{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 } {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 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 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 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 1 }3 3 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 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 22 "Exponentialgleichungen" } }{PARA 19 "" 0 "" {TEXT -1 53 "von Baumann angepasst f\374r Braillenut zer von D.Stephan" }}{PARA 19 "" 0 "" {TEXT -1 30 "08_ Exponentialglei chungen.mws" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 31 "Kann Maple doch nicht rechnen ?" }}{PARA 0 "" 0 "" {TEXT -1 88 "Beispiel aus der ZK von 1999. Ihr habt \+ diese Exponentialgleichung sicher richtig gel\366st." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "expgl1:=3^x+9*3^(-x)=10; " }{TEXT -1 72 " Maple macht hier keinen guten Output ! Ein Malpunkt w\344re nicht schl echt." }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "L:=[solve(expgl1)];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "Die erste L\366sung sieht komisch aus; wir versuchen es mit ein er N\344herung." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "L1:=L[1];L1N:=ev alf(%);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Wir machen vorsichtshalber einmal die Probe:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 19 "subs(x=L1N,expgl1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Versuchen wir es mit einer Vereinfachung der L\366sung 1:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "L1V:=simplify(L1);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Wir ah nen, was passiert ist. Aber vorsichtshalber erst die Probe:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "subs(x=L1V,expgl1);subs(x=L[2],expgl1);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Maple durfte nicht mit gen\374gend Stellen rechnen:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "L1Vbesser:=evalf(L1,15);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Teste aus, ob wen iger als 15 Stellen gereicht h\344tten." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Weiteres Beispiel" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Z K 1997" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "expgl2:=2^x*3^(x+ 1)=1/2;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "solve(%);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "subs(x=-1,expgl2);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Auch aus den ZK" }}{PARA 0 "" 0 " " {TEXT -1 5 "L\366se " }{MPLTEXT 0 21 22 "3^(2*x-1)-3^(x-1) = 2;" } {TEXT -1 12 " . L\366se " }{MPLTEXT 0 21 16 "4^x-5*2^x+4 = 0;" } {TEXT -1 1 " " }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "L\366sungen eins " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "3^(2*x-1)-3^(x-1) = 2;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "LM:=[solve(%)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " l[1]:=simplify(LM[1]);evalf(%);l[2]:=LM[2];" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "L\366sungen zwei" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "4^x-5*2^x+4 = 0;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "solve(%);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Also m\374ssen wir es n umerisch versuchen:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fsolve(4^x-5 *2^x+4 = 0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}} {MARK "4 3 3 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }