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\deflang1033\pard\ri4\plain\f4\fs36\cf2 Example 12.3 - Asymptotes of Functions
\par \plain\f3\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}h := x -> (x^2-1)/abs(x-2):\
\pard\li600\ri1\fi-300\plain\f2\fs22\cf1 export(plot, Function2d):\
R := 20:\
\
U := Function2d(h(x), x=-R..R, y=-R..R):\
plot(U)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}a1 := limit(h(x)/x, x=+infinity):\
\pard\li600\ri1\fi-300\plain\f2\fs22\cf1 b1 := limit(h(x) - a1*x, x=+infinity):\
a2 := limit(h(x)/x, x=-infinity):\
b2 := limit(h(x) - a2*x, x=-infinity):\
\
    
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}asymptote1 := Function2d(a1*x + b1, x=-R..R,\
\pard\li600\ri1\fi-300\plain\f2\fs22\cf1    Color=RGB::Blue\
):\
asymptote2 := Function2d(a2*x + b2, x=-R..R,\
   Color=RGB::Black\
):\
asymptote3 := plot::implicit(x=2, x=0..3, y=-R..R):\
    
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}plot(U,\
\pard\li600\ri1\fi-300\plain\f2\fs22\cf1    asymptote1,\
   asymptote2,\
   asymptote3,\
   Scaling=UnConstrained\
)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}
\par }
 