{VERSION 2 3 "APPLE_68K_MAC" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 
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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 35 "Derivatives and Partial \+
Derivatives" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 130 "The cell below shows how Maple can be used to look at the grap
h of a surface near a point under higher and higher magnification.  " 
}{TEXT 256 15 "Evaluate it now" }{TEXT -1 96 ".  Notice that as the ma
gnification increases the surface looks more and more like a flat plan
e." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 210 "m := 1:\nplot3d(x^2 - y^2, x=-m..m, y=-m..m, scaling
=constrained);\n\nm := 0.25:\nplot3d(x^2 - y^2, x=-m..m, y=-m..m, scal
ing=constrained);\n\nm := 0.0625:\nplot3d(x^2 - y^2, x=-m..m, y=-m..m,
 scaling=constrained);\n \n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 59 "The next cell looks at another point on \+
the same surface.  " }{TEXT 257 15 "Evaluate it now" }{TEXT -1 107 ". \+
 Notice that once again as the magnification increases the surface loo
ks more and more like a flat plane." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 245 "m := 1:\nplot3d(x^2-y^2, \+
x=0.5-m..0.5+m, y=0.5-m..0.5+m, scaling=constrained);\n\nm := 0.25:\np
lot3d(x^2-y^2, x=0.5-m..0.5+m, y=0.5-m..0.5+m, scaling=constrained);\n
\nm := 0.0625:\nplot3d(x^2-y^2, x=0.5-m..0.5+m, y=0.5-m..0.5+m, scalin
g=constrained);\n\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 101 " The next cell illustrates how Maple can be us
ed to draw the tangent plane to a surface at a point.  " }{TEXT 258 
16 "Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 271 "f := (x, y) -> x^2 + y^2:\n\nx0 := 0.5:
\ny0 := 0.5:\n\nfx := diff(f(x, y), x):\nfy := diff(f(x, y), y):\n\na \+
:= subs(\{x=x0, y=y0\}, fx):\nb := subs(\{x=x0, y=y0\}, fy):\nc := f(x
0, y0) - a * x0 - b * y0:\n\nT := (x, y) -> a * x + b * y + c:\n\nplot
3d(\{f(x, y), T(x, y)\},x=-1..1,y=-1..1); " }}}}{MARK "1 0 0" 209 }
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