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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 257 48 
"PARAMETRIC EQUATIONS IN 3-DIMENSIONS: Tube Plots" }{TEXT 258 0 "" }
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 0 "" }{TEXT 260 19 
"Calculus II Project" }{TEXT 261 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 262 10 
"Objective:" }}{PARA 0 "" 0 "" {TEXT -1 65 "Use tubeplots to understan
d parametric equations in 3-dimensions." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 124 "Maple allows students to easily man
ipulate and view the effect of the change in parameter for a set of pa
rametric equations." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 
3 "" 0 "" {TEXT -1 0 "" }{TEXT 263 15 "Solved Example:" }{TEXT 264 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 36 "Draw the letter T using a tube plot.
" }}{PARA 0 "" 0 "" {TEXT -1 50 "A tube plot draws a hollow tube inste
ad of a line." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 265 0 "" }{TEXT 266 102 "To draw a set of tube pl
ots in 3-dimensions using parametric equations use the following Maple
 syntax:" }}{PARA 0 "" 0 "" {TEXT -1 177 "plots[tubeplot]( \{ [g(t),  \+
h(t),  k(t), t = a..b],  [m(t),  n(t), p(t), t = c..d] \},   numpoints
=5,  radius = 1,  axes = normal, scaling = constrained,  orientation =
 [44,88] );" }}{PARA 0 "" 0 "" {TEXT -1 4 "    " }}}{SECT 0 {PARA 3 "
" 0 "" {TEXT -1 0 "" }{TEXT 267 9 "Solution:" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 157 "plots[tubeplot](\{[0, t, 10, t = 6..14],  [0, 10,
 t,  t = 0..10]\}, numpoints = 5, radius = 1, axes = normal, scaling =
 constrained, orientation = [44, 88] );\n" }}{PARA 13 "" 1 "" 
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7%FBFIFgr7%FGFDFgr7%FMFarFgr7%FRF:Fgr7%FWF4FgrFfr7,7%F)F.$\"\"&F+7%F1F
YFcs7%F8FTFcs7%F=F\\rFcs7%FBFIFcs7%FGFDFcs7%FMFarFcs7%FRF:Fcs7%FWF4Fcs
Fbs7,7%F)F.$\"3++++++++vF67%F1FYF_t7%F8FTF_t7%F=F\\rF_t7%FBFIF_t7%FGFD
F_t7%FMFarF_t7%FRF:F_t7%FWF4F_tF^t7,Fbo7%F1FYF.7%F8FTF.7%F=F\\rF.7%FBF
IF.7%FGFDF.7%FMFarF.7%FRF:F.7%FWF4F.Fbo-%(SCALINGG6#%,CONSTRAINEDG-%*A
XESSTYLEG6#%'NORMALG-%+PROJECTIONG6%$\"#WF+$\"#))F+F*" 1 2 0 1 10 0 2 
1 1 4 1 1.000000 88.000000 45.000000 1 0 "Curve 1" "Curve 2" }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 82 "In the Maple command, the first part, [0, t, 10, t = 6..14], dr
aws the horizontal " }}{PARA 0 "" 0 "" {TEXT -1 82 "part of T and the \+
second part [0, 10, t,  t = 0..10] draws the vertical part of T." }}}
{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 66 "________
__________________________________________________________" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 0 "" }{TEXT 268 0 "
" }{TEXT 269 10 "ASSIGNMENT" }{TEXT 270 0 "" }{TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 
271 8 "Problem:" }}{PARA 0 "" 0 "" {TEXT -1 156 "a) Using tube plots, \+
sketch the first three letters of your first name.  If you name contai
ns a curved letter, you can draw it by connecting a set of tubes." }}
{PARA 0 "" 0 "" {TEXT -1 132 "b) For the first letter of your name, ex
plain which parametric function draws which part of the letter and why
.  Use full sentences." }}{PARA 0 "" 0 "" {TEXT -1 179 "c) Choose one \+
letter of your first name and sketch it using at least two different o
rientations and a different radius.  Write one or two sentences compar
ing the two orientations." }}{PARA 0 "" 0 "" {TEXT -1 87 "Note: When c
hoosing numbers for the orientation, try both negative and postive num
bers." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 
"_________________________________________________________________" }}
{PARA 0 "" 0 "" {TEXT -1 94 "MSIP Grant #P120A80089-98: \"Three Urban \+
Calculus Reform Programs: Adopting the Best\" 1998-2001" }}}{MARK "8 4
 0" 82 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }