{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 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 2 2 2 1 1 1 1 }1 1 0 0 0 0 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 "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 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Definition der Funktion, deren Extremwert e gesucht sind:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "f:=alpha -> sin (alpha) - mbdmc * (1 + sqrt(l2dl1^2 - hdl1^2) - (cos(alpha) + sqrt(l2d l1^2 - (hdl1 + sin(alpha))^2))); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"fGf*6#%&alphaG6\"6$%)operatorG%&arrowGF(,&-%$sinG6#9$\"\"\"*&%&mbdm cGF1,*F1F1-%%sqrtG6#,&*$)%&l2dl1G\"\"#F1F1*$)%%hdl1GF " 0 "" {MPLTEXT 1 0 32 "mbdmc:=0.5; l2dl1:=2.5; hdl1:=1;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&mbdmcG$\"\"&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&l2dl1G$\"#D!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%hdl1G\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Ein Plot f\374r den interessierenden Bereich (alpha=0..2*Pi) ist f\374r die L okalisierung der Extremwerte sinnvoll:" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }{MPLTEXT 1 0 30 "plot(f(alpha), alpha=0..2*Pi);" }}{PARA 13 "" 1 " " {GLPLOT2D 283 217 217 {PLOTDATA 2 "6%-%'CURVESG6$7en7$$\"\"!F)$!31`' >Wy+/h#!#F7$$\"3i]cC&eb&p8!#=$\"3'o*e8iXXc**!#>7$$\"3YqR*pd)>hDF0$\"3/ ?;.U:WH-')HR#F07$$\"3ab^NehL]_F0$\"3Ihij )Gcy(GF07$$\"3Ls#3kbN;#fF0$\"3!\\2xWfk*[IF07$$\"35*QhW&\\$Hf'F0$\"3uj@ 1&R2L<$F07$$\"3]:5wGaJ:sF0$\"39d!)HE%orC$F07$$\"3zS11.fpPyF0$\"3=gT'Q* 4%=G$F07$$\"3#e!R^M[8#[)F0$\"3[dz)z>yuF$F07$$\"3upr'fwtl7*F0$\"3#F07$$\"3$*)e)pbO(eV\"Fco$\"3#yndkjbao\"F07$$\"396:YIMRr:Fco$ \"3J))GiZYdS5F07$$\"3!=3SCmpuq\"Fco$\"3s\"=w0mg$3LF37$$\"3LmSEEVgQ=Fco $!3q![(*eEq0/%F37$$\"3S`:%R;(od>Fco$!3+\"4RZ1SJ6\"F07$$\"3#=uye<)G*4#F co$!3l7BuRld4?F07$$\"3Ua[#o!GC>AFco$!3.A]B#Qhe\"GF07$$\"3-YwJf&y(eBFco $!3K-qEeer2QF07$$\"3oNrpV8H#[#Fco$!3%p9aP,&)3t%F07$$\"3EzY)QW/yh#Fco$! 3%>\\CCOn]y&F07$$\"35v)>8'\\%ou#Fco$!3#)4?RwKG=oF07$$\"3w$GCS?&[\")GFc o$!3]T*Gqr3>\"zF07$$\"3Z%)='p(p70IFco$!3dM`$)ecm9*)F07$$\"3sA%)\\K8\\Q JFco$!3#3gJJ#Huv**F07$$\"3c&fJlT>qF$Fco$!3H!G*zLMG.6Fco7$$\"39l2\"4_3w R$Fco$!3yKENm]k*=\"Fco7$$\"3MOnGd![y_$Fco$!3OC?zf++v7Fco7$$\"3#*=4JU#) RiOFco$!3[kW<]^V_8Fco7$$\"3%G,f%[$HSz$Fco$!3!\\`<+N.cT\"Fco7$$\"3KoE+7 #*Q@RFco$!3mj61$=^JY\"Fco7$$\"31LT5>\\4#*RFco$!3sue#GbVK[\"Fco7$$\"3y( f0ii+G1%Fco$!3Cb-bQ5c)\\\"Fco7$$\"3ZG'*z[GLETFco$!3<#GND')*43:Fco7$$\" 3;fORr]')*=%Fco$!3,(=ak^AN^\"Fco7$$\"3sxTpz#*pdUFco$!32$H$p\"zlY^\"Fco 7$$\"3R&p%*z[LbK%Fco$!3aM4QL#H4^\"Fco7$$\"3'epgGO,qQ%Fco$!3M4jfEUG.:Fc o7$$\"3M'pExBp%[WFco$!3%Gx&\\q>d\"\\\"Fco7$$\"3oh/x$[qGe%Fco$!3I$os5[` =X\"Fco7$$\"3e;O;#eJ$4ZFco$!35*y#*o%z;(R\"Fco7$$\"3&)oO4o)>:%[Fco$!3MX R?%))QHK\"Fco7$$\"3Ou\"4%z!e2(\\Fco$!3.cIX.+\"[B\"Fco7$$\"3*zX#[4&eg5& Fco$!3[HI(p(p%z7\"Fco7$$\"3n*e![/*ojB&Fco$!3B1fb&*\\685Fco7$$\"3#ob8X5 I'p`Fco$!3;\\IFdR/i))F07$$\"3PA\"GX$yy,bFco$!3OGJ')[UFPvF07$$\"39L1/jq ABcFco$!3CkpJu,!yG'F07$$\"3mweKB,TidFco$!35dhI.I&)\\[F07$$\"3'oIe;6(*o )eFco$!3%QQgTpqne$F07$$\"3nKcu0ii>gFco$!3%R,D!Gmi$H#F07$$\"3w)*zj%)[mY hFco$!3R')3_'pwR8\"F07$$\"3)****>YH&=$G'Fco$!3PIsd-+*z+\"!#D-%'COLOURG 6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q&alpha6\"Q!F^^l-%%VIEWG6$;F($\" +3`=$G'!\"*%(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 -1 118 "Die F unktion hat 2 Extremwerte, die nachfolgend als Nullstellen der Ableitu ng in der N\344he von 1 bzw. 4 gesucht werden:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "fs:=diff(f(alpha),alpha);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fsG,(-%$cosG6#%&alphaG\"\"\"*&$\"\"&!\"\"F*-%$sinGF( F*F.**$F-F.F*,&$\"$D'!\"#F**$),&F*F*F/F*\"\"#F*F.#F.F:F9F*F&F*F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "evalf(convert(fsolve (fs,alp ha=1),degrees));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&$\"+WF*[j%!\") \"\"\"%(degreesGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "eva lf(convert(fsolve (fs,alpha=4),degrees));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&$\"+&3J#HC!\"(\"\"\"%(degreesGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 2 0" 2 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }