{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 128 128 128 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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Out put" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 11 128 0 128 1 2 1 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 128 128 1 2 1 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Gegeben ist die Profilkurv e eines Berges durch eine Funktion f." }}{PARA 0 "" 0 "" {TEXT -1 51 " Berechnet werden: Nullstellen, Maximum, Wendepunkt," }}{PARA 0 "" 0 " " {TEXT -1 89 " der Winkel, den die Wendeta ngente mit der x-Achse einschlie\337t" }}{PARA 0 "" 0 "" {TEXT -1 111 " und der Winkel, den die Tangente in der gr\366 \337eren Nullstelle mit der x-Achse einschlie\337t. " }}{PARA 0 "" 0 "" {TEXT -1 81 " Die Berechnung bezieht sich nur auf Profil kurven dieser Art. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta rt:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " f:=x->0.05*x^2-0.0 02*x^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)opera torG%&arrowGF(,&*&$\"\"&!\"#\"\"\")9$\"\"#F1F1*&$F4!\"$F1)F3\"\"$F1!\" \"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# f:=x->0.038*x ^2-0.004*x^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(f(x), x=0..26, y=-2..5, color=blue);" }}{PARA 13 "" 1 "" {GLPLOT2D 406 406 406 {PLOTDATA 2 "6&-%'CURVESG6#7W7$$\"\"!F)F(7$$\"33LLL$3gsm&!#=$\"3GM hl:y[p:!#>7$$\"3amm\"zFJ)f5!#<$\"3QKz#e@A\"y`F07$$\"3ALL$eszVh\"F4$\"3 F='*o8B'*=7F-7$$\"3cLL$33/E<#F4$\"3qGCQh8+b@F-7$$\"3Fmm\"HHv\"GFF4$\"3 G)*fu!Hd`J$F-7$$\"3#GL$eC4EVKF4$\"3!R>z;Dqqd%F-7$$\"3U***\\7E-mx$F4$\" 3EyLKd&pS0'F-7$$\"3!GL$eMY=GVF4$\"3Q5mt&ox\\u(F-7$$\"3#****\\i2)*z([F4 $\"3i_FVzk+w&*F-7$$\"3Lmmm\"y[NW&F4$\"3sbdTgA+f6F47$$\"3=LL$3:'oTfF4$ \"3kOJe&[bcM\"F47$$\"3R+++X3Z-lF4$\"3Ec\"orvHUc\"F47$$\"3g*****\\3wF4$\"3&>N7jKPM,#F47$$\"37KLeM`'45)F 4$\"31XKq3*>!=AF47$$\"3=mmmhV\"po)F4$\"31j%4U$=0iCF47$$\"3[mmmY+H$=*F4 $\"3?9&3IQNxm#F47$$\"3O)**\\7(Hpg(*F4$\"3Qz)f\">>t.HF47$$\"3ammmR#zr- \"!#;$\"3YQuQ#4Qz5$F47$$\"3#***\\7Z\\D$3\"Fdq$\"3Y%e#*yDM\\K$F47$$\"30 +]P\"G_m8\"Fdq$\"3U_x\"Fdq$\"3`cf!e9D#=PF47$$ \"3fm;H;,`V7Fdq$\"3k)Hul]Ff)QF47$$\"3ALL3nmr)H\"Fdq$\"3?OSkg]K_SF47$$ \"3EL$eM)*RgN\"Fdq$\"3/of`C!Hr?%F47$$\"3$***\\())4SfS\"Fdq$\"3*o5cSV&= DVF47$$\"3CLLe!fL)f9Fdq$\"3-5!z#GmULWF47$$\"3()*****4%3^::Fdq$\"31dwN` kHAXF47$$\"3')***\\#o,)*p:Fdq$\"3e'3q%Rfp%e%F47$$\"3v**\\7V?oA;Fdq$\"3 u!fQNeE,i%F47$$\"3o***\\(*[)>\"o\"Fdq$\"3>9gtAwcGYF47$$\"3\\mmm>\"yPt \"Fdq$\"3h^$R6O0lg%F47$$\"3-++](4=**y\"Fdq$\"31n&[&\\/$*\\XF47$$\"3AL$ e9E*yS=Fdq$\"3Iw2x0zZnWF47$$\"35++]!)[S'*=Fdq$\"3X,Sa\"R![TVF47$$\"3?m ;zV[t[>Fdq$\"3eV^ssK$p=%F47$$\"31+]iLZV.?Fdq$\"3ceEp-%yh)RF47$$\"3Imm; uQ\"p0#Fdq$\"3cdhAq9I\\PF47$$\"3q**\\7y:!H6#Fdq$\"3sSf-j!)GcMF47$$\"3[ LLL\"RCo;#Fdq$\"3z\")=F?UgGJF47$$\"31LL3c#o>A#Fdq$\"3a8p;=\\OXFF47$$\" 3em;z,blwAFdq$\"3zav)4mg_J#F47$$\"32+++,u!pK#Fdq$\"3!G2*[!3>W(=F47$$\" 3YmmT[<]%Q#Fdq$\"3SE)4996MJ\"F47$$\"3c**\\(QGe-T#Fdq$\"39D[#)y6oU5F47$ $\"3/LLL>[,OCFdq$\"3IuEo([wRf(F-7$$\"3Ym\"H#emZjCFdq$\"3177Y\"o'*HV%F- 7$$\"3))**\\7(\\Q4\\#Fdq$\"3:*)3*ol\"\\C6F-7$$\"3v*****4)HA*)\\Y\"\\*F-7$$\"#EF)$!3w'**********>N\"F4-%+AXESLABELSG6$Q\"x6 \"Q\"yF`\\l-%'COLOURG6&%$RGBGF(F($\"*++++\"!\")-%%VIEWG6$;F(Fh[l;$!\"# F)$\"\"&F)" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "C urve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 " Die ersten zwei Ablei tungen: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f1:=unapply(diff(f(x),x ),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1Gf*6#%\"xG6\"6$%)operato rG%&arrowGF(,&*&$\"#5!\"#\"\"\"9$F1F1*&$\"\"'!\"$F1)F2\"\"#F1!\"\"F(F( F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f2:=unapply(diff(f1(x ),x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2Gf*6#%\"xG6\"6$%)oper atorG%&arrowGF(,&$\"#5!\"#\"\"\"*&$\"#7!\"$F09$F0!\"\"F(F(F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 14 " Nullstellen: " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 24 "nstf:=\{solve(f(x)=0,x)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "print(`1. Nullstelle: `, nstf[1]):" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$%01.~Nullstelle:~G$\"\"!F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "print(`2. Nullstelle: `, nstf[2]):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%02.~Nullstelle:~G$\"#D\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 " Extrema" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "nstf1:=\{solve(f1(x)=0,x)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "print(`1. Extremum(x,y): `, nstf1[1] ,f(nstf1[1]) ): " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%31.~Extremum(x,y):~G$\"\"!F%F$" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "print(`2. Extremum(x,y): ` , nstf1[2] ,f(nstf1[2]) ):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%32.~Ex tremum(x,y):~G$\"+nmmm;!\")$\"+O'H'HY!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 " Wendepunkt " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "nstf2: =solve(f2(x)=0,x): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "St eigung_im_Wendepunkt:=f1(nstf2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "print(`Wendepunkt(x,y): `,nstf2, f(nstf2)):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%2Wendepunkt(x,y):~G$\"+LLLL$)!\"*$\"+:[\"[J #F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 " Winkel (Grad)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "Winkel_im_Wendepunkt:=evalf(arctan(Steigung _im_Wendepunkt)*180/Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%5Winkel_ im_WendepunktG$\"+%\\')>E#!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "Winkel_in_der_ersten_Nullstelle:=evalf(arctan( f1(nstf[1]))*18 0/Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%@Winkel_in_der_ersten_Null stelleG$\"\"!F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Winkel_i n_der_zweiten_Nullstelle:=evalf(arctan( f1(nstf[2]))*180/Pi);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%AWinkel_in_der_zweiten_NullstelleG$! +t\">S8&!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }