{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 "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 2 0 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 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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Out put" -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 "Maple Plot" -1 13 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 3 "" 0 "" {TEXT 260 94 "Nach bestem Wissen gerechnet, ab er:\nKeine Gew\344hr f\374r die Richtigkeit der L\366sungen - WK/12/20 05" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 "Probeklausur 1b - 01.07.20 05" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 23 "Aufgabe P.1.1 und P.1.2" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Aufgabe P.1.1(a)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "ungleichung:= ln(x)-2*ln(2-x)+ln(2*x)>ln( 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,ungleichungG2-%#lnG6#\"\"$,( -F'6#%\"xG\"\"\"*&\"\"#F.-F'6#,&F0F.F-!\"\"F.F4-F'6#,$*&F0F.F-F.F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Definitionsbereich" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(\{x>0,2-x>0,2*x>0\},x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$2%\"xG\"\"#2\"\"!F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "L\366sungsmenge:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(ungleichung);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$-%%OpenG6#,&\"\"'\"\"\"*&\"\"#F+F*#F+F-! \"\"-F'6#F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Aufgabe P.1.2: Gre nzwert:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "limit(x*sin(x)/( 1-cos(2*x)^2),x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"%" } }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 22 "Aufgabe P.1.3 (Taylor)" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Aufgabe P.1.3(a):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x->sqrt(x-1);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"fGj+6#%\"xG6\"6$%)operatorG%&arrowGF(-%%sqrtG6#,& 9$\"\"\"F1!\"\"F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(f(x),x=0..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6%-%'CURVESG6$7O7$$\"3)******fl_E+\"!#<$\"3?$et'fTR]^!#>7 $$\"35+++)R^g+\"F*$\"3EB(z&4K2zxF-7$$\"3!******>))[G,\"F*$\"3x\"zO44HN 8\"!#=7$$\"3++++njk>5F*$\"3]c*yg)\\l,9F87$$\"3!******fLTK.\"F*$\"3eb?% om?K#=F87$$\"3-+++0j$o/\"F*$\"3c#Q=AqpT;#F87$$\"3-+++GTt%4\"F*$\"3%3'* Hi'4*y2$F87$$\"3!******>&>jU6F*$\"3ulT;gXmwPF87$$\"3%******H;v/D\"F*$ \"3wKVMu$\\Z+&F87$$\"3!******z=h(e8F*$\"37AoCqwm*)fF87$$\"35+++Q[6j9F* $\"3Bb*=>8a_!oF87$$\"35+++\\z(yb\"F*$\"3K/)HkwA\"puF87$$\"3%******\\Xg 0n\"F*$\"31fT-!ev()=)F87$$\"3)******pJpW`(>F*$\"3+$G=14af()*F87$$\"3#* *****4f#=$3#F*$\"3CF#RHeg2/\"F*7$$\"3%)*****Hxpe=#F*$\"3!)zRazk(*)3\"F *7$$\"35+++uI,$H#F*$\"3iG#)QFt5P6F*7$$\"3=+++rSS\"R#F*$\"3yb()p?zdz6F* 7$$\"3-+++`?`(\\#F*$\"32=F[@ptB7F*7$$\"3!********>pxg#F*$\"3)R1$)4RyzE \"F*7$$\"38+++g4t.FF*$\"3=CMta/F08F*7$$\"3*********Gst!GF*$\"3NKeFpaQW 8F*7$$\"38+++ERW9HF*$\"3#\\.>!=Vj$Q\"F*7$$\"3@+++KE>>IF*$\"3iyt*3)H)4U \"F*7$$\"3%******>RU07$F*$\"3]6=7C#3iX\"F*7$$\"36+++?S2LKF*$\"3'>XreNZ V\\\"F*7$$\"3?+++$p)=MLF*$\"3*=Fq\")=0y_\"F*7$$\"3\"*******)=]@W$F*$\" 3/puMU!QFc\"F*7$$\"3')******\\$z*RNF*$\"3Enlbm7t$f\"F*7$$\"3#)*****RYK pk$F*$\"3@])*f+'Rpi\"F*7$$\"3))*****z+nvu$F*$\"3goP;e'yvl\"F*7$$\"3)** ****R5fF&QF*$\"3O)p4+G6!*o\"F*7$$\"3')*****\\g.c&RF*$\"3a/%)G-p=>$y94=F*7$$\"3G+++fO=yVF*$\"3/*ft]e$)z$ =F*7$$\"3u*****f#>#[Z%F*$\"3iv>XCu3k=F*7$$\"3)******pG!e&e%F*$\"3%GU2` &Gc$*=F*7$$\"3%)*****\\)Qk%o%F*$\"3r,\"3RiU&>>F*7$$\"3y*****>Mm-z%F*$ \"3/=$Rvjgo%>F*7$$\"3C+++60O\"*[F*$\"3op%4a;`E(>F*7$$\"\"&\"\"!$\"\"#F cy-%'COLOURG6&%$RGBG$\"#5!\"\"$FcyFcyF]z-%+AXESLABELSG6$Q\"x6\"Q!Fbz-% %VIEWG6$;F]zFay%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Aufgab e P.1.3.(b)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "convert(tayl or(f(x),x=5,4),polynom):\nT:=unapply(%,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TGj+6#%\"xG6\"6$%)operatorG%&arrowGF(,*#\"\"$\"\"% \"\"\"*&#F0F/F09$F0F0*&#F0\"#kF0*$),&F3F0\"\"&!\"\"\"\"#F0F0F;*&#F0\"$ 7&F0*$)F9F.F0F0F0F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Aufgabe P1.3.(c)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "diff(f (u),u$4):\nr:=unapply(%,u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGj +6#%\"uG6\"6$%)operatorG%&arrowGF(,$*&#\"#:\"#;\"\"\"*&F1F1*$),&9$F1F1 !\"\"#\"\"(\"\"#F1F7F1F7F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Die Funktion r(u) hat f\374r " }{XPPEDIT 18 0 "`in`(u,[5, 6]);" "6#-%#inG6$%\"uG7$\"\"&\"\"'" }{TEXT -1 61 " ihren kleinsten We rt bei u=5 und ihren gr\366\337ten Wert bei u=6:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "r(5.);r(6.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+](=UK(!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+s>5aL!#7" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Das Restglied lautet f\374r die St elle x0=5: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "R:=(x,u)->r( u)*(x-5)^4/(1*2*3*4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RGj+6$%\" xG%\"uG6\"6$%)operatorG%&arrowGF),$*&#\"\"\"\"#CF0*&-%\"rG6#9%F0),&9$F 0\"\"&!\"\"\"\"%F0F0F0F)F)F)6$\"\"!F>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "und es hat f\374r x=6. den Minimal- und Maximalwert" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Rmin:=R(6.,5.); Rmax:=R(6.,6 .);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%RminG$!+7yv^I!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%RmaxG$!+)[UvR\"!#8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "Probe: Wenn alles richtig ist, muss f(6) - T(6) in \+ den Schranken [Rmin,Rmax] des Restgliedes liegen:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "f(6.)-T(6.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!'[,E!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Stimmt!" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 31 "Aufgabe P.1.4 (Lineare Algebra)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Aufgabe P.1.4.(a)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "with(linalg):vector" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have bee n redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "A:=matrix(3,3,[[1, 2, 1],[3, 2, 6],[1, -2, 4]]);\nb:=matrix(3,1, [1,5,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7%7%\" \"\"\"\"#F*7%\"\"$F+\"\"'7%F*!\"#\"\"%Q)pprint326\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"bGK%'matrixG6#7%7#\"\"\"7#\"\"&7#\"\"$Q)pprint336 \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "t:='t';x:=linsolve(A, b); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGK%'matrixG6#7%7#,&\"\"#\"\"\"*&#\"\"&F+F,&&%#_tG6 #F,F3F,!\"\"7#,&#F,F+F4*&#\"\"$\"\"%F,F0F,F,7#F0Q)pprint376\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Probe: " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "evalm(A &* x - b); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7#\"\"!F'F'Q)pprint396\"" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 7 "Stimmt!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Aufgabe \+ P.1.4.(b)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "E:=Matrix(3,3, shape=identity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG-%'RTABLEG6% \")/D+D-%'MATRIXG6#7%7%\"\"\"\"\"!F/7%F/F.F/7%F/F/F.%'MatrixG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "det((A-E) &* (A-E));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"$p\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{MARK "0 0" 4 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 25002504 }{RTABLE M7R0 I5RTABLE_SAVE/25002504X,%)anythingG6#%)identityG6"[gl!""!!!#!"$"$F' }