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{SECT 0 {PARA 212 "" 0 "" {TEXT -1 20 "SOLIDS OF REVOLUTION" }{TEXT 
-1 0 "" }}{PARA 213 "" 0 "" {TEXT -1 0 "" }}{PARA 214 "" 0 "" {TEXT 
208 7 "Author:" }{TEXT -1 10 " Ken Monks" }{TEXT -1 0 "" }}{PARA 215 "
" 0 "" {TEXT -1 40 "               Department of Mathematics" }{TEXT 
-1 0 "" }}{PARA 216 "" 0 "" {TEXT -1 37 "               University of \+
Scranton" }{TEXT -1 0 "" }}{PARA 217 "" 0 "" {TEXT -1 33 "            \+
   Scranton, PA 18510" }{TEXT -1 0 "" }}{PARA 218 "" 0 "" {TEXT -1 29 
"               (717) 941-6101" }{TEXT -1 0 "" }}{PARA 219 "" 0 "" 
{TEXT -1 31 "               monks@uofs.edu  " }{TEXT -1 0 "" }}{PARA 
213 "" 0 "" {TEXT -1 0 "" }}{PARA 213 "" 0 "" {TEXT -1 13 "Description
: " }{TEXT 209 78 "RevSolid is a Maple worksheet for displaying solids
 of revolution (animated). " }{TEXT -1 0 "" }}{PARA 220 "" 0 "" {TEXT 
-1 98 "                       Please send suggestions or improvements \+
to the author at the above address." }{TEXT -1 0 "" }}{PARA 213 "" 0 "
" {TEXT -1 0 "" }}{PARA 213 "" 0 "" {TEXT -1 8 "Revised:" }{TEXT 209 
16 "  Sept. 15, 1994" }{TEXT -1 0 "" }}{PARA 221 "" 0 "" {TEXT -1 57 "
                November 23, 1996 - Upgrade to Maple V R4" }{TEXT -1 
0 "" }}{PARA 222 "" 0 "" {TEXT -1 78 "                March 12, 1997 -
 Added the ability to rotate around the Y-axis" }{TEXT -1 0 "" }}
{PARA 213 "" 0 "" {TEXT -1 0 "" }}{PARA 223 "" 0 "" {TEXT 210 67 "(You
 must execute the source code first or else nothing will work.)" }
{TEXT 210 0 "" }}{SECT 0 {PARA 224 "" 0 "" {TEXT -1 15 "The Source Cod
e" }{TEXT -1 0 "" }}{EXCHG {PARA 213 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 
1 211 12 "with(plots):" }{TEXT -1 0 "" }}{PARA 225 "" 0 "" {TEXT -1 
57 "This routine shows a cool region under the curve in 3d..." }{TEXT 
-1 0 "" }}{PARA 213 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 211 33 "RegionB
etweenCurves:=proc(F,G,rg)" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 66 "
\n    local lp,a,b,inc,x1,x2,xaxis,f,g,fx1,fx2,gx1,gx2,top,bot,h,m;" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 30 "\n    a:=op(1,rg); b:=op(2,rg)
;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 28 "\n    f:=evalf@F; g:=evalf
@G;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 64 "\n    inc:=evalf((b-a)/1
0);  # change this value for a finer grid" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 45 "\n    lp:=[[a-.3*(b-a),0,0],[b+.3*(b-a),0,0]];" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 35 "\n    x1:=a; top:=f(x1); bot:=
g(x1);" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 37 "\n    for x2 from a+i
nc by inc to b do" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 56 "\n        \+
fx1:=f(x1); fx2:=f(x2); gx1:=g(x1); gx2:=g(x2);" }{MPLTEXT 1 211 0 "" 
}{MPLTEXT 1 211 59 "\n        m:=max(fx1,fx2,gx1,gx2); if m>top then t
op:=m; fi;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 59 "\n        m:=min(
fx1,fx2,gx1,gx2); if m<bot then bot:=m; fi;" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 62 "\n        lp:=lp,[[x1,0,fx1],[x1,0,gx1],[x2,0,gx2],
[x2,0,fx2]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 16 "\n        x1:=x
2;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 8 "\n    od;" }{MPLTEXT 1 
211 0 "" }{MPLTEXT 1 211 62 "\n    lp:=lp,[[0,0,top+0.3*(top-bot)],[0,
0,bot-0.3*(top-bot)]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 37 "\n   \+
 polygonplot3d(\{lp\},style=patch);" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 
211 5 "\nend:" }{MPLTEXT 1 211 0 "" }{TEXT -1 1 "\n" }}{PARA 213 "" 0 
"" {TEXT -1 87 "Solid_Of_Rev - revolves the region between the graph o
f F and G over range Rg about the" }{TEXT -1 0 "" }}{PARA 213 "" 0 "" 
