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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "mag:=proc(q);sqrt(ad
d(q[i]^2,i=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "do
t:=proc(r,q);simplify(add(r[i]*q[i],i=1..3)) end:" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 2 "Q1" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "r:=[t,t^2,0]: rd:=diff(r,t):  rdd:=diff(rd,t):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "L:=int(mag(rd),t=0..1.);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG$\"+eG%*y9!\"*" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 61 "evalm([int(t*mag(rd),t=0..1.),int(t^2*mag
(rd),t=0..1.),0]/L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7%
$\"+$pqit&!#5$\"+t@!)*4%F)$\"\"!F-Q(pprint06\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 73 "eval(sqrt((dot(rd,rd)*dot(rdd,rdd)-dot(rd,rdd)
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rq!#5" }}}{EXCHG {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 
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{MPLTEXT 1 0 31 "A:=int(int(1,y=0..x^2),x=0..1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"AG#\"\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "evalm([int(int(x,y=0..x^2),x=0..1),int(int(y,y=0..x^2
),x=0..1),0]/A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7%#\"
\"$\"\"%#F(\"#5\"\"!Q(pprint16\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "int(int(x^2+y^2-(x+y)^2/2,y=0..x^2),x=0..1.);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+[!>w/%!#6" }}}{EXCHG {PARA 0 "" 0 
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{MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 
"eq:=4*x*diff(y(x),x,x)-12*diff(y(x),x)+9*y(x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#eqG,(*(\"\"%\"\"\"%\"xGF(-%%diffG6$-%\"yG6#F)-%\"$G6
$F)\"\"#F(F(*&\"#7F(-F+6$F-F)F(!\"\"*&\"\"*F(F-F(F(" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 38 "eq1:=expand(eval(eq,y(x)=x^2*u(x))/x);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,**&\"#;\"\"\"-%\"uG6#%\"xGF(!
\"\"*(\"\"%F(F,F(-%%diffG6$F)F,F(F(*(F/F()F,\"\"#F(-F16$F)-%\"$G6$F,F5
F(F(*(\"\"*F(F,F(F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
Z:=3*sqrt(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "eq2:=expa
nd(4*x^2*(diff(u(z),z,z)*diff(Z,x)^2+diff(u(z),z)*diff(Z,x,x))\n+4*x*d
iff(u(z),z)*diff(Z,x)+(9*x-16)*u(z));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%$eq2G,**(\"\"*\"\"\"%\"xGF(-%%diffG6$-%\"uG6#%\"zG-%\"$G6$F0\"\"#
F(F(*(\"\"$F(F)#F(F4-F+6$F-F0F(F(*(F'F(F-F(F)F(F(*&\"#;F(F-F(!\"\"" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "eq2:=expand(eval(eq2,\{sqrt
(x)=z/3,x=z^2/9\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G,**&)%
\"zG\"\"#\"\"\"-%%diffG6$-%\"uG6#F(-%\"$G6$F(F)F*F**&F(F*-F,6$F.F(F*F*
*&F.F*F'F*F**&\"#;F*F.F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "
Bessel,  n = 4:      u = A.J4(z) + B.Y4(z)" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "y(x):=x^2*(A*BesselJ(4,3*sqr
t(x))+B*BesselY(4,3*sqrt(x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%
\"yG6#%\"xG*&)F'\"\"#\"\"\",&*&%\"AGF+-%(BesselJG6$\"\"%,$*&\"\"$F+F'#
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{MPLTEXT 1 0 13 "simplify(eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"
!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q4" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 21 "solve(r*(r-1)+1/4,r);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$#\"\"\"\"\"#F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "y:=add(c[i]*x^(i+1/2),i=0..10):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 68 "eq:=expand((4*x^2*diff(y,x,x)-8*x^2*diff(y,x)+(1+4*x^
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\"\"%\"xGF(&%\"cG6#\"\"!F(!\"\"*(\"#7F()F)\"\"#F(&F+6#F(F(F.*(\"#?F()F
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6#FenF(F.*(\"#%)F()F)\"#6F(&F+6#F[oF(F.*(F'F(F1F(F*F(F(*(F'F(F7F(F3F(F
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "solve(\{seq(coeff(eq,x^i),i=
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%\"cG6#\"\"\"&F&6#\"\"!/&F&6#\"\"),$*&#F(\"&?.%F(F)F(F(/&F&6#\"\"(,$*&
#F(\"%S]F(F)F(F(/&F&6#\"\"',$*&#F(\"$?(F(F)F(F(/&F&6#\"\"&,$*&#F(\"$?
\"F(F)F(F(/&F&6#\"\"%,$*&#F(\"#CF(F)F(F(/&F&6#\"\"$,$*&#F(F?F(F)F(F(/&
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15 "seq(i!,i=0..8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6+\"\"\"F#\"\"#\"
\"'\"#C\"$?\"\"$?(\"%S]\"&?.%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 35 "Y:=sum(x^(i+1/2)/i!,i=0..infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"YG*&%\"xG#\"\"\"\"\"#-%$expG6#F&F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "plugin:=proc(g,r);eval(g,\{x=r[1],y=r[2],z=r[3]\})end
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dot:=proc(r,q);simplif
y(add(r[i]*q[i],i=1..3)) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 29 "g:=[x*y-z^2,x*z-y^2,y*z-x^2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"gG7%,&*&%\"xG\"\"\"%\"yGF)F)*$)%\"zG\"\"#F)!\"\",&*&F(F)F-F)F)*$)
F*F.F)F/,&*&F*F)F-F)F)*$)F(F.F)F/" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "r:=evalm([3,-1,4]+[-1,1,-10]*t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"rGK%'vectorG6#7%,&\"\"$\"\"\"%\"tG!\"\",&F+F-F,F+,&
\"\"%F+*&\"#5F+F,F+F-Q(pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "int(dot(plugin(g,r),[-1,1,-10]),t=0..1);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6##\"$E#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "r:=evalm([2,0,-6]+[-5,2,7]*t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"rGK%'vectorG6#7%,&\"\"#\"\"\"*&\"\"&F+%\"tGF+!\"\",
$*&F*F+F.F+F+,&\"\"'F/*&\"\"(F+F.F+F+Q(pprint36\"" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 38 "int(dot(plugin(g,r),[-5,2,7]),t=0..1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#!)\"\"$" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 11 "(226+80)/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$
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