\begin{filecontents*}{graph.eps}
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 0 0 288 288
%%Creator: Mathematica
%%CreationDate: Thu Nov 14 21:38:21 PST 1996
%%EndComments

/Mathdict 150 dict def
Mathdict begin
/Mlmarg		0 72 mul def
/Mrmarg		0 72 mul def
/Mbmarg		0 72 mul def
/Mtmarg		0 72 mul def
/Mwidth		4 72 mul def
/Mheight	4 72 mul def
/Mtransform	{  } bind def
/Mnodistort	true def
/Mfixwid	true	def
/Mfixdash	false def
/Mrot		0	def
/Mpstart {
MathPictureStart
} bind def
/Mpend {
MathPictureEnd
} bind def
/Mscale {
0 1 0 1
5 -1 roll
MathScale
} bind def
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } def
/ISO8859 { (ISOLatin1) MCreateEncoding } def
/Mcopyfont {
dup
maxlength
dict
exch
{
1 index
/FID
eq
{
pop pop
}
{
2 index
3 1 roll
put
}
ifelse
}
forall
} def
/Plain	/Courier findfont Mcopyfont definefont pop
/Bold	/Courier-Bold findfont Mcopyfont definefont pop
/Italic /Courier-Oblique findfont Mcopyfont definefont pop
/MathPictureStart {
gsave
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
} bind def
/MathPictureEnd {
grestore
} bind def
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} bind def
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} bind def
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} bind def
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} bind def
/Mdot {
moveto
0 0 rlineto
stroke
} bind def
/Mtetra {
moveto
lineto
lineto
lineto
fill
} bind def
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
fill
grestore
0 setgray
stroke
} bind def
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
stroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
/Mfstroke {
stroke
currentdash
pop 0
setdash
} bind def
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
/Mvboxa	{
Mfixwid
{
Mvboxa1
}
{
dup
Mwidthcal
0 exch
{
add
}
forall
exch
Mvboxa1
4 index
7 -1 roll
add
4 -1 roll
pop
3 1 roll
}
ifelse
} bind def
/Mvboxa1 {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
/Mrotshowa {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} bind def
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mfixwid
{
Mshowax
}
{
Mshoway
}
ifelse
pop pop pop pop
Mgmatrix setmatrix
} bind def
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} bind def
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
/Mshoway {
3 index
Mwidthcal
5 1 roll
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
[
6 index
aload
length
2 add
-1 roll
{
pop
Strform
stringwidth
pop
neg 
exch
add
0 rmoveto
}
exch
kshow
cleartomark
} for
pop	
} bind def
/Mwidthcal {
[
exch
{
Mwidthcal1
}
forall
]
[
exch
dup
Maxlen
-1 add
0 1
3 -1 roll
{
[
exch
2 index
{		 
1 index	
Mget
exch
}
forall		
pop
Maxget
exch
}
for
pop
]
Mreva
} bind def
/Mreva	{
[
exch
aload
length
-1 1
{1 roll}
for
]
} bind def
/Mget	{
1 index
length
-1 add
1 index
ge
{
get
}
{
pop pop
0
}
ifelse
} bind def
/Maxlen	{
[
exch
{
length
}
forall
Maxget
} bind def
/Maxget	{
counttomark
-1 add
1 1
3 -1 roll
{
pop
Mmax
}
for
exch
pop
} bind def
/Mwidthcal1 {
[
exch
{
Strform
stringwidth
pop
}
forall
]
} bind def
/Strform {
/tem (x) def
tem 0
3 -1 roll
put
tem
} bind def
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
/MathScale {
Mwidth
Mheight
Mlp
translate
scale
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} bind def
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} bind def
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} bind def
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} bind def	
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} bind def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
/Mrotcheck {
dup
90
eq
{
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} bind def
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
/Mboxrot {
Mrot
90 eq
{
brotaux
4 2
roll
}
if
Mrot
180 eq
{
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
4 2
roll
brotaux
}
if
} bind def
/brotaux {
neg
exch
neg
} bind def
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
/Mabswid {
Mabsproc
setlinewidth	
} bind def
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
/MBeginOrig { Momatrix concat} bind def
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop}
{ /sampledsound {
exch
pop
exch
5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop}
repeat
} bind def
} ifelse
/g { setgray} bind def
/k { setcmykcolor} bind def
/m { moveto} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/setcmykcolor where
{ pop}
{ /setcmykcolor {
4 1
roll
[
4 1 
roll
]
{
1 index
sub
1
sub neg
dup
0
lt
{
pop
0
}
if
dup
1
gt
{
pop
1
}
if
exch
} forall
pop
setrgbcolor
} bind def
} ifelse
/Mcharproc
{
currentfile
(x)
readhexstring
pop
0 get
exch
div
} bind def
/Mshadeproc
{
dup
3 1
roll
{
dup
Mcharproc
3 1
roll
} repeat
1 eq
{
setgray
}
{
3 eq
{
setrgbcolor
}
{
setcmykcolor
} ifelse
} ifelse
} bind def
/Mrectproc
{
3 index
2 index
moveto
2 index
3 -1
roll
lineto
dup
3 1
roll
lineto
lineto
fill
} bind def
/Mcolorimage
{
7 1
roll
pop
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
9 index
Mshadeproc
Mrectproc
} for
pop
} for
pop pop pop pop
} bind def
/Mimage
{
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
Mcharproc
setgray
Mrectproc
} for
pop
} for
pop pop pop
} bind def

%%AspectRatio: 1 
MathPictureStart
%% Graphics
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0.5 0.166667 0.5 0.166667 [
[(-2)] .16667 0 0 2 Msboxa
[(-1)] .33333 0 0 2 Msboxa
[(0)] .5 0 0 2 Msboxa
[(1)] .66667 0 0 2 Msboxa
[(2)] .83333 0 0 2 Msboxa
[(3)] 1 0 0 2 Msboxa
[(-3)] -0.0125 0 1 0 Msboxa
[(-2)] -0.0125 .16667 1 0 Msboxa
[(-1)] -0.0125 .33333 1 0 Msboxa
[(0)] -0.0125 .5 1 0 Msboxa
[(1)] -0.0125 .66667 1 0 Msboxa
[(2)] -0.0125 .83333 1 0 Msboxa
[(3)] -0.0125 1 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 1.001 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
[ ] 0 setdash
0 g
p
p
[ .001 .006 ] 0 setdash
.001 w
.83333 0 m
.83333 1 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
.66667 0 m
.66667 1 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
.5 0 m
.5 1 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
.33333 0 m
.33333 1 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
.16667 0 m
.16667 1 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
0 .83333 m
1 .83333 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
0 .66667 m
1 .66667 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
0 .5 m
1 .5 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
0 .33333 m
1 .33333 L
s
P
p
[ .001 .006 ] 0 setdash
.001 w
0 .16667 m
1 .16667 L
s
P
p
.002 w
.16667 0 m
.16667 .00625 L
s
P
[(-2)] .16667 0 0 2 Mshowa
p
.002 w
.33333 0 m
.33333 .00625 L
s
P
[(-1)] .33333 0 0 2 Mshowa
p
.002 w
.5 0 m
.5 .00625 L
s
P
[(0)] .5 0 0 2 Mshowa
p
.002 w
.66667 0 m
.66667 .00625 L
s
P
[(1)] .66667 0 0 2 Mshowa
p
.002 w
.83333 0 m
.83333 .00625 L
s
P
[(2)] .83333 0 0 2 Mshowa
p
.002 w
1 0 m
1 .00625 L
s
P
[(3)] 1 0 0 2 Mshowa
p
.001 w
.03333 0 m
.03333 .00375 L
s
P
p
.001 w
.06667 0 m
.06667 .00375 L
s
P
p
.001 w
.1 0 m
.1 .00375 L
s
P
p
.001 w
.13333 0 m
.13333 .00375 L
s
P
p
.001 w
.2 0 m
.2 .00375 L
s
P
p
.001 w
.23333 0 m
.23333 .00375 L
s
P
p
.001 w
.26667 0 m
.26667 .00375 L
s
P
p
.001 w
.3 0 m
.3 .00375 L
s
P
p
.001 w
.36667 0 m
.36667 .00375 L
s
P
p
.001 w
.4 0 m
.4 .00375 L
s
P
p
.001 w
.43333 0 m
.43333 .00375 L
s
P
p
.001 w
.46667 0 m
.46667 .00375 L
s
P
p
.001 w
.53333 0 m
.53333 .00375 L
s
P
p
.001 w
.56667 0 m
.56667 .00375 L
s
P
p
.001 w
.6 0 m
.6 .00375 L
s
P
p
.001 w
.63333 0 m
.63333 .00375 L
s
P
p
.001 w
.7 0 m
.7 .00375 L
s
P
p
.001 w
.73333 0 m
.73333 .00375 L
s
P
p
.001 w
.76667 0 m
.76667 .00375 L
s
P
p
.001 w
.8 0 m
.8 .00375 L
s
P
p
.001 w
.86667 0 m
.86667 .00375 L
s
P
p
.001 w
.9 0 m
.9 .00375 L
s
P
p
.001 w
.93333 0 m
.93333 .00375 L
s
P
p
.001 w
.96667 0 m
.96667 .00375 L
s
P
p
.002 w
0 0 m
1 0 L
s
P
p
.002 w
0 0 m
.00625 0 L
s
P
[(-3)] -0.0125 0 1 0 Mshowa
p
.002 w
0 .16667 m
.00625 .16667 L
s
P
[(-2)] -0.0125 .16667 1 0 Mshowa
p
.002 w
0 .33333 m
.00625 .33333 L
s
P
[(-1)] -0.0125 .33333 1 0 Mshowa
p
.002 w
0 .5 m
.00625 .5 L
s
P
[(0)] -0.0125 .5 1 0 Mshowa
p
.002 w
0 .66667 m
.00625 .66667 L
s
P
[(1)] -0.0125 .66667 1 0 Mshowa
p
.002 w
0 .83333 m
.00625 .83333 L
s
P
[(2)] -0.0125 .83333 1 0 Mshowa
p
.002 w
0 1 m
.00625 1 L
s
P
[(3)] -0.0125 1 1 0 Mshowa
p
.001 w
0 .03333 m
.00375 .03333 L
s
P
p
.001 w
0 .06667 m
.00375 .06667 L
s
P
p
.001 w
0 .1 m
.00375 .1 L
s
P
p
.001 w
0 .13333 m
.00375 .13333 L
s
P
p
.001 w
0 .2 m
.00375 .2 L
s
P
p
.001 w
0 .23333 m
.00375 .23333 L
s
P
p
.001 w
0 .26667 m
.00375 .26667 L
s
P
p
.001 w
0 .3 m
.00375 .3 L
s
P
p
.001 w
0 .36667 m
.00375 .36667 L
s
P
p
.001 w
0 .4 m
.00375 .4 L
s
P
p
.001 w
0 .43333 m
.00375 .43333 L
s
P
p
.001 w
0 .46667 m
.00375 .46667 L
s
P
p
.001 w
0 .53333 m
.00375 .53333 L
s
P
p
.001 w
0 .56667 m
.00375 .56667 L
s
P
p
.001 w
0 .6 m
.00375 .6 L
s
P
p
.001 w
0 .63333 m
.00375 .63333 L
s
P
p
.001 w
0 .7 m
.00375 .7 L
s
P
p
.001 w
0 .73333 m
.00375 .73333 L
s
P
p
.001 w
0 .76667 m
.00375 .76667 L
s
P
p
.001 w
0 .8 m
.00375 .8 L
s
P
p
.001 w
0 .86667 m
.00375 .86667 L
s
P
p
.001 w
0 .9 m
.00375 .9 L
s
P
p
.001 w
0 .93333 m
.00375 .93333 L
s
P
p
.001 w
0 .96667 m
.00375 .96667 L
s
P
p
.002 w
0 0 m
0 1 L
s
P
P
p
p
.002 w
0 .99375 m
0 1 L
s
P
p
.002 w
.16667 .99375 m
.16667 1 L
s
P
p
.002 w
.33333 .99375 m
.33333 1 L
s
P
p
.002 w
.5 .99375 m
.5 1 L
s
P
p
.002 w
.66667 .99375 m
.66667 1 L
s
P
p
.002 w
.83333 .99375 m
.83333 1 L
s
P
p
.001 w
.03333 .99625 m
.03333 1 L
s
P
p
.001 w
.06667 .99625 m
.06667 1 L
s
P
p
.001 w
.1 .99625 m
.1 1 L
s
P
p
.001 w
.13333 .99625 m
.13333 1 L
s
P
p
.001 w
.2 .99625 m
.2 1 L
s
P
p
.001 w
.23333 .99625 m
.23333 1 L
s
P
p
.001 w
.26667 .99625 m
.26667 1 L
s
P
p
.001 w
.3 .99625 m
.3 1 L
s
P
p
.001 w
.36667 .99625 m
.36667 1 L
s
P
p
.001 w
.4 .99625 m
.4 1 L
s
P
p
.001 w
.43333 .99625 m
.43333 1 L
s
P
p
.001 w
.46667 .99625 m
.46667 1 L
s
P
p
.001 w
.53333 .99625 m
.53333 1 L
s
P
p
.001 w
.56667 .99625 m
.56667 1 L
s
P
p
.001 w
.6 .99625 m
.6 1 L
s
P
p
.001 w
.63333 .99625 m
.63333 1 L
s
P
p
.001 w
.7 .99625 m
.7 1 L
s
P
p
.001 w
.73333 .99625 m
.73333 1 L
s
P
p
.001 w
.76667 .99625 m
.76667 1 L
s
P
p
.001 w
.8 .99625 m
.8 1 L
s
P
p
.001 w
.86667 .99625 m
.86667 1 L
s
P
p
.001 w
.9 .99625 m
.9 1 L
s
P
p
.001 w
.93333 .99625 m
.93333 1 L
s
P
p
.001 w
.96667 .99625 m
.96667 1 L
s
P
p
.002 w
0 1 m
1 1 L
s
P
p
.002 w
.99375 0 m
1 0 L
s
P
p
.002 w
.99375 .16667 m
1 .16667 L
s
P
p
.002 w
.99375 .33333 m
1 .33333 L
s
P
p
.002 w
.99375 .5 m
1 .5 L
s
P
p
.002 w
.99375 .66667 m
1 .66667 L
s
P
p
.002 w
.99375 .83333 m
1 .83333 L
s
P
p
.001 w
.99625 .03333 m
1 .03333 L
s
P
p
.001 w
.99625 .06667 m
1 .06667 L
s
P
p
.001 w
.99625 .1 m
1 .1 L
s
P
p
.001 w
.99625 .13333 m
1 .13333 L
s
P
p
.001 w
.99625 .2 m
1 .2 L
s
P
p
.001 w
.99625 .23333 m
1 .23333 L
s
P
p
.001 w
.99625 .26667 m
1 .26667 L
s
P
p
.001 w
.99625 .3 m
1 .3 L
s
P
p
.001 w
.99625 .36667 m
1 .36667 L
s
P
p
.001 w
.99625 .4 m
1 .4 L
s
P
p
.001 w
.99625 .43333 m
1 .43333 L
s
P
p
.001 w
.99625 .46667 m
1 .46667 L
s
P
p
.001 w
.99625 .53333 m
1 .53333 L
s
P
p
.001 w
.99625 .56667 m
1 .56667 L
s
P
p
.001 w
.99625 .6 m
1 .6 L
s
P
p
.001 w
.99625 .63333 m
1 .63333 L
s
P
p
.001 w
.99625 .7 m
1 .7 L
s
P
p
.001 w
.99625 .73333 m
1 .73333 L
s
P
p
.001 w
.99625 .76667 m
1 .76667 L
s
P
p
.001 w
.99625 .8 m
1 .8 L
s
P
p
.001 w
.99625 .86667 m
1 .86667 L
s
P
p
.001 w
.99625 .9 m
1 .9 L
s
P
p
.001 w
.99625 .93333 m
1 .93333 L
s
P
p
.001 w
.99625 .96667 m
1 .96667 L
s
P
p
.002 w
1 0 m
1 1 L
s
P
P
p
p
.002 w
0 .5 m
1 .5 L
s
P
p
.002 w
.5 0 m
.5 1 L
s
P
P
0 0 m
1 0 L
1 1 L
0 1 L
closepath
clip
newpath
p
p
.004 w
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
P
P
% End of Graphics
MathPictureEnd
end
\end{filecontents*}
\begin{filecontents*}{hyperbola1.eps}
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 0 0 288 288
%%Creator: Mathematica
%%CreationDate: Thu Nov 14 19:24:49 PST 1996
%%EndComments

/Mathdict 150 dict def
Mathdict begin
/Mlmarg		0 72 mul def
/Mrmarg		0 72 mul def
/Mbmarg		0 72 mul def
/Mtmarg		0 72 mul def
/Mwidth		4 72 mul def
/Mheight	4 72 mul def
/Mtransform	{  } bind def
/Mnodistort	true def
/Mfixwid	true	def
/Mfixdash	false def
/Mrot		0	def
/Mpstart {
MathPictureStart
} bind def
/Mpend {
MathPictureEnd
} bind def
/Mscale {
0 1 0 1
5 -1 roll
MathScale
} bind def
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } def
/ISO8859 { (ISOLatin1) MCreateEncoding } def
/Mcopyfont {
dup
maxlength
dict
exch
{
1 index
/FID
eq
{
pop pop
}
{
2 index
3 1 roll
put
}
ifelse
}
forall
} def
/Plain	/Courier findfont Mcopyfont definefont pop
/Bold	/Courier-Bold findfont Mcopyfont definefont pop
/Italic /Courier-Oblique findfont Mcopyfont definefont pop
/MathPictureStart {
gsave
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
} bind def
/MathPictureEnd {
grestore
} bind def
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} bind def
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} bind def
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} bind def
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} bind def
/Mdot {
moveto
0 0 rlineto
stroke
} bind def
/Mtetra {
moveto
lineto
lineto
lineto
fill
} bind def
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
fill
grestore
0 setgray
stroke
} bind def
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
stroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
/Mfstroke {
stroke
currentdash
pop 0
setdash
} bind def
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
/Mvboxa	{
Mfixwid
{
Mvboxa1
}
{
dup
Mwidthcal
0 exch
{
add
}
forall
exch
Mvboxa1
4 index
7 -1 roll
add
4 -1 roll
pop
3 1 roll
}
ifelse
} bind def
/Mvboxa1 {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
/Mrotshowa {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} bind def
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mfixwid
{
Mshowax
}
{
Mshoway
}
ifelse
pop pop pop pop
Mgmatrix setmatrix
} bind def
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} bind def
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
/Mshoway {
3 index
Mwidthcal
5 1 roll
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
[
6 index
aload
length
2 add
-1 roll
{
pop
Strform
stringwidth
pop
neg 
exch
add
0 rmoveto
}
exch
kshow
cleartomark
} for
pop	
} bind def
/Mwidthcal {
[
exch
{
Mwidthcal1
}
forall
]
[
exch
dup
Maxlen
-1 add
0 1
3 -1 roll
{
[
exch
2 index
{		 
1 index	
Mget
exch
}
forall		
pop
Maxget
exch
}
for
pop
]
Mreva
} bind def
/Mreva	{
[
exch
aload
length
-1 1
{1 roll}
for
]
} bind def
/Mget	{
1 index
length
-1 add
1 index
ge
{
get
}
{
pop pop
0
}
ifelse
} bind def
/Maxlen	{
[
exch
{
length
}
forall
Maxget
} bind def
/Maxget	{
counttomark
-1 add
1 1
3 -1 roll
{
pop
Mmax
}
for
exch
pop
} bind def
/Mwidthcal1 {
[
exch
{
Strform
stringwidth
pop
}
forall
]
} bind def
/Strform {
/tem (x) def
tem 0
3 -1 roll
put
tem
} bind def
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
/MathScale {
Mwidth
Mheight
Mlp
translate
scale
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} bind def
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} bind def
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} bind def
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} bind def	
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} bind def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
/Mrotcheck {
dup
90
eq
{
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} bind def
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
/Mboxrot {
Mrot
90 eq
{
brotaux
4 2
roll
}
if
Mrot
180 eq
{
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
4 2
roll
brotaux
}
if
} bind def
/brotaux {
neg
exch
neg
} bind def
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
/Mabswid {
Mabsproc
setlinewidth	
} bind def
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
/MBeginOrig { Momatrix concat} bind def
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop}
{ /sampledsound {
exch
pop
exch
5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop}
repeat
} bind def
} ifelse
/g { setgray} bind def
/k { setcmykcolor} bind def
/m { moveto} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/setcmykcolor where
{ pop}
{ /setcmykcolor {
4 1
roll
[
4 1 
roll
]
{
1 index
sub
1
sub neg
dup
0
lt
{
pop
0
}
if
dup
1
gt
{
pop
1
}
if
exch
} forall
pop
setrgbcolor
} bind def
} ifelse
/Mcharproc
{
currentfile
(x)
readhexstring
pop
0 get
exch
div
} bind def
/Mshadeproc
{
dup
3 1
roll
{
dup
Mcharproc
3 1
roll
} repeat
1 eq
{
setgray
}
{
3 eq
{
setrgbcolor
}
{
setcmykcolor
} ifelse
} ifelse
} bind def
/Mrectproc
{
3 index
2 index
moveto
2 index
3 -1
roll
lineto
dup
3 1
roll
lineto
lineto
fill
} bind def
/Mcolorimage
{
7 1
roll
pop
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
9 index
Mshadeproc
Mrectproc
} for
pop
} for
pop pop pop pop
} bind def
/Mimage
{
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
Mcharproc
setgray
Mrectproc
} for
pop
} for
pop pop pop
} bind def

%%AspectRatio: 1 
MathPictureStart
%% Graphics
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0.5 0.166667 0.5 0.166667 [
[(-2)] .16667 0 0 2 Msboxa
[(-1)] .33333 0 0 2 Msboxa
[(0)] .5 0 0 2 Msboxa
[(1)] .66667 0 0 2 Msboxa
[(2)] .83333 0 0 2 Msboxa
[(3)] 1 0 0 2 Msboxa
[(-3)] -0.0125 0 1 0 Msboxa
[(-2)] -0.0125 .16667 1 0 Msboxa
[(-1)] -0.0125 .33333 1 0 Msboxa
[(0)] -0.0125 .5 1 0 Msboxa
[(1)] -0.0125 .66667 1 0 Msboxa
[(2)] -0.0125 .83333 1 0 Msboxa
[(3)] -0.0125 1 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 1.001 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
[ ] 0 setdash
0 g
p
p
.002 w
.16667 0 m
.16667 .00625 L
s
P
[(-2)] .16667 0 0 2 Mshowa
p
.002 w
.33333 0 m
.33333 .00625 L
s
P
[(-1)] .33333 0 0 2 Mshowa
p
.002 w
.5 0 m
.5 .00625 L
s
P
[(0)] .5 0 0 2 Mshowa
p
.002 w
.66667 0 m
.66667 .00625 L
s
P
[(1)] .66667 0 0 2 Mshowa
p
.002 w
.83333 0 m
.83333 .00625 L
s
P
[(2)] .83333 0 0 2 Mshowa
p
.002 w
1 0 m
1 .00625 L
s
P
[(3)] 1 0 0 2 Mshowa
p
.001 w
.03333 0 m
.03333 .00375 L
s
P
p
.001 w
.06667 0 m
.06667 .00375 L
s
P
p
.001 w
.1 0 m
.1 .00375 L
s
P
p
.001 w
.13333 0 m
.13333 .00375 L
s
P
p
.001 w
.2 0 m
.2 .00375 L
s
P
p
.001 w
.23333 0 m
.23333 .00375 L
s
P
p
.001 w
.26667 0 m
.26667 .00375 L
s
P
p
.001 w
.3 0 m
.3 .00375 L
s
P
p
.001 w
.36667 0 m
.36667 .00375 L
s
P
p
.001 w
.4 0 m
.4 .00375 L
s
P
p
.001 w
.43333 0 m
.43333 .00375 L
s
P
p
.001 w
.46667 0 m
.46667 .00375 L
s
P
p
.001 w
.53333 0 m
.53333 .00375 L
s
P
p
.001 w
.56667 0 m
.56667 .00375 L
s
P
p
.001 w
.6 0 m
.6 .00375 L
s
P
p
.001 w
.63333 0 m
.63333 .00375 L
s
P
p
.001 w
.7 0 m
.7 .00375 L
s
P
p
.001 w
.73333 0 m
.73333 .00375 L
s
P
p
.001 w
.76667 0 m
.76667 .00375 L
s
P
p
.001 w
.8 0 m
.8 .00375 L
s
P
p
.001 w
.86667 0 m
.86667 .00375 L
s
P
p
.001 w
.9 0 m
.9 .00375 L
s
P
p
.001 w
.93333 0 m
.93333 .00375 L
s
P
p
.001 w
.96667 0 m
.96667 .00375 L
s
P
p
.002 w
0 0 m
1 0 L
s
P
p
.002 w
0 0 m
.00625 0 L
s
P
[(-3)] -0.0125 0 1 0 Mshowa
p
.002 w
0 .16667 m
.00625 .16667 L
s
P
[(-2)] -0.0125 .16667 1 0 Mshowa
p
.002 w
0 .33333 m
.00625 .33333 L
s
P
[(-1)] -0.0125 .33333 1 0 Mshowa
p
.002 w
0 .5 m
.00625 .5 L
s
P
[(0)] -0.0125 .5 1 0 Mshowa
p
.002 w
0 .66667 m
.00625 .66667 L
s
P
[(1)] -0.0125 .66667 1 0 Mshowa
p
.002 w
0 .83333 m
.00625 .83333 L
s
P
[(2)] -0.0125 .83333 1 0 Mshowa
p
.002 w
0 1 m
.00625 1 L
s
P
[(3)] -0.0125 1 1 0 Mshowa
p
.001 w
0 .03333 m
.00375 .03333 L
s
P
p
.001 w
0 .06667 m
.00375 .06667 L
s
P
p
.001 w
0 .1 m
.00375 .1 L
s
P
p
.001 w
0 .13333 m
.00375 .13333 L
s
P
p
.001 w
0 .2 m
.00375 .2 L
s
P
p
.001 w
0 .23333 m
.00375 .23333 L
s
P
p
.001 w
0 .26667 m
.00375 .26667 L
s
P
p
.001 w
0 .3 m
.00375 .3 L
s
P
p
.001 w
0 .36667 m
.00375 .36667 L
s
P
p
.001 w
0 .4 m
.00375 .4 L
s
P
p
.001 w
0 .43333 m
.00375 .43333 L
s
P
p
.001 w
0 .46667 m
.00375 .46667 L
s
P
p
.001 w
0 .53333 m
.00375 .53333 L
s
P
p
.001 w
0 .56667 m
.00375 .56667 L
s
P
p
.001 w
0 .6 m
.00375 .6 L
s
P
p
.001 w
0 .63333 m
.00375 .63333 L
s
P
p
.001 w
0 .7 m
.00375 .7 L
s
P
p
.001 w
0 .73333 m
.00375 .73333 L
s
P
p
.001 w
0 .76667 m
.00375 .76667 L
s
P
p
.001 w
0 .8 m
.00375 .8 L
s
P
p
.001 w
0 .86667 m
.00375 .86667 L
s
P
p
.001 w
0 .9 m
.00375 .9 L
s
P
p
.001 w
0 .93333 m
.00375 .93333 L
s
P
p
.001 w
0 .96667 m
.00375 .96667 L
s
P
p
.002 w
0 0 m
0 1 L
s
P
P
p
p
.002 w
0 .99375 m
0 1 L
s
P
p
.002 w
.16667 .99375 m
.16667 1 L
s
P
p
.002 w
.33333 .99375 m
.33333 1 L
s
P
p
.002 w
.5 .99375 m
.5 1 L
s
P
p
.002 w
.66667 .99375 m
.66667 1 L
s
P
p
.002 w
.83333 .99375 m
.83333 1 L
s
P
p
.001 w
.03333 .99625 m
.03333 1 L
s
P
p
.001 w
.06667 .99625 m
.06667 1 L
s
P
p
.001 w
.1 .99625 m
.1 1 L
s
P
p
.001 w
.13333 .99625 m
.13333 1 L
s
P
p
.001 w
.2 .99625 m
.2 1 L
s
P
p
.001 w
.23333 .99625 m
.23333 1 L
s
P
p
.001 w
.26667 .99625 m
.26667 1 L
s
P
p
.001 w
.3 .99625 m
.3 1 L
s
P
p
.001 w
.36667 .99625 m
.36667 1 L
s
P
p
.001 w
.4 .99625 m
.4 1 L
s
P
p
.001 w
.43333 .99625 m
.43333 1 L
s
P
p
.001 w
.46667 .99625 m
.46667 1 L
s
P
p
.001 w
.53333 .99625 m
.53333 1 L
s
P
p
.001 w
.56667 .99625 m
.56667 1 L
s
P
p
.001 w
.6 .99625 m
.6 1 L
s
P
p
.001 w
.63333 .99625 m
.63333 1 L
s
P
p
.001 w
.7 .99625 m
.7 1 L
s
P
p
.001 w
.73333 .99625 m
.73333 1 L
s
P
p
.001 w
.76667 .99625 m
.76667 1 L
s
P
p
.001 w
.8 .99625 m
.8 1 L
s
P
p
.001 w
.86667 .99625 m
.86667 1 L
s
P
p
.001 w
.9 .99625 m
.9 1 L
s
P
p
.001 w
.93333 .99625 m
.93333 1 L
s
P
p
.001 w
.96667 .99625 m
.96667 1 L
s
P
p
.002 w
0 1 m
1 1 L
s
P
p
.002 w
.99375 0 m
1 0 L
s
P
p
.002 w
.99375 .16667 m
1 .16667 L
s
P
p
.002 w
.99375 .33333 m
1 .33333 L
s
P
p
.002 w
.99375 .5 m
1 .5 L
s
P
p
.002 w
.99375 .66667 m
1 .66667 L
s
P
p
.002 w
.99375 .83333 m
1 .83333 L
s
P
p
.001 w
.99625 .03333 m
1 .03333 L
s
P
p
.001 w
.99625 .06667 m
1 .06667 L
s
P
p
.001 w
.99625 .1 m
1 .1 L
s
P
p
.001 w
.99625 .13333 m
1 .13333 L
s
P
p
.001 w
.99625 .2 m
1 .2 L
s
P
p
.001 w
.99625 .23333 m
1 .23333 L
s
P
p
.001 w
.99625 .26667 m
1 .26667 L
s
P
p
.001 w
.99625 .3 m
1 .3 L
s
P
p
.001 w
.99625 .36667 m
1 .36667 L
s
P
p
.001 w
.99625 .4 m
1 .4 L
s
P
p
.001 w
.99625 .43333 m
1 .43333 L
s
P
p
.001 w
.99625 .46667 m
1 .46667 L
s
P
p
.001 w
.99625 .53333 m
1 .53333 L
s
P
p
.001 w
.99625 .56667 m
1 .56667 L
s
P
p
.001 w
.99625 .6 m
1 .6 L
s
P
p
.001 w
.99625 .63333 m
1 .63333 L
s
P
p
.001 w
.99625 .7 m
1 .7 L
s
P
p
.001 w
.99625 .73333 m
1 .73333 L
s
P
p
.001 w
.99625 .76667 m
1 .76667 L
s
P
p
.001 w
.99625 .8 m
1 .8 L
s
P
p
.001 w
.99625 .86667 m
1 .86667 L
s
P
p
.001 w
.99625 .9 m
1 .9 L
s
P
p
.001 w
.99625 .93333 m
1 .93333 L
s
P
p
.001 w
.99625 .96667 m
1 .96667 L
s
P
p
.002 w
1 0 m
1 1 L
s
P
P
p
p
.002 w
0 .5 m
1 .5 L
s
P
p
.002 w
.5 0 m
.5 1 L
s
P
P
0 0 m
1 0 L
1 1 L
0 1 L
closepath
clip
newpath
p
p
p
.004 w
s
s
1 .0288 m
.95695 .07453 L
s
.95695 .07453 m
.89207 .14512 L
.83811 .20583 L
.79356 .25834 L
.75718 .30413 L
.72796 .34447 L
.7051 .38047 L
.68794 .41315 L
.67601 .44341 L
.6719 .4579 L
.6703 .46503 L
.66899 .47209 L
.66797 .47911 L
.66757 .48261 L
.66725 .4861 L
.66699 .48958 L
.66689 .49132 L
.66681 .49305 L
.66675 .49479 L
.66672 .49566 L
.6667 .49653 L
.66669 .4974 L
.66668 .49826 L
.66667 .49913 L
.66667 .5 L
.66667 .50087 L
.66668 .50174 L
.66669 .5026 L
.6667 .50347 L
.66672 .50434 L
.66675 .50521 L
.66681 .50695 L
.66689 .50868 L
.66699 .51042 L
.66725 .5139 L
.66757 .51739 L
.66797 .52089 L
.66899 .52791 L
.6719 .5421 L
.67601 .55659 L
.68794 .58685 L
.7051 .61953 L
.72796 .65553 L
.75718 .69587 L
.79356 .74166 L
.83811 .79417 L
.89207 .85488 L
.95695 .92547 L
s
1 .9712 m
.95695 .92547 L
s
s
s
P
P
p
p
.004 w
s
s
0 .0288 m
.04305 .07453 L
s
.04305 .07453 m
.10793 .14512 L
.16189 .20583 L
.20644 .25834 L
.24282 .30413 L
.27204 .34447 L
.2949 .38047 L
.31206 .41315 L
.32399 .44341 L
.3281 .4579 L
.3297 .46503 L
.33101 .47209 L
.33203 .47911 L
.33243 .48261 L
.33275 .4861 L
.33301 .48958 L
.33311 .49132 L
.33319 .49305 L
.33325 .49479 L
.33328 .49566 L
.3333 .49653 L
.33331 .4974 L
.33332 .49826 L
.33333 .49913 L
.33333 .5 L
.33333 .50087 L
.33332 .50174 L
.33331 .5026 L
.3333 .50347 L
.33328 .50434 L
.33325 .50521 L
.33319 .50695 L
.33311 .50868 L
.33301 .51042 L
.33275 .5139 L
.33243 .51739 L
.33203 .52089 L
.33101 .52791 L
.3281 .5421 L
.32399 .55659 L
.31206 .58685 L
.2949 .61953 L
.27204 .65553 L
.24282 .69587 L
.20644 .74166 L
.16189 .79417 L
.10793 .85488 L
.04305 .92547 L
s
0 .9712 m
.04305 .92547 L
s
s
s
P
P
P
% End of Graphics
MathPictureEnd
end
\end{filecontents*}

\begin{filecontents*}{hyperbola2.eps}
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 0 0 288 288
%%Creator: Mathematica
%%CreationDate: Thu Nov 14 19:28:05 PST 1996
%%EndComments

/Mathdict 150 dict def
Mathdict begin
/Mlmarg		0 72 mul def
/Mrmarg		0 72 mul def
/Mbmarg		0 72 mul def
/Mtmarg		0 72 mul def
/Mwidth		4 72 mul def
/Mheight	4 72 mul def
/Mtransform	{  } bind def
/Mnodistort	true def
/Mfixwid	true	def
/Mfixdash	false def
/Mrot		0	def
/Mpstart {
MathPictureStart
} bind def
/Mpend {
MathPictureEnd
} bind def
/Mscale {
0 1 0 1
5 -1 roll
MathScale
} bind def
/ISOLatin1Encoding dup where
{ pop pop }
{
[
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /minus /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
} ifelse
/MFontDict 50 dict def
/MStrCat
{
exch
dup length
2 index length add
string
dup 3 1 roll
copy
length
exch dup
4 2 roll exch
putinterval
} def
/MCreateEncoding
{
1 index
255 string cvs
(-) MStrCat
1 index MStrCat
cvn exch
(Encoding) MStrCat
cvn dup where
{
exch get
}
{
pop
StandardEncoding
} ifelse
3 1 roll
dup MFontDict exch known not
{
1 index findfont
dup length dict
begin
{1 index /FID ne
{def}
{pop pop}
ifelse} forall
/Encoding 3 index
def
currentdict
end
1 index exch definefont pop
MFontDict 1 index
null put
}
if
exch pop
exch pop
} def
/ISOLatin1 { (ISOLatin1) MCreateEncoding } def
/ISO8859 { (ISOLatin1) MCreateEncoding } def
/Mcopyfont {
dup
maxlength
dict
exch
{
1 index
/FID
eq
{
pop pop
}
{
2 index
3 1 roll
put
}
ifelse
}
forall
} def
/Plain	/Courier findfont Mcopyfont definefont pop
/Bold	/Courier-Bold findfont Mcopyfont definefont pop
/Italic /Courier-Oblique findfont Mcopyfont definefont pop
/MathPictureStart {
gsave
Mtransform
Mlmarg
Mbmarg
translate
Mwidth
Mlmarg Mrmarg add
sub
/Mwidth exch def
Mheight
Mbmarg Mtmarg add
sub
/Mheight exch def
/Mtmatrix
matrix currentmatrix
def
/Mgmatrix
matrix currentmatrix
def
} bind def
/MathPictureEnd {
grestore
} bind def
/MFill {
0 0 		moveto
Mwidth 0 	lineto
Mwidth Mheight 	lineto
0 Mheight 	lineto
fill
} bind def
/MPlotRegion {
3 index
Mwidth mul
2 index
Mheight mul
translate
exch sub
Mheight mul
/Mheight
exch def
exch sub
Mwidth mul
/Mwidth
exch def
} bind def
/MathSubStart {
Momatrix
Mgmatrix Mtmatrix
Mwidth Mheight
7 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
Mgmatrix setmatrix
9 -2 roll
moveto
Mtmatrix setmatrix
currentpoint
2 copy translate
/Mtmatrix matrix currentmatrix def
3 -1 roll
exch sub
/Mheight exch def
sub
/Mwidth exch def
} bind def
/MathSubEnd {
/Mheight exch def
/Mwidth exch def
/Mtmatrix exch def
dup setmatrix
/Mgmatrix exch def
/Momatrix exch def
} bind def
/Mdot {
moveto
0 0 rlineto
stroke
} bind def
/Mtetra {
moveto
lineto
lineto
lineto
fill
} bind def
/Metetra {
moveto
lineto
lineto
lineto
closepath
gsave
fill
grestore
0 setgray
stroke
} bind def
/Mistroke {
flattenpath
0 0 0
{
4 2 roll
pop pop
}
{
4 -1 roll
2 index
sub dup mul
4 -1 roll
2 index
sub dup mul
add sqrt
4 -1 roll
add
3 1 roll
}
{
stop
}
{
stop
}
pathforall
pop pop
currentpoint
stroke
moveto
currentdash
3 -1 roll
add
setdash
} bind def
/Mfstroke {
stroke
currentdash
pop 0
setdash
} bind def
/Mrotsboxa {
gsave
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
grestore
Msboxa
3  -1 roll
/Mtmatrix
exch def
/Mrot
0 def
} bind def
/Msboxa {
newpath
5 -1 roll
Mvboxa
pop
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Msboxa1
5 -3 roll
Msboxa1
Mboxrot
[
7 -2 roll
2 copy
[
3 1 roll
10 -1 roll
9 -1 roll
]
6 1 roll
5 -2 roll
]
} bind def
/Msboxa1 {
sub
2 div
dup
2 index
1 add
mul
3 -1 roll
-1 add
3 -1 roll
mul
} bind def
/Mvboxa	{
Mfixwid
{
Mvboxa1
}
{
dup
Mwidthcal
0 exch
{
add
}
forall
exch
Mvboxa1
4 index
7 -1 roll
add
4 -1 roll
pop
3 1 roll
}
ifelse
} bind def
/Mvboxa1 {
gsave
newpath
[ true
3 -1 roll
{
Mbbox
5 -1 roll
{
0
5 1 roll
}
{
7 -1 roll
exch sub
(m) stringwidth pop
.3 mul
sub
7 1 roll
6 -1 roll
4 -1 roll
Mmin
3 -1 roll
5 index
add
5 -1 roll
4 -1 roll
Mmax
4 -1 roll
}
ifelse
false
}
forall
{ stop } if
counttomark
1 add
4 roll
]
grestore
} bind def
/Mbbox {
1 dict begin
0 0 moveto
/temp (T) def
{	gsave
currentpoint newpath moveto
temp 0 3 -1 roll put temp
false charpath flattenpath currentpoint
pathbbox
grestore moveto lineto moveto} forall
pathbbox
newpath
end
} bind def
/Mmin {
2 copy
gt
{ exch } if
pop
} bind def
/Mmax {
2 copy
lt
{ exch } if
pop
} bind def
/Mrotshowa {
dup
/Mrot
exch def
Mrotcheck
Mtmatrix
dup
setmatrix
7 1 roll
4 index
4 index
translate
rotate
3 index
-1 mul
3 index
-1 mul
translate
/Mtmatrix
matrix
currentmatrix
def
Mgmatrix setmatrix
Mshowa
/Mtmatrix
exch def
/Mrot 0 def
} bind def
/Mshowa {
4 -2 roll
moveto
2 index
Mtmatrix setmatrix
Mvboxa
7 1 roll
Mboxout
6 -1 roll
5 -1 roll
4 -1 roll
Mshowa1
4 1 roll
Mshowa1
rmoveto
currentpoint
Mfixwid
{
Mshowax
}
{
Mshoway
}
ifelse
pop pop pop pop
Mgmatrix setmatrix
} bind def
/Mshowax {	
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
Mfixdash
{
Mfixdashp		
}
if
show
} for
} bind def
/Mfixdashp {
dup
length
1
gt
1 index
true exch
{
45
eq
and
} forall
and
{
gsave
(--)		
stringwidth pop
(-)
stringwidth pop
sub
2 div
0 rmoveto
dup
length
1 sub
{
(-)
show
}
repeat
grestore
}
if
} bind def	
/Mshoway {
3 index
Mwidthcal
5 1 roll
0 1
4 index length
-1 add
{
2 index
4 index
2 index
get
3 index
add
moveto
4 index
exch get
[
6 index
aload
length
2 add
-1 roll
{
pop
Strform
stringwidth
pop
neg 
exch
add
0 rmoveto
}
exch
kshow
cleartomark
} for
pop	
} bind def
/Mwidthcal {
[
exch
{
Mwidthcal1
}
forall
]
[
exch
dup
Maxlen
-1 add
0 1
3 -1 roll
{
[
exch
2 index
{		 
1 index	
Mget
exch
}
forall		
pop
Maxget
exch
}
for
pop
]
Mreva
} bind def
/Mreva	{
[
exch
aload
length
-1 1
{1 roll}
for
]
} bind def
/Mget	{
1 index
length
-1 add
1 index
ge
{
get
}
{
pop pop
0
}
ifelse
} bind def
/Maxlen	{
[
exch
{
length
}
forall
Maxget
} bind def
/Maxget	{
counttomark
-1 add
1 1
3 -1 roll
{
pop
Mmax
}
for
exch
pop
} bind def
/Mwidthcal1 {
[
exch
{
Strform
stringwidth
pop
}
forall
]
} bind def
/Strform {
/tem (x) def
tem 0
3 -1 roll
put
tem
} bind def
/Mshowa1 {
2 copy
add
4 1 roll
sub
mul
sub
-2 div
} bind def
/MathScale {
Mwidth
Mheight
Mlp
translate
scale
/yscale exch def
/ybias exch def
/xscale exch def
/xbias exch def
/Momatrix
xscale yscale matrix scale
xbias ybias matrix translate
matrix concatmatrix def
/Mgmatrix
matrix currentmatrix
def
} bind def
/Mlp {
3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
} if
4 index
2 index
2 index
Mlprun
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} bind def
/Mlpfirst {
3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
/Mlprun {
2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
} forall
pop pop pop pop
3 1 roll
pop pop
aload pop
5 -1 roll
aload pop
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
/Mlprun1 {
aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
/Mlprun2 {
2 copy
add 2 div
3 1 roll
exch sub
} bind def
/Mlpminmax {
cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
/Mlp1 {
5 index
3 index	sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index	div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
} bind def
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/Minner {
outflag
1
eq
{
/outflag 0 def
/intop 0 def
/inrht 0 def
} if		
5 index
gsave
Mtmatrix setmatrix
Mvboxa pop
grestore
3 -1 roll
pop
dup
intop
gt
{
/intop
exch def
}
{ pop }
ifelse
dup
inrht
gt
{
/inrht
exch def
}
{ pop }
ifelse
pop
/inflag
1 def
} bind def
/Mouter {
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
inflag
1 eq
{
dup
0 lt
{
dup
intop
mul
neg
/yadtop
exch def
} if
dup
0 gt
{
dup
intop
mul
/yadbot
exch def
}
if
pop
dup
0 lt
{
dup
inrht
mul
neg
/xadrht
exch def
} if
dup
0 gt
{
dup
inrht
mul
/xadlft
exch def
} if
pop
/outflag 1 def
}
{ pop pop}
ifelse
/inflag 0 def
/inrht 0 def
/intop 0 def
} bind def	
/Mboxout {
outflag
1
eq
{
4 -1
roll
xadlft
leadjust
add
sub
4 1 roll
3 -1
roll
yadbot
leadjust
add
sub
3 1
roll
exch
xadrht
leadjust
add
add
exch
yadtop
leadjust
add
add
/outflag 0 def
/xadlft 0 def
/yadbot 0 def
/xadrht 0 def
/yadtop 0 def
} if
} bind def
/leadjust {
(m) stringwidth pop
.5 mul
} bind def
/Mrotcheck {
dup
90
eq
{
yadbot
/yadbot
xadrht
def	
/xadrht
yadtop
def
/yadtop
xadlft
def
/xadlft
exch
def
}
if
dup
cos
1 index
sin
Checkaux
dup
cos
1 index
sin neg
exch
Checkaux
3 1 roll
pop pop
} bind def
/Checkaux {
4 index
exch
4 index
mul
3 1 roll
mul add
4 1 roll
} bind def
/Mboxrot {
Mrot
90 eq
{
brotaux
4 2
roll
}
if
Mrot
180 eq
{
4 2
roll
brotaux
4 2
roll
brotaux
}	
if
Mrot
270 eq
{
4 2
roll
brotaux
}
if
} bind def
/brotaux {
neg
exch
neg
} bind def
/Mabsproc {
0
matrix defaultmatrix
dtransform idtransform
dup mul exch
dup mul
add sqrt
} bind def
/Mabswid {
Mabsproc
setlinewidth	
} bind def
/Mabsdash {
exch
[
exch
{
Mabsproc
}
forall
]
exch
setdash
} bind def
/MBeginOrig { Momatrix concat} bind def
/MEndOrig { Mgmatrix setmatrix} bind def
/sampledsound where
{ pop}
{ /sampledsound {
exch
pop
exch
5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop}
repeat
} bind def
} ifelse
/g { setgray} bind def
/k { setcmykcolor} bind def
/m { moveto} bind def
/p { gsave} bind def
/r { setrgbcolor} bind def
/w { setlinewidth} bind def
/C { curveto} bind def
/F { fill} bind def
/L { lineto} bind def
/P { grestore} bind def
/s { stroke} bind def
/setcmykcolor where
{ pop}
{ /setcmykcolor {
4 1
roll
[
4 1 
roll
]
{
1 index
sub
1
sub neg
dup
0
lt
{
pop
0
}
if
dup
1
gt
{
pop
1
}
if
exch
} forall
pop
setrgbcolor
} bind def
} ifelse
/Mcharproc
{
currentfile
(x)
readhexstring
pop
0 get
exch
div
} bind def
/Mshadeproc
{
dup
3 1
roll
{
dup
Mcharproc
3 1
roll
} repeat
1 eq
{
setgray
}
{
3 eq
{
setrgbcolor
}
{
setcmykcolor
} ifelse
} ifelse
} bind def
/Mrectproc
{
3 index
2 index
moveto
2 index
3 -1
roll
lineto
dup
3 1
roll
lineto
lineto
fill
} bind def
/Mcolorimage
{
7 1
roll
pop
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
9 index
Mshadeproc
Mrectproc
} for
pop
} for
pop pop pop pop
} bind def
/Mimage
{
pop
matrix
invertmatrix
concat
2 exch exp
1 sub
3 1 roll
1 1
2 index
{
1 1
4 index
{
dup
1 sub
exch
2 index
dup
1 sub
exch
7 index
Mcharproc
setgray
Mrectproc
} for
pop
} for
pop pop pop
} bind def

%%AspectRatio: 1 
MathPictureStart
%% Graphics
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0.5 0.166667 0.5 0.166667 [
[(-2)] .16667 0 0 2 Msboxa
[(-1)] .33333 0 0 2 Msboxa
[(0)] .5 0 0 2 Msboxa
[(1)] .66667 0 0 2 Msboxa
[(2)] .83333 0 0 2 Msboxa
[(3)] 1 0 0 2 Msboxa
[(-3)] -0.0125 0 1 0 Msboxa
[(-2)] -0.0125 .16667 1 0 Msboxa
[(-1)] -0.0125 .33333 1 0 Msboxa
[(0)] -0.0125 .5 1 0 Msboxa
[(1)] -0.0125 .66667 1 0 Msboxa
[(2)] -0.0125 .83333 1 0 Msboxa
[(3)] -0.0125 1 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 1.001 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
[ ] 0 setdash
0 g
p
p
.002 w
.16667 0 m
.16667 .00625 L
s
P
[(-2)] .16667 0 0 2 Mshowa
p
.002 w
.33333 0 m
.33333 .00625 L
s
P
[(-1)] .33333 0 0 2 Mshowa
p
.002 w
.5 0 m
.5 .00625 L
s
P
[(0)] .5 0 0 2 Mshowa
p
.002 w
.66667 0 m
.66667 .00625 L
s
P
[(1)] .66667 0 0 2 Mshowa
p
.002 w
.83333 0 m
.83333 .00625 L
s
P
[(2)] .83333 0 0 2 Mshowa
p
.002 w
1 0 m
1 .00625 L
s
P
[(3)] 1 0 0 2 Mshowa
p
.001 w
.03333 0 m
.03333 .00375 L
s
P
p
.001 w
.06667 0 m
.06667 .00375 L
s
P
p
.001 w
.1 0 m
.1 .00375 L
s
P
p
.001 w
.13333 0 m
.13333 .00375 L
s
P
p
.001 w
.2 0 m
.2 .00375 L
s
P
p
.001 w
.23333 0 m
.23333 .00375 L
s
P
p
.001 w
.26667 0 m
.26667 .00375 L
s
P
p
.001 w
.3 0 m
.3 .00375 L
s
P
p
.001 w
.36667 0 m
.36667 .00375 L
s
P
p
.001 w
.4 0 m
.4 .00375 L
s
P
p
.001 w
.43333 0 m
.43333 .00375 L
s
P
p
.001 w
.46667 0 m
.46667 .00375 L
s
P
p
.001 w
.53333 0 m
.53333 .00375 L
s
P
p
.001 w
.56667 0 m
.56667 .00375 L
s
P
p
.001 w
.6 0 m
.6 .00375 L
s
P
p
.001 w
.63333 0 m
.63333 .00375 L
s
P
p
.001 w
.7 0 m
.7 .00375 L
s
P
p
.001 w
.73333 0 m
.73333 .00375 L
s
P
p
.001 w
.76667 0 m
.76667 .00375 L
s
P
p
.001 w
.8 0 m
.8 .00375 L
s
P
p
.001 w
.86667 0 m
.86667 .00375 L
s
P
p
.001 w
.9 0 m
.9 .00375 L
s
P
p
.001 w
.93333 0 m
.93333 .00375 L
s
P
p
.001 w
.96667 0 m
.96667 .00375 L
s
P
p
.002 w
0 0 m
1 0 L
s
P
p
.002 w
0 0 m
.00625 0 L
s
P
[(-3)] -0.0125 0 1 0 Mshowa
p
.002 w
0 .16667 m
.00625 .16667 L
s
P
[(-2)] -0.0125 .16667 1 0 Mshowa
p
.002 w
0 .33333 m
.00625 .33333 L
s
P
[(-1)] -0.0125 .33333 1 0 Mshowa
p
.002 w
0 .5 m
.00625 .5 L
s
P
[(0)] -0.0125 .5 1 0 Mshowa
p
.002 w
0 .66667 m
.00625 .66667 L
s
P
[(1)] -0.0125 .66667 1 0 Mshowa
p
.002 w
0 .83333 m
.00625 .83333 L
s
P
[(2)] -0.0125 .83333 1 0 Mshowa
p
.002 w
0 1 m
.00625 1 L
s
P
[(3)] -0.0125 1 1 0 Mshowa
p
.001 w
0 .03333 m
.00375 .03333 L
s
P
p
.001 w
0 .06667 m
.00375 .06667 L
s
P
p
.001 w
0 .1 m
.00375 .1 L
s
P
p
.001 w
0 .13333 m
.00375 .13333 L
s
P
p
.001 w
0 .2 m
.00375 .2 L
s
P
p
.001 w
0 .23333 m
.00375 .23333 L
s
P
p
.001 w
0 .26667 m
.00375 .26667 L
s
P
p
.001 w
0 .3 m
.00375 .3 L
s
P
p
.001 w
0 .36667 m
.00375 .36667 L
s
P
p
.001 w
0 .4 m
.00375 .4 L
s
P
p
.001 w
0 .43333 m
.00375 .43333 L
s
P
p
.001 w
0 .46667 m
.00375 .46667 L
s
P
p
.001 w
0 .53333 m
.00375 .53333 L
s
P
p
.001 w
0 .56667 m
.00375 .56667 L
s
P
p
.001 w
0 .6 m
.00375 .6 L
s
P
p
.001 w
0 .63333 m
.00375 .63333 L
s
P
p
.001 w
0 .7 m
.00375 .7 L
s
P
p
.001 w
0 .73333 m
.00375 .73333 L
s
P
p
.001 w
0 .76667 m
.00375 .76667 L
s
P
p
.001 w
0 .8 m
.00375 .8 L
s
P
p
.001 w
0 .86667 m
.00375 .86667 L
s
P
p
.001 w
0 .9 m
.00375 .9 L
s
P
p
.001 w
0 .93333 m
.00375 .93333 L
s
P
p
.001 w
0 .96667 m
.00375 .96667 L
s
P
p
.002 w
0 0 m
0 1 L
s
P
P
p
p
.002 w
0 .99375 m
0 1 L
s
P
p
.002 w
.16667 .99375 m
.16667 1 L
s
P
p
.002 w
.33333 .99375 m
.33333 1 L
s
P
p
.002 w
.5 .99375 m
.5 1 L
s
P
p
.002 w
.66667 .99375 m
.66667 1 L
s
P
p
.002 w
.83333 .99375 m
.83333 1 L
s
P
p
.001 w
.03333 .99625 m
.03333 1 L
s
P
p
.001 w
.06667 .99625 m
.06667 1 L
s
P
p
.001 w
.1 .99625 m
.1 1 L
s
P
p
.001 w
.13333 .99625 m
.13333 1 L
s
P
p
.001 w
.2 .99625 m
.2 1 L
s
P
p
.001 w
.23333 .99625 m
.23333 1 L
s
P
p
.001 w
.26667 .99625 m
.26667 1 L
s
P
p
.001 w
.3 .99625 m
.3 1 L
s
P
p
.001 w
.36667 .99625 m
.36667 1 L
s
P
p
.001 w
.4 .99625 m
.4 1 L
s
P
p
.001 w
.43333 .99625 m
.43333 1 L
s
P
p
.001 w
.46667 .99625 m
.46667 1 L
s
P
p
.001 w
.53333 .99625 m
.53333 1 L
s
P
p
.001 w
.56667 .99625 m
.56667 1 L
s
P
p
.001 w
.6 .99625 m
.6 1 L
s
P
p
.001 w
.63333 .99625 m
.63333 1 L
s
P
p
.001 w
.7 .99625 m
.7 1 L
s
P
p
.001 w
.73333 .99625 m
.73333 1 L
s
P
p
.001 w
.76667 .99625 m
.76667 1 L
s
P
p
.001 w
.8 .99625 m
.8 1 L
s
P
p
.001 w
.86667 .99625 m
.86667 1 L
s
P
p
.001 w
.9 .99625 m
.9 1 L
s
P
p
.001 w
.93333 .99625 m
.93333 1 L
s
P
p
.001 w
.96667 .99625 m
.96667 1 L
s
P
p
.002 w
0 1 m
1 1 L
s
P
p
.002 w
.99375 0 m
1 0 L
s
P
p
.002 w
.99375 .16667 m
1 .16667 L
s
P
p
.002 w
.99375 .33333 m
1 .33333 L
s
P
p
.002 w
.99375 .5 m
1 .5 L
s
P
p
.002 w
.99375 .66667 m
1 .66667 L
s
P
p
.002 w
.99375 .83333 m
1 .83333 L
s
P
p
.001 w
.99625 .03333 m
1 .03333 L
s
P
p
.001 w
.99625 .06667 m
1 .06667 L
s
P
p
.001 w
.99625 .1 m
1 .1 L
s
P
p
.001 w
.99625 .13333 m
1 .13333 L
s
P
p
.001 w
.99625 .2 m
1 .2 L
s
P
p
.001 w
.99625 .23333 m
1 .23333 L
s
P
p
.001 w
.99625 .26667 m
1 .26667 L
s
P
p
.001 w
.99625 .3 m
1 .3 L
s
P
p
.001 w
.99625 .36667 m
1 .36667 L
s
P
p
.001 w
.99625 .4 m
1 .4 L
s
P
p
.001 w
.99625 .43333 m
1 .43333 L
s
P
p
.001 w
.99625 .46667 m
1 .46667 L
s
P
p
.001 w
.99625 .53333 m
1 .53333 L
s
P
p
.001 w
.99625 .56667 m
1 .56667 L
s
P
p
.001 w
.99625 .6 m
1 .6 L
s
P
p
.001 w
.99625 .63333 m
1 .63333 L
s
P
p
.001 w
.99625 .7 m
1 .7 L
s
P
p
.001 w
.99625 .73333 m
1 .73333 L
s
P
p
.001 w
.99625 .76667 m
1 .76667 L
s
P
p
.001 w
.99625 .8 m
1 .8 L
s
P
p
.001 w
.99625 .86667 m
1 .86667 L
s
P
p
.001 w
.99625 .9 m
1 .9 L
s
P
p
.001 w
.99625 .93333 m
1 .93333 L
s
P
p
.001 w
.99625 .96667 m
1 .96667 L
s
P
p
.002 w
1 0 m
1 1 L
s
P
P
p
p
.002 w
0 .5 m
1 .5 L
s
P
p
.002 w
.5 0 m
.5 1 L
s
P
P
0 0 m
1 0 L
1 1 L
0 1 L
closepath
clip
newpath
p
p
p
.004 w
s
s
.0288 1 m
.07453 .95695 L
s
.07453 .95695 m
.14512 .89207 L
.20583 .83811 L
.25834 .79356 L
.30413 .75718 L
.34447 .72796 L
.38047 .7051 L
.41315 .68794 L
.44341 .67601 L
.4579 .6719 L
.46503 .6703 L
.47209 .66899 L
.47911 .66797 L
.48261 .66757 L
.4861 .66725 L
.48958 .66699 L
.49132 .66689 L
.49305 .66681 L
.49479 .66675 L
.49566 .66672 L
.49653 .6667 L
.4974 .66669 L
.49826 .66668 L
.49913 .66667 L
.5 .66667 L
.50087 .66667 L
.50174 .66668 L
.5026 .66669 L
.50347 .6667 L
.50434 .66672 L
.50521 .66675 L
.50695 .66681 L
.50868 .66689 L
.51042 .66699 L
.5139 .66725 L
.51739 .66757 L
.52089 .66797 L
.52791 .66899 L
.5421 .6719 L
.55659 .67601 L
.58685 .68794 L
.61953 .7051 L
.65553 .72796 L
.69587 .75718 L
.74166 .79356 L
.79417 .83811 L
.85488 .89207 L
.92547 .95695 L
s
.9712 1 m
.92547 .95695 L
s
s
s
P
P
p
p
.004 w
s
s
.0288 0 m
.07453 .04305 L
s
.07453 .04305 m
.14512 .10793 L
.20583 .16189 L
.25834 .20644 L
.30413 .24282 L
.34447 .27204 L
.38047 .2949 L
.41315 .31206 L
.44341 .32399 L
.4579 .3281 L
.46503 .3297 L
.47209 .33101 L
.47911 .33203 L
.48261 .33243 L
.4861 .33275 L
.48958 .33301 L
.49132 .33311 L
.49305 .33319 L
.49479 .33325 L
.49566 .33328 L
.49653 .3333 L
.4974 .33331 L
.49826 .33332 L
.49913 .33333 L
.5 .33333 L
.50087 .33333 L
.50174 .33332 L
.5026 .33331 L
.50347 .3333 L
.50434 .33328 L
.50521 .33325 L
.50695 .33319 L
.50868 .33311 L
.51042 .33301 L
.5139 .33275 L
.51739 .33243 L
.52089 .33203 L
.52791 .33101 L
.5421 .3281 L
.55659 .32399 L
.58685 .31206 L
.61953 .2949 L
.65553 .27204 L
.69587 .24282 L
.74166 .20644 L
.79417 .16189 L
.85488 .10793 L
.92547 .04305 L
s
.9712 0 m
.92547 .04305 L
s
s
s
P
P
P
% End of Graphics
MathPictureEnd
end
\end{filecontents*}

\documentclass[12pt]{article}

\usepackage{amsmath,graphicx}

\begin{document}

\title{Mathematics 2A, Section D, Fall 1996}
\author{Marcel Oliver}
\date{Midterm Exam II}

\maketitle

\begin{enumerate}

\item The graph of the equation
\[ x^2 - y^2 = 1 \]
is the pair of hyperbolae shown in the following figure.
\begin{center}
  \includegraphics[width=50mm]{hyperbola1.eps}
\end{center}
\begin{enumerate}
\item Find by implicit differentiation the points on the graph where the
tangent line is vertical.
\item Label these points in the above figure and sketch the corresponding
tangent lines.
\end{enumerate}
\hfill(15+5)

\item Compute the following limits.
\begin{enumerate}
\item $\displaystyle \lim_{x \to -\infty} \frac{1 + a \, x^2}{x^2}$
\item $\displaystyle \lim_{\theta \to \infty} \frac{\sin \theta}{\theta}$
\end{enumerate}
\hfill(10+10)

\item Let $k(x) = \sqrt{3 \,x + 1}$.
\begin{enumerate}
\item Show that $k'(1) = \tfrac34$.
\item Use the result from part (a) to estimate $k(\tfrac{11}{10})$.
\end{enumerate}
\hfill(10+10)

\item Let $h(t) = t^2 + \tfrac14 (t + \sin t \, \cos t)$.
\begin{enumerate}
\item Show that $h''(t) = 2 - \sin t \, \cos t$.
\item Use the result from part (a) to show that $h$ does not have a point of
inflection. 
\end{enumerate}
\hfill(10+10)

\item A rectangular box with square base and no top is to have a fixed
volume $V$.  What dimensions of such box minimize the surface area?  Use
the first derivative test to verify that you have found the minimum.
\hfill(30)

\item Consider the function
\[ f(x) = 4 \, x^3 + 3 \, x^4 . \]
Sketch the graph of $f$ \emph{into the coordinate system provided on the
next page}.  Your drawing must show clearly where the graph is increasing,
where decreasing, where concave upward, and where concave downward.
Locate, identify, and label all extrema and inflection points.  Pay special
attention to the behavior of the function when $|x|$ is large.  Find and
label all intercepts.  \hfill(30)

\end{enumerate}

\begin{center}
\makebox[0cm][c]{
\includegraphics[width=6in]{graph.eps}}
\end{center}

\end{document}
