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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 20 "Solids of revolution" }}
{PARA 19 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 165 "By lett
ing the domain  bounded by the graph of a function turn around the  x \+
 -axis, one gets a solid of revolution.  Clearly, domains can rotate a
round other lines." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 56 "To get a picture of such solids, consider the function  \+
" }{XPPEDIT 18 0 "f(x) = sqrt(x)" "6#/-%\"fG6#%\"xG-%%sqrtG6#F'" }
{TEXT -1 17 " for  x = 0..5.  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=unapp
ly(sqrt(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "The graph of this function looks l
ike" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(f(x),x=0..5);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 84 "Letting this graph rotate around the  x-axis, one gets \+
a surface whose equation is  " }{XPPEDIT 18 0 "y^2+z^2=f(x)^2" "6#/,&*
$%\"yG\"\"#\"\"\"*$%\"zGF'F(*$-%\"fG6#%\"xGF'" }{TEXT -1 3 ".  " }}
{PARA 0 "" 0 "" {TEXT -1 36 "This surface can be pictured by the " }
{MPLTEXT 1 0 14 "implicitplot3d" }{TEXT -1 30 " command in the plots l
ibrary." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 
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0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "implicitplot3d(y^2+z^2=f(x)^2,x=0..5,y=-3..3,z=-3..3)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 10 "Exercises." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 0 "" }{TEXT -1 39 "Form the above plo
ts for the function  " }{XPPEDIT 18 0 "f(x)=sin(2*x)+x" "6#/-%\"fG6#%
\"xG,&-%$sinG6#*&\"\"#\"\"\"F'F.F.F'F." }{TEXT -1 2 ", " }{XPPEDIT 18 
0 "x=0..4" "6#/%\"xG;\"\"!\"\"%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
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{SECT 1 {PARA 4 "" 0 "" {TEXT -1 75 "Form a picture of the solid  obta
ined by letting the graph of the function " }{XPPEDIT 18 0 "f(x)=sqrt(
x)" "6#/-%\"fG6#%\"xG-%%sqrtG6#F'" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "x=
0..5" "6#/%\"xG;\"\"!\"\"&" }{TEXT -1 26 " rotate around the y-axis." 
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