{VERSION 5 0 "APPLE_PPC_MAC" "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 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 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 "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 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 14 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 "" 0 257 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 " " 0 258 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 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 45 "Project 2: A Lava Lamp \+ for the New Millenium" }}{PARA 257 "" 0 "" {TEXT -1 54 "Some hints on \+ Maple and the math you might find useful" }}{PARA 258 "" 0 "" {TEXT -1 29 "Pilfered from Janice Sklensky" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 120 "You're g oing to be doing more complicated plots than usual, so you'll need to \+ load a special Maple package. Here it is:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "(I surpressed the output by using a colon). " }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 317 "I want to make a \+ simple little vase. Designing it lying on it's side is easier (it avo ids the whole problem with functions not having two outputs for any in put). I'm going to start with a simple parabola. This is not my firs t attempt; I shifted it up and over several times until I got it wher e I wanted it to be:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f : = x -> 4-(x-3)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6 \"6$%)operatorG%&arrowGF(,&\"\"%\"\"\"*$),&9$F.\"\"$!\"\"\"\"#F.F4F(F( F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot(f(x), x=1..4, y= 0..4, scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 246 172 172 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"\"\"\"!$F*F*7$$\"30++]i9Rl5!#<$\"3 G96Km!)*Gd#!#=7$$\"34+]PC#)GA6F/$\"3,)4#zw[)>u%F27$$\"3$****\\Peui=\"F /$\"3kTw[W6+/rF27$$\"33++D'3&o]7F/$\"3w-$=`Kt*)R*F27$$\"3/+](oX*y98F/$ \"3&GMS`Ul+;\"F/7$$\"3#***\\P9CAu8F/$\"3fX$z?CZoN\"F/7$$\"3.+]P*zhdV\" F/$\"3Tiaq^)eJb\"F/7$$\"3++]P>fS*\\\"F/$\"3*3@$>0u@[F/7$$\"3#*****\\#y,\"G;F/$\"3TA.#3G&*y6#F/7$$\"36++ Dr\"zbo\"F/$\"3lj\"[\\)yHsAF/7$$\"3%*****\\(4&G]F/$\"3+wP6WH>lGF/7$$\"3,++]siL-?F/$\"3j03$o3nY+$F/7$$\"3 ,+++!R5'f?F/$\"34[SS\"Qnc6$F/7$$\"3)***\\P/QBE@F/$\"3;9IQNE`OKF/7$$\"3 !******\\\"o?&=#F/$\"3!ebxc17hL$F/7$$\"3%)**\\Pa&4*\\AF/$\"3u)3#QBVOPM F/7$$\"3&)**\\7j=_6BF/$\"3uG^/by*f_$F/7$$\"33++vVy!eP#F/$\"3jvf2_TQ5OF /7$$\"3K+](=WU[V#F/$\"3y(=%\\Mpf!o$F/7$$\"3)****\\7B>&)\\#F/$\"304RdQq ^[PF/7$$\"3(***\\P>:mkDF/$\"3d;rG2/[5QF/7$$\"3'***\\iv&QAi#F/$\"3>rTD1 jHdQF/7$$\"30++vtLU%o#F/$\"3*zmkHR6/!RF/7$$\"37+++bjm[FF/$\"3=95*))RJo $RF/7$$\"3\"****\\(yb^6GF/$\"3V_g%HitW'RF/7$$\"3)***\\PMaKsGF/$\"3dnCH 0#*p$)RF/7$$\"3=++D6W%)RHF/$\"3%39U^I\"Q'*RF/7$$\"3z*****\\@80+$F/$\"3 oj.hO(*****RF/7$$\"30++]7,HlIF/$\"3SP(47?Pd*RF/7$$\"3')**\\P4w)R7$F/$ \"3as9ssqi%)RF/7$$\"3;++]x%f\")=$F/$\"3rEp-6gfkRF/7$$\"3!)**\\P/-a[KF/ $\"3OL#4owF#QRF/7$$\"3/+](=Yb;J$F/$\"3C![$3t3(G!RF/7$$\"3')****\\i@OtL F/$\"3jBLh&p+1'QF/7$$\"3')**\\PfL'zV$F/$\"3wk\\%e4)=3QF/7$$\"3>+++!*>= +NF/$\"3eR'zo(z\")\\PF/7$$\"3-++DE&4Qc$F/$\"3g](4\"=)=@o$F/7$$\"3=+]P% >5pi$F/$\"3X*p)=3O)pg$F/7$$\"38+++bJ*[o$F/$\"3)e9MiO@4`$F/7$$\"33++Dr \"[8v$F/$\"3g!Gfb#fZNMF/7$$\"3++++Ijy5QF/$\"30J^3FbiULF/7$$\"31+]P/)fT (QF/$\"3qh]TOY%eB$F/7$$\"31+]i0j\"[$RF/$\"3]Ewtu%=h7$F/7$$\"\"%F*$\"\" $F*-%'COLOURG6&%$RGBG$\"#5!\"\"F+F+-%+AXESLABELSG6$Q\"x6\"Q\"yFc[l-%(S CALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F(Fdz;F+Fdz" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "I forced the graph to be to scale, so I'll have a feel f or what my shape really is going to look like." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 194 "I want to be able to plo t this curve along with several others I have yet to define, each one \+ over a different interval. I could do this by defining a piecewise fu nction, but I don't want to. " }}{PARA 0 "" 0 "" {TEXT -1 53 "(If you want to, look up piecewise in the help menu)." }}{PARA 0 "" 0 "" {TEXT -1 83 "Instead, I'm going to name each of my plots, and then dis play them all at one time." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot1:=plot(f(x),x=1.4..4, y=0..4, \+ scaling=constrained):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "I surpr essed the output when I defined plot1, because if you don't, you get l ong lines of gobbledook." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "g:=x -> 2.1*(x-1)^2+1.5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&* $),&9$\"\"\"F1!\"\"\"\"#F1$\"#@F2$\"#:F2F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot(g(x), x=0..1.8, scaling=constrained);" } }{PARA 13 "" 1 "" {GLPLOT2D 186 166 166 {PLOTDATA 2 "6&-%'CURVESG6$7S7 $$\"\"!F)$\"33+++++++O!#<7$$\"3U******\\x[BR!#>$\"3#Q7'G.iWQMF,7$$\"3q ****\\iMHPtF0$\"3-<&*R3#RJI$F,7$$\"3.++]-vk<6!#=$\"3PMno.*>o:$F,7$$\"3 (*****\\<06/:F;$\"3jOf2+Hy:IF,7$$\"3t***\\7uO())=F;$\"34,xqCWk\")GF,7$ $\"3#****\\i[M`C#F;$\"3Z9I$=eJGw#F,7$$\"3x***\\izqXh#F;$\"3pqc*\\&eVXE F,7$$\"3-++D;bV'*HF;$\"3BK*Q]A[+`#F,7$$\"3+++D\"fvqP$F;$\"3?ZV?#oD6U#F ,7$$\"3M+++&p5'oPF;$\"3$e$)zgYMaJ#F,7$$\"3#)****\\F]Z8TF;$\"3())=*G,Zn FAF,7$$\"3*******\\e5<]%F;$\"3j@JJ;\\&[8#F,7$$\"3w*****\\FS:*[F;$\"3\" *))3+wN-[?F,7$$\"3]+++:M@n_F;$\"3:vA/YYQq>F,7$$\"3$****\\ihg$3cF;$\"3y &)\\,Ek,0>F,7$$\"3k*****\\j\\5F,$\"3T$Re`I$30:F,7$$\"3)****\\sM4p3\"F,$\"3@%yUFzhe^\"F,7$$\"3%** *\\ig_RB6F,$\"3R%*Qs>a(>`\"F,7$$\"3()***\\nk1R;\"F,$\"3XTDe;tTc:F,7$$ \"3$)******GzI+7F,$\"3$[c#[f)eUe\"F,7$$\"3.++]nSsHrS'fv\"F,7$$\"3(***\\7xK*pQ\"F,$\"3 v))QtsR]9=F,7$$\"3$)****\\(HF,7$$\"3)******R>4,]\"F,$\"3G#**QCLH_-#F,7$$\"31++v: dGQ:F,$\"3))G!RZ#F,7$$\"3&******H *e$4h\"F,$\"3S&)pC(f4QG#F,7$$\"3#****\\F!*33l\"F,$\"3x$=(ey'f%*Q#F,7$$ \"3!******zzrko\"F,$\"3aSO%=T6'*[#F,7$$\"33+]i#)e\\C " 0 "" {MPLTEXT 1 0 68 "plot2:=plot(g(x),x=0..1.8, y=0..4, color=bl ue, scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "display(plot1,plot2);" }}{PARA 13 "" 1 "" {GLPLOT2D 184 156 156 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$\"3!**************R\"!#<$\"3]********* ***R9F*7$$\"3FLL$3gsmX\"F*$\"3F_9)*Q09=;F*7$$\"3lm;zFJ)f]\"F*$\"3UGob& e8zw\"F*7$$\"3;LLeszVh:F*$\"3I\\[F$HR0$>F*7$$\"3FLL33/E<;F*$\"3!)Hh%4A J!)3#F*7$$\"3[m;HHv\"Gn\"F*$\"3WBXW*o'eQAF*7$$\"3CL$eC4EVs\"F*$\"3F*$\"3#p[ \\nP8c)GF*7$$\"3KLL3:'oT*>F*$\"3h?m6DKI))HF*7$$\"3/++]%3Z-0#F*$\"35]#* \\*Rpz4$F*7$$\"3()****\\3;#F*$ \"3y)\\1,XwdH$F*7$$\"37L$eM`'45AF*$\"3wdaa8D0wLF*7$$\"3!ommhV\"poAF*$ \"3vFSY%y(=lMF*7$$\"3Zmmm/!H$=BF*$\"3=i77aYKNNF*7$$\"3#***\\7(HpgP#F*$ \"3=3*4!y/r5OF*7$$\"3qmmmR#zrU#F*$\"3&>9JlPw=n$F*7$$\"3G+]7Z\\D$[#F*$ \"3x8#H.buHt$F*7$$\"3()**\\P\"G_m`#F*$\"3s2]k\"*)3`y$F*7$$\"3omm\"zzmB f#F*$\"3H)GfD\\_&[**RF*7$$\"3@++v*[)>\"3$F*$\"3G>BE0oS$*RF*7$$\"3Immm>\" 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\"3M+++&p5'oPFd\\l$\"3$e$)zgYMaJ#F*7$$\"3#)****\\F]Z8TFd\\l$\"3())=*G, ZnFAF*7$$\"3*******\\e5<]%Fd\\l$\"3j@JJ;\\&[8#F*7$$\"3w*****\\FS:*[Fd \\l$\"3\"*))3+wN-[?F*7$$\"3]+++:M@n_Fd\\l$\"3:vA/YYQq>F*7$$\"3$****\\i hg$3cFd\\l$\"3y&)\\,Ek,0>F*7$$\"3k*****\\j\\5F*$\"3T$Re`I$30:F *7$$\"3)****\\sM4p3\"F*$\"3@%yUFzhe^\"F*7$$\"3%***\\ig_RB6F*$\"3R%*Qs> a(>`\"F*7$$\"3()***\\nk1R;\"F*$\"3XTDe;tTc:F*7$$\"3$)******GzI+7F*$\"3 $[c#[f)eUe\"F*7$$\"3.++]nSsHrS'fv\"F*7$$\"3(***\\7xK*pQ\"F*$\"3v))QtsR]9=F*7$$\"3$)** **\\(HF*7$$ \"3)******R>4,]\"F*$\"3G#**QCLH_-#F*7$$\"31++v:dGQ:F*$\"3))G!RZ#F*7$$\"3&******H*e$4h\"F*$\"3S&)pC(f4QG #F*7$$\"3#****\\F!*33l\"F*$\"3x$=(ey'f%*Q#F*7$$\"3!******zzrko\"F*$\"3 aSO%=T6'*[#F*7$$\"33+]i#)e\\C " 0 "" {MPLTEXT 1 0 27 "h:= x -> a*x^3+b* x^2+c*x+d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGf*6#%\"xG6\"6$%)op eratorG%&arrowGF(,**&%\"aG\"\"\")9$\"\"$F/F/*&%\"bGF/)F1\"\"#F/F/*&%\" cGF/F1F/F/%\"dGF/F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "We als o need to use h', so I need to find it (which is easy enough) and ente r it:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "dh:= x -> 3*a*x^2+ 2*b*x+c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dhGf*6#%\"xG6\"6$%)oper atorG%&arrowGF(,(*&%\"aG\"\"\")9$\"\"#F/\"\"$*(F2F/%\"bGF/F1F/F/%\"cGF /F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 200 "Now we need to find a , b, c, and d so that h(1.3)=g(1.3), h(2)=f(2), dh(1.3)=dg(1.3), and d h(2)=df(2). This is four equations in four unknowns, which would be a pain for us to do, but easy for Maple:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 245 "First, we have Maple do the derivat ives (I know you can, but in this case it's easier, because then you c an just cut and paste as you tweak your functions to get them to look \+ like you want them to), and then define derivative functions in Maple: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&% \"xG!\"#\"\"'\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "df:= x -> -2*x+6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfGf*6#%\"xG6\"6$% )operatorG%&arrowGF(,&9$!\"#\"\"'\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(g(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,&%\"xG$\"#U!\"\"$F&F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dg:= x -> 4.2*x-4.2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dgGf*6# %\"xG6\"6$%)operatorG%&arrowGF(,&9$$\"#U!\"\"$F/F0F0F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "And now we're ready to have Maple to the \+ solving for us:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "solve( \+ \{ h(1.2)=g(1.2), h(1.8)=f(1.8), dh(1.2)=dg(1.2), dh(1.8)=df(1.8)\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&/%\"bG$!+LLLL@!#5/%\"dG$\"+++?^9 !\"*/%\"aG$\"+>&=&=NF(/%\"cG$!+++++9F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 202 "Important: to avoid confusion later, it 's best to now name my new function something other than h, so that I \+ can use h again for my inside function, or even if I want to go back a nd tweak my f and g!!!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Let's \+ see what this gets us. Remember it's quicker to cut and paste, when d ealing with numbers like this!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "m := x -> .3518518519*x^3-.2133333333*x^2-.1400000000*x+1.4512 00000;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mGf*6#%\"xG6\"6$%)operat orG%&arrowGF(,**$)9$\"\"$\"\"\"$\"+>&=&=N!#5*&$\"+LLLL@F4F1)F/\"\"#F1! \"\"*&$\"+++++9F4F1F/F1F:$\"+++?^9!\"*F1F(F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 65 "plot3:= plot(m(x), x=1.2..1.8, color=black, sc aling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "disp lay(plot1,plot2,plot3);" }}{PARA 13 "" 1 "" {GLPLOT2D 212 144 144 {PLOTDATA 2 "6(-%'CURVESG6$7S7$$\"3!**************R\"!#<$\"3]********* ***R9F*7$$\"3FLL$3gsmX\"F*$\"3F_9)*Q09=;F*7$$\"3lm;zFJ)f]\"F*$\"3UGob& e8zw\"F*7$$\"3;LLeszVh:F*$\"3I\\[F$HR0$>F*7$$\"3FLL33/E<;F*$\"3!)Hh%4A J!)3#F*7$$\"3[m;HHv\"Gn\"F*$\"3WBXW*o'eQAF*7$$\"3CL$eC4EVs\"F*$\"3F*$\"3#p[ \\nP8c)GF*7$$\"3KLL3:'oT*>F*$\"3h?m6DKI))HF*7$$\"3/++]%3Z-0#F*$\"35]#* \\*Rpz4$F*7$$\"3()****\\3;#F*$ \"3y)\\1,XwdH$F*7$$\"37L$eM`'45AF*$\"3wdaa8D0wLF*7$$\"3!ommhV\"poAF*$ \"3vFSY%y(=lMF*7$$\"3Zmmm/!H$=BF*$\"3=i77aYKNNF*7$$\"3#***\\7(HpgP#F*$ \"3=3*4!y/r5OF*7$$\"3qmmmR#zrU#F*$\"3&>9JlPw=n$F*7$$\"3G+]7Z\\D$[#F*$ \"3x8#H.buHt$F*7$$\"3()**\\P\"G_m`#F*$\"3s2]k\"*)3`y$F*7$$\"3omm\"zzmB f#F*$\"3H)GfD\\_&[**RF*7$$\"3@++v*[)>\"3$F*$\"3G>BE0oS$*RF*7$$\"3Immm>\" yP8$F*$\"33^%)p9M5#)RF*7$$\"34++](4=**=$F*$\"3e!)>C;6$R'RF*7$$\"37L$e9 E*ySKF*$\"3M]jcJ0-URF*7$$\"3!*****\\!)[S'H$F*$\"3$4y:o9W@\"RF*7$$\"3>m ;zV[t[LF*$\"31-cs3SQyQF*7$$\"3:+]iLZV.MF*$\"38D\\q:/CPQF*7$$\"3tmm;uQ \"pX$F*$\"3C2Sf6(H7z$F*7$$\"3q**\\7y:!H^$F*$\"3#\\)o:r>$pt$F*7$$\"3GLL L\"RCoc$F*$\"3='f*Q4,ryOF*7$$\"3]LL3c#o>i$F*$\"31dYU)[bJh$F*7$$\"3mm;z ,blwOF*$\"3un]*=LP@a$F*7$$\"31+++,u!ps$F*$\"36D9PIcgrMF*7$$\"3`mmT[<]% y$F*$\"3T$>Jn+dXQ$F*7$$\"3@LLL>[,OQF*$\"3)R0b=Az5I$F*7$$\"31+]7(\\Q4*Q F*$\"3LY1M%fGi?$F*7$$\"39+]([Y2N%RF*$\"3?]^sjOz4JF*7$$\"\"%\"\"!$\"\"$ Fez-%'COLOURG6&%$RGBG$\"#5!\"\"$FezFezF_[l-F$6$7S7$F_[l$\"33+++++++OF* 7$$\"3U******\\x[BR!#>$\"3#Q7'G.iWQMF*7$$\"3q****\\iMHPtFi[l$\"3-<&*R3 #RJI$F*7$$\"3.++]-vk<6!#=$\"3PMno.*>o:$F*7$$\"3(*****\\<06/:Fd\\l$\"3j Of2+Hy:IF*7$$\"3t***\\7uO())=Fd\\l$\"34,xqCWk\")GF*7$$\"3#****\\i[M`C# Fd\\l$\"3Z9I$=eJGw#F*7$$\"3x***\\izqXh#Fd\\l$\"3pqc*\\&eVXEF*7$$\"3-++ D;bV'*HFd\\l$\"3BK*Q]A[+`#F*7$$\"3+++D\"fvqP$Fd\\l$\"3?ZV?#oD6U#F*7$$ \"3M+++&p5'oPFd\\l$\"3$e$)zgYMaJ#F*7$$\"3#)****\\F]Z8TFd\\l$\"3())=*G, ZnFAF*7$$\"3*******\\e5<]%Fd\\l$\"3j@JJ;\\&[8#F*7$$\"3w*****\\FS:*[Fd \\l$\"3\"*))3+wN-[?F*7$$\"3]+++:M@n_Fd\\l$\"3:vA/YYQq>F*7$$\"3$****\\i hg$3cFd\\l$\"3y&)\\,Ek,0>F*7$$\"3k*****\\j\\5F*$\"3T$Re`I$30:F *7$$\"3)****\\sM4p3\"F*$\"3@%yUFzhe^\"F*7$$\"3%***\\ig_RB6F*$\"3R%*Qs> a(>`\"F*7$$\"3()***\\nk1R;\"F*$\"3XTDe;tTc:F*7$$\"3$)******GzI+7F*$\"3 $[c#[f)eUe\"F*7$$\"3.++]nSsHrS'fv\"F*7$$\"3(***\\7xK*pQ\"F*$\"3v))QtsR]9=F*7$$\"3$)** **\\(HF*7$$ \"3)******R>4,]\"F*$\"3G#**QCLH_-#F*7$$\"31++v:dGQ:F*$\"3))G!RZ#F*7$$\"3&******H*e$4h\"F*$\"3S&)pC(f4QG #F*7$$\"3#****\\F!*33l\"F*$\"3x$=(ey'f%*Q#F*7$$\"3!******zzrko\"F*$\"3 aSO%=T6'*[#F*7$$\"33+]i#)e\\C\"F*$\"3,+78+++%e\"F*7$$\"3) )****\\#HyI@\"F*$\"3w\")[04H`&f\"F*7$$\"3(***\\([kdWA\"F*$\"30V7hiW'eg \"F*7$$\"3*****\\n\"\\DP7F*$\"3?`#QGT6T#z\")ym\"F*7$$ \"3'***\\(Q=\"))*H\"F*$\"3L6La%yb:o\"F*7$$\"3)***\\P'=pDJ\"F*$\"3g-0d2 'fbp\"F*7$$\"3)*****\\c.iD8F*$\"3')GB%>1e.r\"F*7$$\"3-++DMe6P8F*$\"35$ *3@NqsBq0]8F*$\"3x@)>%pj:R2p(*fqJ!=F*7$$\"3\"****** z2A>T\"F*$\"3SH>ywLg==F*7$$\"3!***\\(3wY_U\"F*$\"3kU4pIs(p$=F*7$$\"31+ ++j8/P9F*$\"3;Ih8gNi`=F*7$$\"30+](3\">)*\\9F*$\"35ap[(f/B(=F*7$$\"3,+] isVIi9F*$\"393@hVL]!*=F*7$$\"3$****\\(o:;v9F*$\"3Y4]!*GD#*4>F*7$$\"31+ ]P)[op[\"F*$\"3M=6M9m9G>F*7$$\"33++DYQq*\\\"F*$\"3iMc:bxA[>F*7$$\"3++] (QIKH^\"F*$\"3rP6(3\"pbp>F*7$$\"3****\\7:xWC:F*$\"3cYVb$3=&))>F*7$$\"3 ,++vuY)o`\"F*$\"3IfhCpDT4?F*7$$\"3-+++rKt\\:F*$\"3.&[gWSc9.#F*7$$\"3-+ +v:JIi:F*$\"3C!>W6YwM0#F*7$$\"33+](o3lWd\"F*$\"31!\\T_\"Q@v?F*7$$\"3)* ***\\A))oze\"F*$\"3kJ?fo;&)*4#F*7$$\"30+++VE5+;F*$\"3-g:!4zWC7#F*7$$\" 3'*****\\A!eIh\"F*$\"3O_z99v/Z@F*7$$\"3$***\\(=_(zC;F*$\"3:0am\")Gxp@F *7$$\"3@++]&*=jP;F*$\"3?Q)pOY\"4&>#F*7$$\"3++](3/3(\\;F*$\"3m)\\Rl-q$> AF*7$$\"34+]P#4JBm\"F*$\"3?w7$[x\"F*$ \"3M.RRi1%y\\#F*7$$\"3#***\\7hK'py\"F*$\"3)yo,GfPv_#F*7$Fdjl$\"3g+))Q+ ++gDF*-Fiz6&F[[lFezFezFez-%+AXESLABELSG6%Q\"x6\"Q\"yFijm%(DEFAULTG-%(S CALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F_[lFczFc[n" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 242 "This looks like it will probably \+ be pretty good. I'll now go back and change the domains of plot 1 and plot 2. In the ordinary course of events, I would just go back up th ere and change them there, but for your benefit, I'll redo them here: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "plot1:=plot(f(x),x=1.8 ..4, y=0..4, scaling=constrained): plot2:=plot(g(x),x=0..1.2, y=0..4, \+ color=blue, scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "display(plot1,plot2,plot3);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6$7S7$$\"3/+++++++=!#<$ \"30++++++gDF*7$$\"3rmm;RP&z%=F*$\"3UN***GT*ysEF*7$$\"3VL$37.y'*)=F*$ \"3v(f=c7&=nFF*7$$\"3$om;9O,m$>F*$\"3T8\"faL$=pGF*7$$\"3omm\"*Hd$Q)>F* $\"3L1g?w,TnHF*7$$\"3F_(R21$F*7$$\"3xm;aq(HW2#F*$\" 3U[/M](>L9$F*7$$\"3*)**\\(Gle&>@F*$\"35:FFMI#[A$F*7$$\"3jm;a25Bm@F*$\" 3p:]@n#H[I$F*7$$\"3*)**\\P$o`F@#F*$\"34q.'pBV-Q$F*7$$\"3MLL$Q(zggAF*$ \"3;^6kJ%*H`MF*7$$\"3'pm;*e!eFI#F*$\"3#fM%fvO&Q^$F*7$$\"38++]r!4-N#F*$ \"3!z5R#\\Dk08UPOF*7$$\"3)*****\\G0xVCF *$\"3kI[.v(31p$F*7$$\"3fm;a(Hma[#F*$\"3)*=X.p]DNPF*7$$\"3eLL$)*fY]`#F* 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"" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 98 "Now, I need to see what this would look l ike from the outside, were it revolved around the x-axis." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "t1: =tubeplot( [x,0,0], x=0..1.2, radius= g(x)): t2:=tubeplot([x,0,0], x= 1.2..1.8, radius=m(x)): t3:=tubeplot([x,0,0], x=1.8..4, radius=f(x)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "display(t1,t2,t3);" }} {PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6%-%%MESHG6#7T7,7% $\"\"!F*$\"33+++++++O!#$\"3a;:OKBS)\\$F-F)7%Fen$\"3!>,+lmJ*zEF-$\"35t/%HnH([AF-7%Fen$\"3_j Jg(*=\"\\2'F6$\"3N8c1SPDXMF-7%Fen$!3gd2=m6?\\\"F-7%Fen$!3EG.EcGU(G$F-$!3OR^7nS_'>\"F-7% Fen$!3#)f2=m6?\\V>$F-$\"3ptu1]rji6F-7%Fgq$!3!zXHoJ>V>$F-$!3!GZn+:PE ;\"F-7%Fgq$!3Ow,e2=m*p\"F-$!3[=KT11!R%HF-7%Fgq$\"3c\\vs5N'G!fF6$!3?+u? ^-oZLF-7%FgqF\\r$!3QF*R65V]=#F-7%FgqFiq$!3C>Q^;F-$\"3OFAT&Rx-'GF-7%F ft$!3zgm`;Ge.JF-$\"3G4%*zkC>Q^;F-$!3-EAT&Rx-'GF-7%Fft$\"3V*o#QN#*=NdF6$!377$pUW(e_KF-7% 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" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 126 "This demonstrates the techniques I wanted to show you , so I'll stop here. You, however, would still need to do the followi ng:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 230 "1 ) Make sure that the actual 3-D vase is to the scale I want it to be. \+ This vase will be 8 inches wide at it's widest spot, but only 4 inch es tall, which sounds distorted. It doesn't look that distorted in my plot -- why not? " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 84 "Because I didn't force \+ it to be too scale. 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In some cases, \+ you'll be be able to go the simple route and just shift your outside c urve down some. In other cases, you either won't want to do that, or \+ you won't be able to. So don't put this part off!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 146 "3) You need to calculate the volume, using the techniques you've learned, (and putting them in the units you're using for your to-scale object). " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 326 "Do not put this off ei ther -- it will often not be as easy as it sounds, as you'll have seve ral different curves. In fact, if you go for the more interesting sha pes, as George wants you to do, where the inside doesn't match the out side exactly, you may have to break your volume finding process into m any different intervals." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "1 7 2 0" 157 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 1 0 2 33 1 1 }