1(N:NEWTON-RAPHSON METHO9} Dl)-@@S)(S:SECANT METHODn A@IIINTERPOLATION METHO}DS }*9} ****-@@*(- 6-@:>@B(V:NEVILLE'S METHOD##(D:DIVIDED DIFFERENCE METH9}7O}D(C:CUBIC SPLINE A@p""INSTRUCTIONSG*XzAR@\j* (}*(r 9}̠U(} (U(GTHIS DISK IS A FUNCTIONAL LIBRARY OF DIFFERENT METHODS OF MATHEMATICALOO(GANALYSES. ALTHOUGH THE9} PROGRAMS DO} NOT ALWAYS GIVE ANSWERS, ITKK(CWILL ALLOW THE USER TO GET VERY CLOSE APPROXIMATIONS IN MOST CASES.9}]](UTH}IS PROGRAM, WITH CERTAIN EXCEPTIONS,WILL GIVE VERY GOOD ANSWERS TO GIVEN PROBLEMS.q(q(fTHE INSTRUCTIONS WHICH 9} FOL}LOW WILL GIVE YOU AN OVERVIEW OF THE METHODS THAT ARE AVAILABLE TO YOU.:(:(/HIT TO RETURN TO THE MENU WHENE9 }}VERYOU WISH.6-@@"!V6(HIT TO CONTINUE . . .4F:Ad,"@Z*AdAU4 A`E4F9!}}C :Ad,"@()*AdAU4 A@-H A`@##INTERVAL]*k$ (}$(x INTER9"}"4VALSY( (Y(KTH}IS OPTION WILL ALLOW THE USER TO8 GENERATE SOME OR ALL OF THE INTERVALS))(!OF A GIVEN EQUATION WHER9#}6E F(X)=0.P( }P(ETHIS PROGRAM IS USEFULL IN THAT IT: WILL GIVE YOU AN IDEA WHERE THE$$(FUNCTION CROSSES THE X-AXIS.9$}b(/($TH!}E INPUT NEEDED TO RUN THE PROGRAM:2(E(1:THE EQUATIONb(2:THE DOMAIN OF INTEREST(3:THE LEAST VALUE9%}NG(G("}}' TO CONTINUE . . .84F:Ad,"@+[*AdAU4 Ab:4F:Ad,"@(_w*AdAU<}4 A@{<9?} Ab HB4 (} ((1:THE EQUATION4(2:THE VALUE OF XD6-@LP@"T6(HIT TO CONTINUE=} . . .F4F:9@} Ad,"@@*AdAU4 Ab H4F:Ad,"@(D\*AdAU4 A@`J Ab>}L (}N!(9A}!( DINTEGRALPU(U(JTHIS PROGRAM WILL DETERMINE THEK INTEGRAL OF AN EQUATION FROM A TO B.RPP(H?}IN ESS9B}ENCE, THE INTEGRAL OF AN iEQUATION FRON A TO B IS SIMPLY THETCC(;THE AREA UNDER THE CURVE OF THEp FUNCTION FR@}OM9C} A TO B.V6-@@"R6(HIT TO CONTINUE . . .X4F:Ad,"@V*AdAU4 Ab@Z4FA}:A9D} d,"@( %*AdAU4 A@)?\ Ab2` ACJb% +Pd(}%AR@hdSS(KIN ORDER TOB} F9E}ChIND THE AREA UNDER THE GRAPH, THE PROGRAM 'DRAWS' RECTANGLESfPP(HUNDER THE GRAPH. THE AREAS OF EACHl RECTANGLE IC}S COMP9F}F:UTED, AND THE SUMh>>(6OF THE AREAS IS TAKEN AS THE AREA? XUNDER THE CURVE.jB-@\`@"d6(HIT D}TO CONTIN9G}UE . . .B6-@(l4F:Ad,"@,\*AdAU4 Ab`n4F:Ad,"@(`x*AdAUE}4 A@|9H}p AbRt; +@@#)10@-/57=C; AG^v (}AR@bxMM(EYOU MAY HAVE NOF}TICE9I} D THAT THE ZRECTANGLES ARE NOT PERFECT. THEz]](UPROGRAM TAKES INTO ACCOUNT THESE` DISCREPANCIES WHEN COMPUTING G}9J}THE INTEGRAL.|a(/($THE INPUT NEEDED TO RUN THE PROGRAM:2(E(1:THE EQUATIONa(2:THE VALUES OF A AND B~,,($H}3:9K}NTHE NUMBER OF ROWS TO BE GENERATEDRR(J (NOTE:THIS IS SORT OF LIKE SETTINGR A TOLERANCE. THE PROGRAM BUILDS ANI}NN(F 9L}k INTERNAL MATRIX OF VALUES. THE MORE ROWS GENERATED, THE CLOSER THE( THE APPROXIMATION.)6-@os@"J}w6(H9M}/IT TO CONTINUE . . .4F:Ad,"@3c*AdAU4 Ab4F:Ad,"@(g*AdK}AU4 9N}A@$ Ab (}(0 gPOLYNOMIALP(P(ETHIS PROGRAM WILL EVALUATE AN N-THk DEGREE POLYNL}OMIAL 9O}6AT A GIVEN X.KK(CALSO, THE DERIVATIVE AT X WILL BE; COMPUTED, AN APPROXIMATE ROOTQQ(IWILL BE CALCULATED, M}AND THE P9P}OLYNOMIALWILL BE REDUCED TO AN ORDER OF N-1./(/($THE INPUT NEEDED TO RUN THE PROGRAM:^(&(1:THE COEFN}FICIENTS A0 T9Q}EO AN;(2:THE VALUE OF X^(3:THE DEGREE OF THE POLYNOMIAL6-@IM@"Q6(HIT TO CONTINUE O}. . .4F:A9R} d,"@ =*AdAU4 Ac 4F:Ad,"@(AY*AdAU4 A@] AcP} (} ( 9S} INITIAL VALUET(T(ITHIS PROGRAM WILL COMPUTE AN INITAL VALUE FUNCTION FOR A GIVEN EQUATIONQ}(IN Y AND T 9T}FROM A TO B./(/($THE INPUT NEEDED TO RUN THE PROGRAM:m($(1:THE EQUATION IN Y AND T<(2:THR}E INITIAL VALUEJ( 39U}:A AND Bm(4:THE NUMBER OF ITERATIONS (N)V(V(KTHE NUMBER OF ITERATIONS INPUTED WILL DETERMINS}E THE SUBINTERVALS EVALUA9V}ATED.4'(THE SIZE OF THE SUBINTERVALS IS4((B-A)/N.6-@EI@"M6(HIT TO CT}ONTINUE . . .4F:Ad9W}C,"@ 9*AdAU4 AcP4F:Ad,"@(=U*AdAU4 A@Yw U}Ac8 (} (} 9X}X INTERPOLATIONJ(J(?THERE ARE THREE TYPES OF INTERPOLATIONINCLUDED IN THIS SECTION:V}+(+( 1:NEVILLE'S INTERPOLAT9Y}ION METHODU(U(JGIVEN A SET OF EVENLY SPACED X VALUES (EG., X0=1, X1=.8, X2=.6, ETC.W}), ANDOO(GTHE CORRESPONDING Y VA9Z} LUES, THIS PROGRAM WILL DETERMINE THE PROPERTT(LVALUE OF F(XN) GIVEN AN XN SUCX}H THAT XN LIES BETWEEN YOUR SET OF KN9[}OWN X'S.P,($THE INPUT NEEDED TO RUN THE PROGRAM:/(P(1:THE NUMBER OF KNOWN PY}OINTSS(2:YOUR X AND Y VALUESS(13:T9\}HE VALUE OF X THAT YOU WANT% 7EVALUATED6-@;?@"Cx6(HIT TO CZ}ONTINUE . . .4F:Ad,"@|9]}/*AdAU4 Ac4F:Ad,"@(3K*AdAU4 A@O [}Acp (}66(.2:DIVIDED DIFFER9^}ENCE INTERPOLATION METHODP(P(ETHIS METHOD IS SIMILAR TO NEVILLE'S METH\}OD OF INTERPOLATION, AND ITSS(KREQUIRE9_}kS THE SAME INPUT. AS A MATTER OF FACT, IT WORKS MUCH BETTER AS LONGPP(HAS]} THE VALUE OF X THAT YOU WANTr EVALUATED I9`}@S CLOSE TO YOUR TOP X'SKK(C(I.E., YOUR X'S ARE ARRANGED IN AE STACK: X0,^} X1, X2, X3, ETC.).HH(@IF THIS REQUIREMENT9a}W CAN NOT BE MET, THEN USE NEVILLE'S METHOD.d(d(YTHIS PROGRAM WILL _}ALSO GENERATE^ xFORWARD DIVIDED DIFFERENCE} 9b} COEFFICIENTS.6-@!%@")^6(HIT TO CONTINUE . . .4F`}:Ad,"@b*AdAU4 Ad9c}4F:Ad,"@(1*AdAU4 A@5 Ac  (} a}(3:NATURAL CUBIC SPLINER(R(GTHIS PROG9d}RAM WILL GERNERATE THE bNATURAL CUBIC SPLINE COEFFICIENTSOO(GGIVEN POb}INTS OF A GRAPH OF Al CONTINUOUS FUNCTI9e}6ON (THAT IS, THE``(XFUNCTION IS EVERYWHERE DIFFER-> ENTIABLE). THE EQUATIONc} OF THE SPLINE IS GIVEN BY:_(<(1S(9f} X)=Si(X)=Ai+Bi(X-Xi)+Ci(X-Xi)^2+$ +Di(X-Xi)^3_(ON THE INTERVAL [X(i),X(i+1)]d}.R(R(GAi, Bi, Ci, Di, AND Xi ARE THE 9g} TNUMBERS GENERATED IN THE PROGRAM.R(R(GIF PROPERLY USED, THE CUBIC Se}PLINEX EQUATIONS THAT YOU CONSTRUCT WILL-9q}ABddC B BISEC B FIXEDPT (B%DOS- 8SYSB*?DUP= KSYSBf}iNEWTONP [BxSECANT` lBSTEFFENp BINTERVAL jBAUTORUN SYSBHORNER ,B NEVILLE0 s6(HIT TO CONTINUE . . .4F:Ad,"@w*A9r}*dAU4 Ad@ 4F:Adr},"@(.F*AdAU4 A@J" Ad0( (}*PP(HIT IS IMPORTANT THAT 9s}\THE FUNCTION IS CONTINUOUS. IF ITs} IS NOT, THEN YOU,SS(KCOULD SIMPLY GENERATE A SERIES OFa SPLINES - EACH SERIES FOR EA9t}CH DOMAIN.))(!WHERE THE FUNCTt}ION IS CONTINUOUS.0/(/($THE INPUT NEEDED TO RUN THE PROGRAM:2H(!(1:THE NUMBER OF P9u}OINTSH("2:ALL CORRESPONDINu}G X AND Y POINTS4S(S(HTHIS PROGRAM ASSUMES SOME KNOWLEDGE OF CUBIC SPLINE INTERPOLATION. 9v}xIF6LL(DYOU WISH TO Lv}EARN MORE, THEN I WOULD SUGGEST THAT YOU GET A BOOK ON866(.NUMERICAL ANALYSIS FROM YOUR LOCAL| L9w}IBRARY.<6-@w}@"Q6(HIT TO CONTINUE . . .>4F:Ad,"@U*AdAU4 Adp@4F:Ad9x},"@( $*Ax}dAU4 A@(FB AdbF (}H%%(M GENERAL CONSIDERATIONSJO(O(DWHEN TYPING IN 9y}EQUATIONS, BE SUREy} THAT THEY ARE WELL-NESTED. FORLa%(INSTANCE, INSTEAD OF WRITING:((@((3*(X^4))+(5*(X^2))C(^(9z}USE THIS FORM INz}STEAD:a(N((3*X*X*X*X)+(5*X*X)PU(U(JTHE PROGRAM WILL RUN MUCH FASTER, AND THE APPROXIMATIONS GENER9{}GATED WILL BE{}R&&(MUCH CLOSER TO THE TRUE VALUE.TP(P(EBE SURE TO NOTE THE TOLERANCE IN THE DERIVATIVE PROGRAM. THE PR9|}|.OGRAM|}VSS(KPERFORMS ITERATIONS SUCH THAT THE3 aDENOMINATOR GETS SMALLER AND SMALLER.Z6-@ei@"m6(HIT 9}}%TO C}}ONTINUE . . .\4F:Ad,"@)Y*AdAU4 Ad^4F:Ad,"@(]u*AdAU4 A@y` 9~}8 ~}Adc (}dQQ(ITHIS CAN SOMETIMES RESULT IN A@ DIVERGING SEQUENCE, AND THUS A VERYf(BAD APPROXIMATION!9}*h}n(n(cI WOULD SAY THAT A TOLERANCE OF1 <=0.0001 IS GOOD. A TOLERANCE OF 3, HOWEVER, REALLY STINKS!jQ(Q(FI HA9}VE} NOT SET ANY PROTECTIONS ON THE PROGRAMS. THIS WILL ALLOW YOU TOl=:(2MAKE MODIFICATIONS TO THE PROGRAMS IF YOU WISH TO.9}},=(nQQ(ISOME OF THESE PROGRAMS PRESUPPOSES0 SOME MATHEMATICAL KNOWLEDGE. AGAIN,pDD( 5 ?c! u>Vq>SI> C?b6d?aP?`ac@6xy(?c! u@y=} } A` %%4* jjTHIS PROGRAM WILL EMPLOY THE ADAMS-BASHFORTH METHOD AS PREDICTOR =} AND THE ADAMS-MOULTON METHO}D AS hhCORRECTOR IN ORDER TO APPROXIMATE THE INITIAL VALUE PROBLEM AT N+1 EQUALLY SPACED NU=}EMBERS IN THE 33INTERV}AL [A,B] GIVEN Y'=F(T,Y) AND Y(A)=ALPHA%%d*C(0(%DO YOU WANT A =}#PRINT-OUT (0=NO,1=YES)?4@"@'3C3 }Ap7b(H(=HAVE YOU ENTERED YOUR EQUATION INTO LINE 4000 (0=NO,1=YES=} )?LX"b A0)((ENTER A}(%(ENTER B)-(( ENTER ALPHA()(ENTER N-6-+&=},'9,9,!68(,-!68.=,-}"("(8CL,,8R^,-@bf@jy76-8&@}=} ,%6-8&@,/ A@376-$ O 6-8&@7?,}%+'@CP,=6-8&@T\,%+'@`g,G A@kO6-$!O 6-8=}C&@ ,%+'@",=6-8&@&.,%+'@29,G A@=}TO6-$";6-8&@Xg,%)6-8&@kt,%3 A@x;6-=}$#;;68,-8&@",%++%@&,$%@09$%,'@=}n,$68,-%+$,&(8,,8,'"@r38,,=}8,( 2-@946-%+$,516-8@}=H,!6-8@LS,+ A@Wj16-616-8@ny,!6-8@}=},+ A@ 16-716-8@"-,!6-8@18,+ A@<O}16-9FF6-8@S\,%++'@`g,$++@#ks$,&+@w$,%+=}@&$,,,<%6-%+$,6- A@*=%6->HH6-8@A}J,%++'@$NU,$++@ Ya$,%+@em$,&+@q$,%,,@ =}(,A"@*3,F-04@8JH+68,-}8%@N^,+68,-8%@bu,J P!68@y,-=}!68@ @,-Z _ ( (APPROXIMATE ANSWER=`)"@D})3APPROXIMATE ANSWER=c B(B(7ENTER YOUR EQU=}EATION INTO LINE 4000 USING THE FORMAT: ( (4000 E}Q=YOUR EQUATION 2(/($RERUN THE PROGRAM WHEN YOU ARE DONE.2=}6-6%%@$p0(-("TURN ON THE PRINTER} AND TRY AGAIN.0X((FLOATING POINT ERROR D:PREDCORR<z4!"$ASPRINTOXEDECHECKTAN}@9:AE=qI\>yqC? )@a@RFc@Qx@Qx @ A}A6GA - @@ # A`'29A6=, %}%\* ffTHIS PROGRAM WILL DETERMINEA}[ THE DERIVATIVE OF AN EQUATION AT X GIVEN THE EQUATION IN TERMS OF X. ppA TOLER}ANCE OF .a01 WILL TRY TO BE ACHIEVED.A} IF IT IS NOT POSSIBLE TO ACHIEVE THIS TOLERANCE, IITHEN THE PROGRAM WILL }GIVE THE DERIVATIVE AT X AS WELL AS POSSIA} BLE.%%)*b(H(=HAVE YOU ENTERED YOUR EQUATION INTO LINE 4000 (0=NO,1}=YES)?LX"A} b A0JC(0(%DO YOU WANT A PRINT-OUT (0=NO,1=YES)?4@"@NZC3 Ap^i6-@m}+('(WHAT A},IS THE VALUE OF YOUR X?+ 6-% A@0G6-  6-& A@K]6-"##6-+@af'+@j}$,,$+&,$ ( (A} %"@+3( 68,-2!@/5 @p9F46-%@Jd66-'@8 @0hF}R7O:8,&8&@A},,!O:8&@,&8&@ .,,H6-8&@29,R @=QM,"O:8,&8&@U[,, <_e, @iN}$P"("(F'(A} ) IS APPROX.=R+"@#V+3F'( ) IS APPROX.=UZ$$6-O:8&@Zc,&8&@g,,}\(( TOLERANCEA}=^ "@, 3 TOLERANCE=b @0] B(B(7ENTER YOUR EQUATION INTO LINE 4000a USING T}HE FORMAT: ( (A}X4000 EQ=YOUR EQUATION 2(/($RERUN THE PROGRAM WHEN YOU ARE DONE.26-G:,$+@\$+$$,},$p1(.(#TURN ONA}X YOUR PRINTER AND TRY AGAIN.1X)(&(ERROR ENCOUNTED. TRY AGAIN.) D:DER@\$+$}$,,$p1(.(#TURN ON@V=/0  PRINASPPTONQEQUATIOQAPPROXFFFGJ@ObSeGSeedS=g}j@Uor@wSeedE}S# r rO SeecA N Thuu@DSP?QB9SY A`]E( (2(}$DO YOU WANT A PRINE}CT-OUT(0=NO,1=YES)?6B"@".E3 Ap2b(H(=HAVE YOU ENTERED YOUR EQUATION INTO LIN}E 4000 (0=NO,1=YES)?LE}X" b A0B"((ENTER THE TOLERANCE" AFQ 8()(V } ,(/(2(8(E}4-()(ENTER MAX NUMBER OF ITERATIONS-%%S*RRTHIS PROGRAM WILL APPROXIMATE A ROOT}E} OF AN EQUATION USING THE SECANT METHOD.mmGIVEN TWO INITIAL APPROXIMATIONS (P0 & P1), THIS METHOD PROVIDES RAPID CO}NVERE}GENCE TO THE ROOT. THIS__METHOD DOES NOT REQUIRE THE DERIVATIVE OF THE EQUATION AS THE NEWTON-RAPHSON METHOD DOE}S.%%E}**6-@.7 AP;J 6- A@Nf! 6-# 6- A@j6-( ! E}Ac26-}&++$+&,,'+&,,3#(#(NOW WORKING ITERATION 4((P=5"@g3P=<O:E} &,  A} F6-%@!BP+ 6-6-6-6-% A@FU+6-Z @1Y,,(METHOD FAILED AFTER  ITE}ERATIONS}9"@j93METHOD FAILED AFTER  ITERATIONS. ( ((ROOT="@n3ROOT=E} B}(B(7ENTER YOUR EQUATION INTO LINE 4000 USING THE FORMAT: )(&(4000 EQUATION=YOUR EQUATION)( '('(RERUE}*N T}HE PROGRAM WHEN DONE. ''6-+@.5$+#@9A,,%%@E$(( (((Q1-Q0=0: OVERFLOW ERROR.3"@E}}83 33Q1-Q0=0: OVERFLOW ERROR.( A <p0(-("TURN ON THE PRINTER AND TRY AGAIN.0X)(&(ERROR E}}pENCOUNTED. TRY AGAIN.)@9A3,All**THIS PROGRAM WILL FIND A SOLUTION TO F(X)=0 GIVEN THE CONTINUOUSt FUNCTION} E}5F ON THE INTERVAL [A,B]BWITH F(A)F(B)<0C# Ap9A6-@EK# A@OxD3((PLEASE ENTER A#6-- A@|}E}.36-E3((PLEASE ENTER B#6-- A@2C36-FK$!I(;("THERE IS NO ROOT IN THIS INTERVAL.>(A(}K E}7AJ"("(WORKING ON ITERATION K/ 6- A@;M6-6-) A@Qk/6-T/6-%++&,'@o,6-)} A@E}/6-W 68,-Y"$u A0Z,,3a=b=f(p)=[ 3p=]3^1'"{})+E} +&,'@ , ?1 A -h6-%@1<r!$!B6-! A| 6- A(#-($(FIRST APPRO}XIE}CMATION=8,-6-8,)# A"J*#>(-(SECOND APPROXIMATION=8&@N[,>6-8&@_k,,#-"@o-3FIRST }APPE}ROXIMATION=8,.#6"@A63SECOND APPROXIMATION=8&@EO,2# @ S#>(-(SECOND APPROXIMATION=8},&>E}>6-8,&>#6"@#F63SECOND APPROXIMATION=8,&>JS# @ WD:ZEROPPROXIMATION=}8,&>DfǔLLu ÝDEHILV 9 .l 9 .l  `` s$B }BH }CsI|DE V BLV nB,DE JLV B V BLVDEIʩ BꭝLu }}}EEsI|DE V BLV nB,DE JLV B V BLVDEIʩ BꭝLu SORT.BXE9!`O$ @%@-#q"FTaBM&.|j@B dAu m{Op!a I*0 (P7}! o <:t dp7 =@ ;Aq #BAip4@`s N۰38}b`2h#@2xe@g9v`B:6 7<ˎ@ H2 64񐧴NZu 8qDE~VdYyw: @u@ }9aur&4J% >vt'{g%XĴÂ)% r@ Kp4).' cICUl6hD ~!@,`A: z@ (e}F;ѐR$@B'A V3z,I|n}/ B~an+ߺpj=Ϣx \`˙KT ŭp]\z =1` Ƀ}߰D FDbz-R )>X+&07{(YjOQx2Q P&aTA @ 6ȧ h#L)=#,\%p ,}{@T]}'$5/\R1XoAVAKa6aF@ t 33 g05! j }mnqk̖(b.ލA67}i;7wJ8'`*=ro h@`O gƉv8RЄ$Pl<ˊ1uYΉXE+;H B4Hm/L9}o1Q jTCɻC$!  ރ1XNܶLqm~bY@HBe"(P!$t0V.@N@ T/}`-!R ! L"x'~!#@}|;*>Ok=o|_i, b o@ /}GK- /g.`~}G}%Pd(@,@~_*5 v6|#"@ƧN;3=0x/ׁ"#&P `p/1H:ȃ@5("!.Pp6`7 Y`|`0}LpFS`SE^QwL<4`*0-3Q`S1ՅrfS-0oc@V{٣xɳT5,!30 Ԑ p c T E8RpHш* }a\沆f0&~\`UP 6I83$?p0']XH@8X2^!C1XO:X "p` 0 7};؃!h A|IF1 + 0-UWh ߘDȊ@%k %`ppisF!rV8 P31&vhcF}MrG$lKebH}n , :6p@ f n>@ fQ0 - I69D:0MCTSDD D:@  (& @=@a,ˑi+ -6ʔ.Nhq}(iH?,cilUcn$eG(VD8FalA2<X ʃ;-)=L@3EV@}By%ؑ<ȴ[ v×IG9I[x)@z'{Gw4ʓ{{|G~|}g}w~~)Z|6#@K~7?J}W}R%G( Ac @`>x.c 2H)8~gz0h kN@88j@( ޡjʄ@(Pit1; [j.`@`'}`@50Ib"Ug˳4ՒvP;j,[p @P` @͚P  P\ic6eY]Ϣim9pI}@vx|~ L9iz"X8s1  P@O0s8y頱: P`(Pl P:} `2P<ЕO3Wee%6P $5T,EP׵b6_7hpa pr6*C00#ZP2~"X>!Bs[C@nP}RhP;1e㟂PV`Ig#` ,%/6%[6;  Pk-d8Cy #{Qy DHp*R3лKš_}dLS,P } 2 ͡ =s+̊ @Ƌ˼ y6=ϻ'I p{v(i71>s  LǛ˛},WAD!``Du `S[w{9hc 9p+R7`;w:p Ţ@pV`ZmGYZ}Ǖ~TY}nK6`6Ӹ =PRԸ?y{;)WdW6`c`UQ+ܒ7,S00Jp[; ˀ`4' N,|d}*ZǚڬJ[zٺ@0ٶ*Ȣ쪖En`ܯ |.Jr`>-/k>3p Ϻ/{8 }p@ &՜Lq mњϫ I  ,0 ៮`4`@ ?t   ӶI 8 @ ̰ @02 0}`,ɝ6-] 1[ÍP` xܷ,|GJU N|, WYڄ( f^ y̰H:0"e7A}r `x @@n@R@̰oT&`C`&++6bfD`_`g }-)+ 0ݫA;p#%})ҔP/,B" 7}uH|mSP3$Dn8"nDrRP\`\@,>[8d\sn e'ް0yVvp=ƜD#IYcJppJn}mGfDb<NXN9L PnKtFwa1ygТJpt 0wDtM\)@׌E}`.hFNuI UW $ =p`}^#([0P| z 5@ko5PD?>U4tip}?LEov-R]ϽGO}&گ`Ovp͝}{};?i,OKC0brB0최x’ 5K.b nG "zHp #w+ypX7{"ae:Z$Np{} 9"~z!`n5pIj^f~+#I0s^@-kp)"f' {녗449cSORT.DOCy!`fi =D }BAɐ*M8J'N6m 0bI3& n)#Isȡ1@yBF  )f1oI3g35o b3TΜMeqQH32ˀR8}Z8rޜچ6Liv6 aܐ)Z2gaCLK;jұr ڼi Μ2QyCSN8uҸ&WLA!y1R7ݤ)fLu^|SǍ~7:k} SlPA ST Nsyy4 x톙knxT wA&ݕ^a2aԀGu`dAGUPv_^FXo!Ȥj}-^!Z1̈́ڇ8ZgUuK5wII5R!yu%Z]5,q!lErE(Qq[P "~AQBG\WꁐMiƛo1b}Qk9DGKщnlX9hWFvPcT:YzIVoh%MerYyhZT][ njgXcʮ :$kaҨWHZj{b}n^TOڥWutmuZaïڊ5W(Gʥ-_2qFll %Ǥ7lAQ~oK5M Xz\2W`ݷV[}Ij}2nus(ջim&"awD˚2Wdp,(4{[I-ab4QZ 6ziaQGs1Hǧo| ¨}r&=nT {MVA2+KdAIksԤF-p0 d [5 ԠN6!0aYizD~C M(2hG;xr@J~&2Hc< #$k3#_BV^W2Z۶V$)8dsxցUJHr}m=i* EJi}1`EH[BH H>r@J~&2Hc< #$k3#_BV^W2Z۶V$)8dsxցUJHr}m=i* EJi%MENU. !`TO $8XWb]ueZWj]uXBb %dZBj %V,TH)b$TPaR'A$D*F|Vq2$gD>qB }, < `뀭j`끭&ت`낭 6`냀A (_ |'𥰵V [/lŀW  2 fBH)I"9AyL9Z@,$%eq3:̘5a }u2^䈱)Ɔʜ2s@0ٍ7rڀi'P\x,  Ce@I#ʗ[YI[ 4B| 6҂ATC@PЁ H Մ }` -@A6 ҂ 3h6 =HA6!E8 PH6a!-B{ p|`C"- 2V,`"-$;ذH b60"zx Ha#-46< }҂#Z@  YbC2,p<(Cȡ@xP ]Cz؀2 v }#>zD`2` ,p$$%D14Hd lH 6}@s pI 2`e j r)J@o ^Mt @ UP }RINT.ME ,!`r  S GΛ3r´M2e0F#4߸!ȓ)Ē2vҸA(aƬ #LʂDʌ)FLF1r@$ M }0СsԌÉ"ˀxc4byسaD-s&RI-Fy$ MP& )s7HwyUbԑa62F$Io4=p&o-ۦ坎k@ h }2ϙCT L¸9S'fΝMF\2;Ec4V!D.6i {0B7\rݑlPdIoсM%xfȗzbXSttL4RI }'0 0~uVJOF WpvgFlH# GrHT5SfEADMx]֘U8DDNT$iwfFXqt-fG]1g } @[SetXcU0WngP)Ya&$IY1w\蟂 ZUDY _nb C0QE* (sQ3X5k l1 }O,Z39۶f<:f%w$Y/Tlgbeƈ,CNc,ǥ!XɉHoa~P]c|'ul7cFmd#Aמ }/Dm5ҁ@v:O*eg B UZ @%pĹAq_J(`QuM0I'UIxQ[cWaO%@6k~zq)B ur1-w$qYG-\MmQZT:} `ǵ08hĒ${i*ʘ`mM F  } `ǵ08hĒ${i*ʘ`mM F 9BIRTHDAT.LSTe!` 5@ $C) D4)X# #I(FF"ADQ2c'NHdQDiM%AI":$B ,." }bӌ5oD $N@tĈ3b|28`q ' fȰ*CdYcF 3ֶ}Cma^6&M" 9x"QxECo[("K'))_Ku}&o- >C k98r^rmr0Ѓ28SM0dScja =S0lS?Cp? 2'&> =40~= b/RQ@dJ|8_5QiP}}8^z0b@h0! 33Ag gX#7o" 9Q R&^$:8[19/{B"&6$E6wz+M1K[{+:ω}t"%yg1DCb\ \T@ʐg lH7!XrxX uhe+M@ oxJyJ(6qrjOI%$ "YP}l". e2( n`'K( iP8g1@as84ь:Փ7|(ħ>ٌbc޳@)&ao9`0p:]A}:c?T}aP)D 0!WrK[jox @`4$kUp6iCX<*0il%ZZNjTf >UVd)4ȁh UbZ}VNSsH;85@NQ}OE,RXlaz2tðlZU̩+3< le KRVmed'KWR$BRԫJs*aa Kc}" g*n [yϤ'BQyȹT,datIgjV\j!/% 1g=Gi \$Y Q1y|(p%G }x'ȨMFQBJi}RL_p,#ARB)V"< Kb܄No'"D !,PLbr{)EH3!)" LaB/WU ShPPj0-FyFGyD}T&CQ0NWOfB'p u :,PLbr{)EH3!)" LaB/WU ShPPj0-FyFGyD 1INSEARCH.1!`qfn @0'fH)RI&ɓ&*>i,A"Y0(M }& $z"F_Bm=!8@E ), $тBP@B0~L@ZE,֕:%[#J * ز |ExȝDDovSt5 !}Ar5 L@PEIJ&5_9 ;YXò PL>B}n(JHW4SHv*\h1zˑ)-g,OD#0"}0LSL^ VP`HWX|`'1*3y- U6C@d:գC'seoլuxt*Q%G2hMպVխJoi(-#}[5~ 1S* v[<fTqAI\0$}091V>)rzX)͡F~_j ZUb1FI0c:x,"kɂn,4Y7m=,L>@3fM&fbsm LJӜN gt煈V EAwlb zΆ5ȟh<^l j-{n(}XxYۂmhv 0hrC(6 "O^j @k |[|!檞KQ ϜR;A{ W^,NaY$Ҏ0_ܓ<f”ڜ  ;f|?)}ȄH7 cYm|g//k]<,!b{P X X*gp BP:lr&4f<ϭs+}W{G2xxI TDyWyy 'z *s,32p p 2W;<s;<$"BIu6cUj:7H5:~V hX&6yX+R-zSFrB~9/FJ62}Tb eF P׷p 7/P: F6 iaZjDZ--IZ7*e RiɦFYee0I3NW3Tt/"?Tt,3}M˲R7Dơբj*PRw- Q7s,lˆ)]H 5I5wrLN_*0DC 3AC4}Н"'9ĭKZoPF{ 2 ݹ P [*p * *y&L" P -K:ʹ*z4<˲b8{55}H58_{3Lt*)վ,{繻-kN< ]S 8pL<}\k꺓qƫk8s<,c[:  5Ԍ+Gu J;y`XW-L=ȯ *\ C}Djͩ 7Ǭ]ЄnkaTˌէ\lí)b,ѷ,]-^.ߣڮNԠBm~'+inqn@lnp.˻"K p<]isZ**y{Ʒث2S=Ջ۝NlnL ǰV yݝ@}a Q`k50| {ɩ*Н04ڵR^ے.fkOp*n.>L -@S SO[KƤ\ͼ9SAA}8SlNJ|KpNNS :@@>70@:XPo["UY`]*,M +*to~$ HB}fZ؁'@w͎vώk۲،}VlE-Y4SP Mճ[{o9*pJ}uC}ʽ_ ldp ߢzêoLԸ=ݴԳ.c/d- ώ\Mhpܳ^cLٳŽٳ7݉G|k.@Ng !D}K7!~'K'+k~ ju:l +@ *R-z:qW^js,7j\! pKjق{E}묠n}0 pKǀD1m? !j gJZiW@nu(vҩdBkꁆ /ЩB/i b6Na\/F}m~g ;pӏ R0>5OO-o:.A Qe n4M w \5n1m?^ \ J}G}}?: LAK*}jU5>^pXFJRWXUC HLA-R5^uZ  `jӬ~Zͭy;zH}oo×a^ (/0֣[l ,A{-NŽyNnht'L>*0$ yNZ }: 0XE0i)?I}X%0X-o׽*X*0anC*mUPԈFHn*/0吝-MRѺ4=_*UmdJ}ն_]d>P뱹PN0(A + J=Cnώ櫂Nk)  +Y 3CN FحOzθ>0|uK}rn*>N1+ TRˎؿ^>++rn*/"wmn ! +Y 3H5QQL}Ɯ0|0t;Ե*gP~T ` +IJ]͎>NR T~ٟ"*_ܠ2tk  +Ii 34OM}dN tǶ0t;ԵT.IKh00t;Ե2OO-O0yt;0C I=)N} PFQ  +Ii 34OO*` 0(  +IJ]͎>NRT}h00t;O}*gP~T}h00t;ԵT.PN[˝Ɏ0t;0C I.OTNn0eTP} /<0t;0C I.OTNnp7Keg`^1+Ii 34OdN@@OoO^Q}Sf:' *RTOYo0Rm"ISU C@ТrR0Io XRUjYo0F@"!,I aZD<R}NaF0IonA%D Y_ KFR@ТRjUOCrR@IonA-RUْ`]-AS}K*D \( P?^F@IonA,I -U Yo@IonAR@aUYo@IonARТU Yo@F@T}jRUpCeAfR@fZo&D fROU1f6ǎU} ND ?8@IonARR_ ؜)DIonA%D U_jY`]-A)( 5^D pXCFG@R@V}ТRPUC@r" ]-A-*( T2d %_)fOXROUjYoV@F@RW}[D-:lF[@IonT RUOYo`@ziCW^P/(aQf`kzXRТUOfRP U(aX}J6 RP Q@T& %~nZ!pnM=۝m];5֒@@7Cq@hݝm=}Nl{!pmҜ$kY}!r@X{' v' 6 }R0gНX{'^ӭ`w5۝6*Н6'!@ Af %묠.I -fZ"_Z} aZ(fF^-R .PF5*pXR\IZa:^e J_,DUТC0rjRP@x 1@eXm[} *MН}[ *תR _ PziXm-R.PF@6Z %IZ\(ZK:d[ajQfZLAR\}UjYoPIo((Z-UjYoPIo((Zb[_Z5fRR}4Z>%}ݫRd[f@ !]}4-IZV_ZfZrYRO UYohLoԩ/ FώH @aS(f %묠-R'h@.^};С"uB3A;C9 `9  9  ;pi/ ;gS'n`@؀RՀP΀ hP̀ h h hPP` _}P ̀i i @ 1@ @Ԡ @  ̀@ ` P `Pq'Pu`pVS`F<.Z h-P hP`}PP hP̀ h h hPP `Ԑ `   А@ 1   @ P P ('0a}7p`wcC>wZ> ?`<<67C,b}>` /n`p3K6H.\'*`- Y$0 0m0*' +0dfd">OT4;pFj @Mv8UVp[|Twc}b'uFV>w@cy]cVlTfW'н>wcRR>@C@sFrF1¢~FV%+o`x^lg!7@j^}Fa)'b}2vg'e(_d}h*nb.nvr`aN2H.VTBܓe,yp7!NvDkp;`vʌ faXfA jfAT'T)DH)b.nEE<<"+PHgge}v*<PiInpjBb/VTT3P("/y.+u+">$`v*<PiIpp`Bb/Vu_A@CJ_Pw_gv*:W>'F (RkDtp5W-tkDs5W-]FD PX@PƦF,Њ 0 P@@ i}P*c5wB/p"'ph#rrcRS1nppLj,wr*I,FT Z'Tj@j1TIN p m{2pTɨ.0j}I8qE A  `DjTNdQg&*thDĴz/FX,smDFPA>`M0I_k}pcRpr>07+Q26OFPAR\28`,268 ,68 ,208 ,68 ,68 ,68 ,0l}0,,0p131 2131 2131 21 132 ,0p0100,0p2 , NprkMm}GUI710N0( a .y91H@ɑE@YIPT@ .`@PƦ,Q`"Ȥ+]bp:(41 `g(rARwpn}:(.: Sx]i+x& (0up:(4 72hg(rAG`I;scSˈ a  ab XyoXIDPCwD72o} r/rw!:w!:w!:w!:w!:w!:w!:wA@Q5Eg:W-Rn3X:˾*zp5W-Qn3p}W'TY a7 mɑp) x'p3]pI%zK%P9quBˁ9VQLزy;p:>[C{p3Iw2]?P9quBq}pS0O(y9w"]?F>[Xqp3W'T a7AYIPTy[P9quBr}Q?p#mmtKXҹ^ x'Xҹ*p]?P9quBɑYP Ek>[ x'p泵 *~pjt컫P9quB~ɑs}GEP88p컫 x'v쳵 *~p]* aP`RZT' aN)B>lx5@E^cGxD6fC\pyRQvgP0WT) a62t})B>lQ׃N;HO}OTnpyRQvgP`TI abp X7xI pO 0TQT@AIp7IPTOI@'pHLu}R`i`Mx# a`&q 0 P@@ P 5 apa5P0FTY a'X zqApAP8WGv}t, &C%Qb-UZT' a@p(<"K,*E0xBP9qDTE  aN)r2qx5@E^cGxD6fC\0`ew}-QvgP$a62)r2qQ׃N;HO}OTn0`e-QvgP$ a0VP9q{EL0I2E^P!uE9G'aPXv[P\cx}5})u  |26"!'*g.> sg~*wp2xˠ ,v Q2{OF PrA7Ptr#i:W-y7{BXD5{By}tp5W-:{0P5W-T''u0VŹb:P):::0 ,79p,:::y 0}q#@%I,FGU:%P:z} 7pG0?`|]PԂxZx*',9pTj] 4GUGUS`iy%`f2d8nd3WDCfa`dn&/VJpF$3:]owFR-I63T{}@`   2 `p  ``0p `P    `@  `ɠP@  `  < ` |}DC,?x zI;[,}p耟ɨۢ  @:Np91H0]}}  @:Np91H0]/QUEST.BAS,w^$ C |)AYXHM6RB.bKƄ2#֓*T<ހ!RH1ʰ`ϖ !אY;CB֔;kQF [;a}jȭ%Hb fBCVCl) 3ml šQIB !5`ABH!NȒbl`T!FE3# 1YREH" +ȄI*¨` RLP˝)E}"l'Di!%0۷"!ՙ])I-B &I qmMQBJG$鏠B*3'M]kPAtNDE(CT, 15ND6%H @@2a@"}a*@2a:$Ba$JRaZbaj$ra$z"!t(B#tHB%thB't)tB+tB-tB/tC1t(C3HC5th7C9t}C;tC=tC?tDA(DCHDEthGtDIDKDMtDOtQ(SHUthEWY[]ŗ_| a(c|IethFgitkt}FmtFotG@р1Q*($2 (<4 S 3̀"3Pp1Ӏ23H (K,@L5OS3L2%oc  R Th$X`$B}=@}]APvAR }J3݁QRN]5(BA6҂:8 Tm%  `!!S"%$B P p&01H s^!}P5 5 Ľ(XiBl0 #Tݦg <޽oV7h $PPX6t E@i6 $h`J%$h:e}l%J Q`DH8 FwXI<$ ; h@"TBD"&(L@/H|@qX@$T-O H6QLX`P 8(YRi\c7aU }6ЀJ] ~!,!g>0RLh1-/><) (H \ hA B{ 1KJX _!}vP5QO Am k*) LPA `K,؀4jReς0>:  h#1[  %(X;YNx+nݝT qA+}*na:=Uڠ 4k ĵ--pi)Y%Q[u|s.P5[(T|_F"8@LV@!$W\}UZNp(1t@f`Z @0!|e P!l VcVG#XJf~cR`Ș 8<3`ٶyd*fp;}F8 X%4ď]]gE@"wj^S%E`Z@l P>,@6$( (9wjU }<C4U 14 P5;F`V8f\$$:@)D8Pǘ;%P Ϙr p X ؍LjPN"k "0OU# x}v K:!hP̰ˠ 0`ɰ  @ dHHw $I\X#S<k 8`$ s6 qE;Uc39Y?}c>kS-hl LP99X`QP 8`K, hF/p]>\w9`BHPp cv 9;$Ĩ D:!S@.FXĘ} I@7p6 ړbA ,eI@` C:=`pl$ә>չ;% =:^yi哝,ji Jx] 1Y}W8ǟ׌E0 FIgI `iPwGi  @ @o$Z 0c eu ` >`V @PdGa? ӕ:#@A}8VA 05*[DPS:(\DV:yp tN(qzd`5':ky‰М CA@K0TE3S(oqJtJv}Xv)`:8To ࣎Jv JPF:l:)0q!* 3J_0CIGCzx:3FUv&SZ kJ:;`e`?CE NR@}_Ĉxp@CzTڟOp T`k 6>H#T -P ,eeV8Tɨ#?{:pU ` nPM[}8]zuX# GORP S07i¹ hR@. Ep ? s[cp z z z z z (4PϠp)i4 4}Pʠt[Tkm# wK0q`@!h;% ݳ0plJ< P CO@+`a, U %{Afg8u:uXI`H     }Ѹ    `K:b;4&) X(wdO0ێ_ ? -d|@(hf* @E@>`) 킆<5`0 }0|? ; 0SC5G 0TpBZy " trLkQPHina0(o`dv10pCu]`C 91P}-ZnpQ( PZVxmq SZ&?gnɴ^MiԐ5^5 %@Py}!x0Zl8 w #rT4B>jx.ؠ;YKfXIQm3 9P5 0@p=M5Vwe4&_p^E@$c'aMCI}Aio?|u3e Aӽ k-0k0Cv֠>~,[ ˲E`!{@T6d bOŲEgnHkòEj&xpwQg41E8}} J@ P (U% P;=_~F0:l8ANB$@Ry 4% IiTd ` #36T>vBJ iZ%d$lX l<Xv6}ztH`N66 U !iFP`p2`==v (8`G.a"")""J'лa"")""67`pn}Og-ubd=C0'a""31t PSP'rV5d=U`ph*Op0V'qZ[:+FE R`F9>@.{"vmB @}`='︞J`xp~C:7S;0?Š$}p  @&#*̺-,[p ;i8@;¬0;¬?;¬ ;} ;&2 ; ; ;¬ ;[y6 ;m8P ;‹20 ; @ ; * , ǰ*0-̾;.2@ ;P} ; ; ;P8`M񘪑g\@ ; ;m8 9.2;(86P CJFPbfp Myy0zupSPpc}@'hDPc`s0ߐ*lP-,*lP-,*0-,* , *̺-,![y, ʰ񘪑'*lP-,'* |G}T -#Ah-}Kj AB$X+;Ԥ -$l- }@6 -P B46 -$l[`@V6 -0V+WO6p -@L*W}- $l?-:N;} -`eEʪUVd -dEu-Ve60 -E0I` V6@ -e}P -@Lp? -DCئCO6 -8) ú06 -8Q`}S Oe`!/ 6 - BT6 -@wp^`\WyX6P !#@j`B?`8x_ ;HD:P|s06 }ړِ   _ I0 I0`0 C P   X  P }v՜P݈D А0 MP  00`0  РP`6 |.62¯}8}WI4+AA"xjҠ= @:IK 0])j=e  I0 I0@ _  }     P А  #  }Pu խK𸺕7 iP ; @}@ `n}` 9FQd 5: ` W6@CPFG>}zMp'D@8XW0-Sy̜@J`0 $ ݩf. gt][0/}}@nvp@0`7{@Uc}  Sie }y)>sfN ĜPk6P7  ݩf.Y7 <@{@KpQ*}y-Ɯ |H߀`z|}  U l 8z- * 8z-0 o@U`|%qÕ%t9f.r`|8pÕ8}Ǟ: of[|O'B3*̺`{e8/G}*̺  | 6odP@ʲiOn$:hˇ{*{𸺕8P`+2ˆnjnfV6}ЎuZs#'&>1*̺} -p+:P ,p*,y'€Py€ -8BI&#: ;|}f -p+"ry'Ps}Պ0ObO?d DS@D`H\P]QUEST.DOCy*g UC*EPIĉ I !OH!pfHPD:aa2\Dp}D7d@S& 2#!yBHPˆ13eܤC7p#GH6}u&6qLѤ,sg.7fmy& 8" *C6D[$g *hr(2XٔfΚ29l}?93:r9z3g:eIƍ0ix2~S7)sdʕ-laDit@sbinYxS{."CR@-ovi;Pj8f"qFKamo}oFmbgZgڹlr1 ]f4J,$cR 0dcdӵbXw(}!q}?1y'Fc)yLe=ӈDo![7}diW xtwWq%Bp(ۥ nayryZzhTqFj1ƔSEk6 F p:ŐO'n&UTcPMQ 9qIPBP0X)@ Q@亂=(rr ~I}vG9zPB&'}i{*A AsdF0F`fˁ0B h1!27Ց` dM9QҌtcp(wR܅ꠞ*5-4BhM[w}FmlɜJkn"iU 8Qt7©w6.ɀ{>if{͘u=ho{jsܞm]Oc]Ђ0C ʥނ>x[]x?nʃxǮ}p@SIzG7c[6ȆH)B|ҍH3#ݫK樀 O