{TEXT -1 43 "                           x-axis or y-axis" }{TEXT -1 0 
"" }{MPLTEXT 1 211 15 "\nSolid_Of_Rev:=" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 18 "\nproc(F,G,Rg,axis)" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 70 "\n    local f,g,ga,gb,fa,fb,gx1,gx2,fx1,fx2,rg,z,i,
frame,P,a,b,dt,dx,R," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 67 "\n     \+
     asides,bsides,face,th1,th2,x1,x2,st1,st2,ct1,ct2,k,segs," }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 35 "\n          frames,surff,surfg
,opts;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 25 "\n    if type(Rg,`=`)
 then" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 82 "\n        f:=evalf@una
pply(F,op(1,Rg)); g:=evalf@unapply(G,op(1,Rg)); rg:=op(2,Rg);" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 9 "\n    else" }{MPLTEXT 1 211 0 "
" }{MPLTEXT 1 211 40 "\n        f:=evalf@F; g:=evalf@G; rg:=Rg;" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 8 "\n    fi;" }{MPLTEXT 1 211 0 ""
 }{MPLTEXT 1 211 44 "\n    a:=evalf(op(1,rg)); b:=evalf(op(2,rg));" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 57 "\n    opts:=NULL; if nargs>4 t
hen opts:=args[5..nargs] fi;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 24 
"\n    dt:=evalf(2*Pi/24);" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 25 "
\n    dx:=evalf((b-a)/10);" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 36 "
\n    R:=RegionBetweenCurves(f,g,rg):" }{MPLTEXT 1 211 0 "" }{MPLTEXT 
1 211 10 "\n    P:=R;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 66 "\n    \+
segs:=2;   # number of segments per frame... should divide 24" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 21 "\n    frames:=24/segs;" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 58 "\n    asides:=NULL; bsides:=NU
LL; surff:=NULL; surfg:=NULL;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 
36 "\n    for frame from 0 to frames-1 do" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 28 "\n        th1:=dt*segs*frame;" }{MPLTEXT 1 211 0 ""
 }{MPLTEXT 1 211 20 "\n        face:=NULL;" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 25 "\n        for k to segs do" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 25 "\n            th2:=th1+dt;" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 34 "\n            st1:=evalf(sin(th1));" }{MPLTEXT 1 
211 0 "" }{MPLTEXT 1 211 34 "\n            st2:=evalf(sin(th2));" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 34 "\n            ct1:=evalf(cos(t
h1));" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 34 "\n            ct2:=eva
lf(cos(th2));" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 52 "\n            \+
ga:=g(a); fa:=f(a); gb:=g(b); fb:=f(b);" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 31 "\n            if axis=XAXIS then" }{MPLTEXT 1 211 
0 "" }{MPLTEXT 1 211 65 "\n            asides:=asides,[[a,ga*st1,ga*ct
1],[a,fa*st1,fa*ct1]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 66 "\n    \+
                        [a,fa*st2,fa*ct2],[a,ga*st2,ga*ct2]];" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 65 "\n            bsides:=bsides,[
[b,gb*st1,gb*ct1],[b,fb*st1,fb*ct1]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 
1 211 66 "\n                            [b,fb*st2,fb*ct2],[b,gb*st2,gb
*ct2]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 33 "\n            elif a
xis=YAXIS then" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 63 "\n           \+
 asides:=asides,[[a*ct1,a*st1,ga],[a*ct1,a*st1,fa]," }{MPLTEXT 1 211 
0 "" }{MPLTEXT 1 211 64 "\n                            [a*ct2,a*st2,fa
],[a*ct2,a*st2,ga]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 63 "\n     \+
       bsides:=bsides,[[b*ct1,b*st1,gb],[b*ct1,b*st1,fb]," }{MPLTEXT 
1 211 0 "" }{MPLTEXT 1 211 64 "\n                            [b*ct2,b*
st2,fb],[b*ct2,b*st2,gb]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 17 "
\n            else" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 76 "\n       \+
         ERROR(`the fourth argument must be either XAXIS or YAXIS`);" 
}{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 16 "\n            fi;" }{MPLTEXT 
1 211 0 "" }{MPLTEXT 1 211 43 "\n            for x1 from a by dx to b-
dx do" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 27 "\n                x2:=
x1+dx;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 64 "\n                fx1
:=f(x1); gx1:=g(x1); fx2:=f(x2); gx2:=g(x2);" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 35 "\n                if axis=XAXIS then" }{MPLTEXT 1 
211 0 "" }{MPLTEXT 1 211 73 "\n                surff:=surff,[[x1,fx1*s
t1,fx1*ct1],[x1,fx1*st2,fx1*ct2]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 
211 74 "\n                              [x2,fx2*st2,fx2*ct2],[x2,fx2*s
t1,fx2*ct1]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 73 "\n            \+
    surfg:=surfg,[[x1,gx1*st1,gx1*ct1],[x1,gx1*st2,gx1*ct2]," }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 74 "\n                            \+
  [x2,gx2*st2,gx2*ct2],[x2,gx2*st1,gx2*ct1]];" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 71 "\n                face:=face,[[x1,fx1*st2,fx1*ct2],
[x2,fx2*st2,fx2*ct2]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 72 "\n    \+
                        [x2,gx2*st2,gx2*ct2],[x1,gx1*st2,gx1*ct2]];" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 21 "\n                else" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 75 "\n                    surff:=s
urff,[[x1*ct1,x1*st1,fx1],[x1*ct2,x1*st2,fx1]," }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 76 "\n                                  [x2*ct2,x2*st2,
fx2],[x2*ct1,x2*st1,fx2]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 75 "
\n                    surfg:=surfg,[[x1*ct1,x1*st1,gx1],[x1*ct2,x1*st2
,gx1]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 76 "\n                   \+
               [x2*ct2,x2*st2,gx2],[x2*ct1,x2*st1,gx2]];" }{MPLTEXT 1 
211 0 "" }{MPLTEXT 1 211 73 "\n                    face:=face,[[x1*ct2
,x1*st2,fx1],[x2*ct2,x2*st2,fx2]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 
211 74 "\n                                [x2*ct2,x2*st2,gx2],[x1*ct2,
x1*st2,gx1]];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 20 "\n            \+
    fi;" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 16 "\n            od;" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 22 "\n            th1:=th2;" }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 12 "\n        od;" }{MPLTEXT 1 
211 0 "" }{MPLTEXT 1 211 77 "\n        P:=P,display3d(\{R,polygonplot3
d([asides,bsides,surff,surfg,face])\}):" }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 8 "\n    od:" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 53 "
\n    display3d([P],insequence=true,opts,style=patch);" }{MPLTEXT 1 
211 0 "" }{MPLTEXT 1 211 5 "\nend:" }{TEXT -1 0 "" }}{PARA 213 "" 0 ""
 {TEXT -1 0 "" }}{PARA 213 "" 0 "" {TEXT -1 47 "Last - shows the last \+
frame of an animation... " }{TEXT -1 0 "" }{MPLTEXT 1 211 81 "\nLast:=
proc(p) display3d(PLOT3D(op(op(nops(op(1,p)),op(1,p)))),style=patch); \+
end:" }{TEXT -1 0 "" }}}}{SECT 0 {PARA 224 "" 0 "" {TEXT -1 8 "Example
s" }{TEXT -1 0 "" }}{PARA 213 "" 0 "" {TEXT -1 93 "Be sure to execute \+
the commands in the Source Code section above before using these examp
les." }{TEXT -1 0 "" }}{EXCHG {PARA 213 "" 0 "" {TEXT -1 8 "A yo-yo." 
}{TEXT -1 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 33 "Solid_Of_Rev(x
^2,0,x=-1..1,XAXIS," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 50 "\n      \+
       title=`f(x)=x\262, g(x)=0, a=-1, b=1`, " }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 61 "\n             titlefont=[TIMES,BOLD,14],orientatio
n=[70,70]);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 213 "" 0 "" {TEXT 
-1 8 "A donut." }{TEXT -1 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 
56 "Solid_Of_Rev(sqrt(1-x^2)+2,-sqrt(1-x^2)+2,x=-1..1,XAXIS," }
{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 28 "        s
caling=CONSTRAINED," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 28 "        orientation=[43,84]," }{MPLTEXT 1 211 0 "" 
}}{PARA 226 "> " 0 "" {MPLTEXT 1 211 54 "        title=`f(x)=sqrt(1-x
\262)+2, g(x)=-sqrt(1-x\262)+2`," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> \+
" 0 "" {MPLTEXT 1 211 35 "        titlefont=[TIMES,BOLD,14]);" }
{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 213 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 213 "" 0 "" {TEXT -1 77 "Take away a small sphere from a \+
big sphere (  not quite!! around the x-axis)." }{TEXT -1 0 "" }}{PARA 
226 "> " 0 "" {MPLTEXT 1 211 51 "Solid_Of_Rev(sqrt(4-x^2),sqrt(1-x^2),
x=-1..1,XAXIS," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 
211 28 "        scaling=CONSTRAINED," }{MPLTEXT 1 211 0 "" }}{PARA 
226 "> " 0 "" {MPLTEXT 1 211 29 "        orientation=[-38,76]," }
{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 51 "        t
itle=`f(x)=sqrt(4-x^2), g(x)=sqrt(1-x^2)`," }{MPLTEXT 1 211 0 "" }}
{PARA 226 "> " 0 "" {MPLTEXT 1 211 35 "        titlefont=[TIMES,BOLD,1
0]);" }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 0 "" }
}{PARA 226 "> " 0 "" {MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 0 "" }}}
{EXCHG {PARA 213 "" 0 "" {TEXT -1 21 "A sphere of radisu 2." }{TEXT 
-1 0 "" }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 41 "Solid_Of_Rev(
sqrt(4-x^2),0,x=-2..2,XAXIS," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 
"" {MPLTEXT 1 211 28 "        scaling=CONSTRAINED," }{MPLTEXT 1 211 0 
"" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 29 "        orientation=[-38,7
6]," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 33 "   \+
     title=`f(x)=sqrt(4-x^2)`," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 
0 "" {MPLTEXT 1 211 35 "        titlefont=[TIMES,BOLD,10]);" }
{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 213 "" 0 "" {TEXT -1 19 "A triangu
lar donut." }{TEXT -1 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 38 "So
lid_Of_Rev(3-abs(x),2,x=-1..1,XAXIS," }{MPLTEXT 1 211 0 "" }}{PARA 
226 "> " 0 "" {MPLTEXT 1 211 28 "        scaling=CONSTRAINED," }
{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 28 "        o
rientation=[50,84]," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 46 "        title=`f(x)=3-|x|, g(x)=2, a=-1, b=1`," }
{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 35 "        t
itlefont=[TIMES,BOLD,14]);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 213 "
" 0 "" {TEXT -1 13 "A leaky vase." }{TEXT -1 0 "" }}{PARA 226 "> " 0 "
