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{SECT 0 {PARA 256 "" 0 "" {TEXT 256 22 "\nCalulus Worksheet IV\n" }}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 379 "In this worksheet we give a few \+
examples for volumes\nof solids of revolution. The solids are obtained
by rotating the graph of the function around the x-axis.\nWe use the \+
plottools package. Notice that the cylinder has to be rotated so that \+
its axis coincides with the x-axis. First recall that the `student' p
ackage contains a routine that generates a graphic for Riemann sums. \+
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(plots):with(student
):" }}{PARA 7 "" 1 "" {TEXT -1 29 "Warning, new definition for D" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Riemannsum:=(f,a,b,n)-> disp
lay(\nrightbox(f(x),x=a..b,n),\nscaling=constrained, color=cyan):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Riemannsum(sin,0,Pi,15);" }}}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 103 "There is no similar routine in t
he student package for volumes of solids of revolution, we create one.
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(plots):with(plotto
ols):" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 33 "Mycylinder is a rotated
cylinder:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "mycylinder:=(a
,b,c,r,h)->rotate(\ncylinder([a,b,c],r,h),0,-Pi/2,0):" }}}{SECT 0
{PARA 5 "" 0 "" {TEXT 257 36 "Here is an example of two cylinders:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "display(\{\nmycylinder(0,0,
0,1,0.1),\nmycylinder(0,0,0.1,0.5,0.1)\},\nscaling=constrained, style=
patchnogrid,\naxes=normal,orientation=[-26,73]);" }}}}}{SECT 0 {PARA
4 "" 0 "" {TEXT -1 20 "Here is the routine:" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 172 "Cylinders:=(f,a,b,n)->\ndisplay(\{ seq(\nmycylinde
r(0,0,a+k*(b-a)/n,f(a+k*(b-a)/n),(b-a)/n),k=0..n)\n\},\nscaling=constr
ained, style=patchnogrid,\naxes=normal, lightmodel=light3):" }}}{SECT
0 {PARA 5 "" 0 "" {TEXT 258 19 "Here is an example:" }}{EXCHG {PARA 0
"> " 0 "" {MPLTEXT 1 0 23 "Cylinders(sin,0,Pi,10);" }}}}{SECT 0 {PARA
5 "" 0 "" {TEXT 259 46 "This should be compared with the actual solid:
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Solid:=(f,a,b)->\nplot3
d([x,f(x)*cos(y),f(x)*sin(y)],x=a..b,y=0..2*Pi,\nscaling=constrained,a
xes=normal,\nstyle=patch, lightmodel=light3):" }}}{SECT 0 {PARA 20 ""
0 "" {TEXT 260 19 "Here is an example:" }}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 16 "Solid(sin,0,Pi);" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}}}}}}{MARK "2 3 3 1 0 0" 70 }{VIEWOPTS 1 1 0 3 2
1804 }