" {MPLTEXT 1 211 52 "Solid_Of_Rev(x*(x+2)*(x-2)+9,exp(x)+1,x=-2..2,XAX
IS," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 28 "   \+
     orientation=[50,84]," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 61 "        title=`f(x)=x(x+2)(x-2)+9, g(x)=exp(x)+1, a
=-2, b=2`," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 
35 "        titlefont=[TIMES,BOLD,14]):" }{MPLTEXT 1 211 0 "" }}}
{EXCHG {PARA 213 "" 0 "" {TEXT -1 17 "A y-axis example." }{TEXT -1 0 "
" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 83 "Solid_Of_Rev(abs(sin(2*(x-1
))/(x-1)^2)+1,-abs(sin(2*(x-1))/(x-1)^2)+1,x=2..4,YAXIS," }{MPLTEXT 1 
211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 28 "        scaling=CONS
TRAINED," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 
29 "        orientation=[-38,76]," }{MPLTEXT 1 211 0 "" }}{PARA 226 ">
 " 0 "" {MPLTEXT 1 211 88 "        title=`f(x)=|sin(2*(x-1))|/(x-1)^2+
1, g(x)=-|sin(2*(x-1))|/(x-1)^2+1, a=2, b=4`," }{MPLTEXT 1 211 0 "" }}
{PARA 226 "> " 0 "" {MPLTEXT 1 211 35 "        titlefont=[TIMES,BOLD,1
0]);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 213 "" 0 "" {TEXT -1 33 "Th
e same thing around the x-axis." }{TEXT -1 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 83 "Solid_Of_Rev(abs(sin(2*(x-1))/(x-1)^2)+1,-abs(sin(2
*(x-1))/(x-1)^2)+1,x=2..4,XAXIS," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> \+
" 0 "" {MPLTEXT 1 211 28 "        scaling=CONSTRAINED," }{MPLTEXT 1 
211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 29 "        orientation=
[-38,76]," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 
88 "        title=`f(x)=|sin(2*(x-1))|/(x-1)^2+1, g(x)=-|sin(2*(x-1))|
/(x-1)^2+1, a=2, b=4`," }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 35 "        titlefont=[TIMES,BOLD,10]);" }{MPLTEXT 1 
211 0 "" }}}}{SECT 0 {PARA 224 "" 0 "" {TEXT -1 26 "Construct a Classr
oom Demo" }{TEXT -1 0 "" }}{PARA 213 "" 0 "" {TEXT -1 122 "Execute thi
s section to create a classroom demo. This might take quite a while to
 run (appx. 15 minutes on a 486 machine)." }{TEXT -1 0 "" }}{PARA 213 
"" 0 "" {TEXT -1 85 "When it is finished you can just reload the demo \+
from disk instead of recomputing it." }{TEXT -1 0 "" }}{EXCHG {PARA 
226 "> " 0 "" {MPLTEXT 1 211 37 "p1:=Solid_Of_Rev(x^2,0,x=-1..1,XAXIS,
" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 45 "\n        title=`f(x)=x\262
, g(x)=0, a=-1, b=1`, " }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 56 "\n   \+
     titlefont=[TIMES,BOLD,14],orientation=[70,70]):" }{MPLTEXT 1 211 
0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 60 "p2:=Solid_Of_Rev(sqrt(1-
x^2)+2,-sqrt(1-x^2)+2,x=-1..1,XAXIS," }{MPLTEXT 1 211 0 "" }{MPLTEXT 
1 211 29 "\n        scaling=CONSTRAINED," }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 29 "\n        orientation=[43,84]," }{MPLTEXT 1 211 0 "
" }{MPLTEXT 1 211 55 "\n        title=`f(x)=sqrt(1-x\262)+2, g(x)=-sqr
t(1-x\262)+2`," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 36 "\n        tit
lefont=[TIMES,BOLD,14]):" }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 42 "p3:=Solid_Of_Rev(3-abs(x),2,x=-1..1,XAXIS," }
{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 29 "\n        scaling=CONSTRAINED,
" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 29 "\n        orientation=[50,8
4]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 47 "\n        title=`f(x)=3-
|x|, g(x)=2, a=-1, b=1`," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 36 "\n \+
       titlefont=[TIMES,BOLD,14]):" }{MPLTEXT 1 211 0 "" }}{PARA 226 "
> " 0 "" {MPLTEXT 1 211 56 "p4:=Solid_Of_Rev(x*(x+2)*(x-2)+9,exp(x)+1,
x=-2..2,XAXIS," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 29 "\n        ori
entation=[50,84]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 62 "\n        \+
title=`f(x)=x(x+2)(x-2)+9, g(x)=exp(x)+1, a=-2, b=2`," }{MPLTEXT 1 
211 0 "" }{MPLTEXT 1 211 36 "\n        titlefont=[TIMES,BOLD,14]):" }
{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 87 "p5:=Solid
_Of_Rev(abs(sin(2*(x-1))/(x-1)^2)+1,-abs(sin(2*(x-1))/(x-1)^2)+1,x=2..
4,YAXIS," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 29 "\n        scaling=C
ONSTRAINED," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 30 "\n        orient
ation=[-38,76]," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 89 "\n        ti
tle=`f(x)=|sin(2*(x-1))|/(x-1)^2+1, g(x)=-|sin(2*(x-1))|/(x-1)^2+1, a=
2, b=4`," }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 36 "\n        titlefont
=[TIMES,BOLD,10]):" }{MPLTEXT 1 211 0 "" }}{PARA 226 "> " 0 "" 
{MPLTEXT 1 211 87 "p6:=Solid_Of_Rev(abs(sin(2*(x-1))/(x-1)^2)+1,-abs(s
in(2*(x-1))/(x-1)^2)+1,x=2..4,XAXIS," }{MPLTEXT 1 211 0 "" }{MPLTEXT 
1 211 29 "\n        scaling=CONSTRAINED," }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 30 "\n        orientation=[-38,76]," }{MPLTEXT 1 211 0 
"" }{MPLTEXT 1 211 89 "\n        title=`f(x)=|sin(2*(x-1))|/(x-1)^2+1,
 g(x)=-|sin(2*(x-1))|/(x-1)^2+1, a=2, b=4`," }{MPLTEXT 1 211 0 "" }
{MPLTEXT 1 211 36 "\n        titlefont=[TIMES,BOLD,10]):" }{MPLTEXT 1 
211 0 "" }}{PARA 226 "> " 0 "" {MPLTEXT 1 211 36 "save p1,p2,p3,p4,p5,
p6,`c:/demo1.m`;" }{MPLTEXT 1 211 0 "" }}}}{SECT 0 {PARA 224 "" 0 "" 
{TEXT -1 16 "A Classroom demo" }{TEXT -1 0 "" }}{PARA 213 "" 0 "" 
{TEXT -1 224 "In order to use this classroom demo you must creat the f
ile c:/demo1.m first by executing the previous section.  This should b
e done prior to class to save time. Then you can simply load and execu
te this demo during lecture." }{TEXT -1 0 "" }}{EXCHG {PARA 226 "> " 0
 "" {MPLTEXT 1 211 18 "read `c:/demo1.m`;" }{MPLTEXT 1 211 0 "" }}}
{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 3 "p1;" }{MPLTEXT 1 211 0 ""
 }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 3 "p2;" }{MPLTEXT 1 211 
0 "" }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 3 "p3;" }{MPLTEXT 1 
211 0 "" }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 3 "p4;" }
{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 3 "p5
;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 
3 "p6;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 
211 0 "" }}}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 211 0 "" }}}}{PARA 
227 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 75 100 
1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }