{VERSION 5 0 "Windows XP" "5.0" }
{USTYLETAB {PSTYLE "Maple Output12" -1 200 1 {CSTYLE "" -1 -1 "Times" 
1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "Normal256" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2
 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 4" -1
 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0
 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -1 202 1 {CSTYLE "" 
-1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 
2 2 -1 1 }{PSTYLE "Ordered List 1" -1 203 1 {CSTYLE "" -1 -1 "Times" 1
 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE
 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 
2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 
15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 
0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Output" -1 12 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0
 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "Courier" 1
 9 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2
 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 
1 {CSTYLE "" -1 -1 "Courier" 1 10 64 128 64 1 2 2 2 2 2 1 1 0 0 1 }1 1
 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1
 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 
1 }{PSTYLE "Ordered List 3" -1 204 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0
 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Mapl
e Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 
0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" 
-1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 
2 -1 1 }{PSTYLE "Annotation Title" -1 205 1 {CSTYLE "" -1 -1 "Times" 1
 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }
{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 
2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 
5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 4" -1 206 1 {CSTYLE "" -1
 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 
2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0
 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Lis
t Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 
0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 
1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0
 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "" -1 
-1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 
255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Erro
r" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 0 
0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE 
"" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0
 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0
 1 2 1 1 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Order
ed List 2" -1 207 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 
1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 }{CSTYLE "Help Variable" -1 25 
"Courier" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Bold" -1 39 
"Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 
"Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Nonterminal" 
-1 24 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Default" -1
 38 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" 
-1 21 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Sma
ll" -1 7 "Times" 1 1 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Inert Ou
tput" -1 200 "Times" 1 12 144 144 144 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "
Popup" -1 31 "Times" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Co
pyright" -1 34 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D I
nput" -1 19 "Times" 1 12 255 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Maple
 Input Placeholder" -1 201 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 
0 1 }{CSTYLE "Annotation Text" -1 202 "Times" 1 12 0 0 0 1 2 2 2 2 2 2
 0 0 0 1 }{CSTYLE "Help Underlined Bold" -1 41 "Times" 1 12 0 0 0 1 1 
1 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Text" -1 28 "Times" 1 8 0 0 0 1 2 2 2
 2 2 2 0 0 0 1 }{CSTYLE "Help Italic" -1 42 "Times" 1 12 0 0 0 1 1 2 2
 2 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "Times" 1 14 0 0 0 1 2 1 
2 2 2 2 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 0 0 1 2 2 
2 2 2 2 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 12 147
 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Emphasized" -1 22 "Times" 1
 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Tim
es" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 
12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times
" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Italic" 
-1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold"
 -1 5 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Itali
c" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 
203 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic \+
Small" -1 204 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple \+
Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "Hel
p Fixed" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Pl
ot Title" -1 27 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D \+
Math Bold Small" -1 10 "Times" 1 1 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }
{CSTYLE "Help Notes" -1 37 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "Hyperlink" -1 17 "Times" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1
 }{CSTYLE "2D Math Symbol 2" -1 16 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 
0 0 1 }{CSTYLE "Equation Label" -1 205 "Courier" 1 12 0 0 0 1 2 1 2 2 
2 2 0 0 0 1 }{CSTYLE "Output Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2
 2 2 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 
2 2 0 0 0 1 }{CSTYLE "Help Maple Name" -1 35 "Times" 1 12 104 64 92 1 
2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2
 1 2 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2
 2 2 2 0 0 0 1 }{PSTYLE "" -1 208 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 
0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 
206 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 209 1 
{CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0
 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 207 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 
0 0 0 1 }{CSTYLE "" -1 208 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 209 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 210 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 211 "T
imes" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 212 "Times" 1 12
 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 213 "Times" 1 12 0 0 0 1 1
 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 214 "Times" 1 12 0 0 0 1 1 2 2 2 2 2
 0 0 0 1 }{CSTYLE "" -1 215 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 216 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 217 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 218 "T
imes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 219 "Times" 1 12
 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 220 "Times" 1 14 0 0 0 1 2
 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 221 "Times" 1 0 0 0 0 1 2 2 2 2 2 2 
0 0 0 1 }{CSTYLE "" -1 222 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 223 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 224 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 225 "T
imes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 226 "Times" 1 12
 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 227 "Times" 1 12 0 0 0 1 1
 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 228 "Times" 1 12 0 0 0 1 1 2 2 2 2 2
 0 0 0 1 }{CSTYLE "" -1 229 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }
{PSTYLE "" -1 210 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 
1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 230 "Times" 1 12 
0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 231 "Times" 1 12 0 0 0 1 2 
1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 232 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 
0 0 0 1 }{CSTYLE "" -1 233 "Times" 1 20 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 234 "Times" 1 20 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 235 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 236 "T
imes" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 237 "Times" 1 12
 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 238 "Times" 1 12 0 0 0 1 2
 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 239 "Times" 1 12 0 0 0 1 1 2 2 2 2 2
 0 0 0 1 }{CSTYLE "" -1 240 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 241 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 242 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 243 "T
imes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 244 "Times" 1 12
 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 245 "Times" 1 12 0 0 0 1 1
 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 246 "Times" 1 12 0 0 0 1 1 2 2 2 2 2
 0 0 0 1 }{CSTYLE "" -1 247 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 248 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 249 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 250 "T
imes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 251 "Times" 1 12
 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 252 "Times" 1 12 0 0 0 1 2
 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 253 "Times" 1 12 0 0 0 1 2 1 2 2 2 2
 0 0 0 1 }{CSTYLE "" -1 254 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "" -1 255 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 256 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 257 "T
imes" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 258 "Times" 1 12
 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 259 "Times" 1 12 0 0 0 1 2
 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 260 "Times" 1 12 0 0 0 1 2 1 2 2 2 2
 0 0 0 1 }{PSTYLE "" -1 211 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 
1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 261 "Ti
mes" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 262 "Times" 1 12 
0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "" -1 263 "Times" 1 12 0 0 0 1 1 
2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 264 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 
0 0 0 1 }{CSTYLE "" -1 265 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }
{CSTYLE "" -1 266 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 267 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "" -1 268 "T
imes" 1 20 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 269 "Times" 1 20
 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 270 "Times" 1 12 0 0 0 1 1
 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 271 "Times" 1 12 0 0 0 1 2 2 1 2 2 2
 0 0 0 1 }{CSTYLE "" -1 272 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }
{CSTYLE "" -1 273 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE ""
 -1 274 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 208 "" 0 ""
 {TEXT 203 0 "" }{TEXT 206 0 "" }{TEXT 203 8 "MATH 151" }}{PARA 209 ""
 0 "" {TEXT 275 0 "" }{TEXT 203 29 "LABORATORY ASSIGNMENT Bonus 1" }}
{PARA 201 "" 0 "" {TEXT 207 2 "  " }{TEXT 275 0 "" }{TEXT 208 24 "IMPL
ICIT DIFFERENTIATION" }}{PARA 201 "" 0 "" {TEXT 275 0 "" }}{PARA 0 "" 
0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 2 "  " }}{PARA 0 "" 0 
"" {TEXT 276 16 "  The function  " }{TEXT 209 1 "f" }{TEXT 276 3 " ( "
 }{TEXT 210 1 "x" }{TEXT 211 3 " ) " }{TEXT 276 13 "is said to be" }
{TEXT 212 19 " implicitly defined" }{TEXT 276 96 "  by the equation   \+
                                                                      \+
      " }}{PARA 0 "" 0 "" {TEXT 276 196 "                             \+
                                                                      \+
                                                                      \+
                           " }{MPLTEXT 1 0 0 "" }{TEXT 276 70 "       \+
                                                    (*)     E( " }
{TEXT 213 1 "x" }{TEXT 276 3 " , " }{TEXT 214 1 "y" }{TEXT 276 7 " ) =
  0" }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 20 "
provided that    E( " }{TEXT 215 1 "x" }{TEXT 276 3 " , " }{TEXT 216 
3 " f " }{TEXT 276 2 "( " }{TEXT 217 1 "x" }{TEXT 276 22 " ) )  =  0  \+
 for all  " }{TEXT 218 2 "x " }{TEXT 276 17 "in some interval " }{TEXT
 219 2 "I " }{TEXT 276 1 "." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 
0 "" 0 "" {TEXT 276 32 "  For example, if  E( x , y ) = " }{XPPEDIT 18
 0 "x^2+y^2-4;" "6#,(*$)%\"xG\"\"#\"\"\"F(*$)%\"yGF'F(F(\"\"%!\"\"" }
{TEXT 276 9 ", then   " }{XPPEDIT 18 0 "f[1](x) = sqrt(4-x^2);" "6#/-&
%\"fG6#\"\"\"6#%\"xG-%%sqrtG6#,&\"\"%F(*$)F*\"\"#F(!\"\"" }{TEXT 276 
6 " and  " }{XPPEDIT 18 0 "f[2](x) = -sqrt(4-x^2);" "6#/-&%\"fG6#\"\"#
6#%\"xG,$-%%sqrtG6#,&\"\"%\"\"\"*$)F*F(F1!\"\"F4" }{TEXT 276 98 " both
 satisfy the equation  E( x , y ) = 0, and thus both are implicitly de
fined by this equation." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 ""
 0 "" {TEXT 276 183 "  It is, however, frequently difficult or impossi
ble to solve an equation of the form E(x,y) = 0 for y in terms of  x; \+
this is the case in the example and exercises below. (Try it!)  " }
{TEXT 220 0 "" }{TEXT 276 0 "" }{TEXT 221 0 "" }{TEXT 276 81 "Neverthe
less, such an equation may implicitly define one or more functions of \+
x. " }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 183 
"  It is possible to find the derivative of an implicitly defined func
tion at a given point  without first solving the equation (*) for  y i
n terms of  x  by using a technique called  " }{TEXT 222 24 "implicit \+
differentiation" }{TEXT 223 1 "." }{TEXT 276 65 " We differentiate bot
h sides of the equation (*) with respect to " }{TEXT 224 2 " x" }{TEXT
 276 9 ", viewing" }{TEXT 225 4 "  y " }{TEXT 276 19 " as a function o
f  " }{TEXT 226 1 "x" }{TEXT 276 72 ", applying the usual differentiat
ion rules  and ultimately solving for  " }{TEXT 227 3 "dy " }{TEXT 
276 1 "/" }{TEXT 228 3 " dx" }{TEXT 276 78 " in terms of x and y . Thi
s procedure can be carried out by using appropriate " }{TEXT 229 5 "Ma
ple" }{TEXT 276 10 " commands." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}
{PARA 210 "" 0 "" {TEXT 203 9 "  Example" }}{PARA 0 "" 0 "" {TEXT 276 
0 "" }}{PARA 0 "" 0 "" {TEXT 276 17 "  Find the slope," }{TEXT 230 2 "
 m" }{TEXT 276 42 ", of the tangent line to the graph of the " }{TEXT 
231 8 "cardioid" }{TEXT 276 17 " with equation:  " }}{PARA 0 "" 0 "" 
{TEXT 276 70 "                                                        \+
              " }}{PARA 0 "" 0 "" {TEXT 276 9 "         " }{XPPEDIT 18
 0 "x^4+y^4-4*(y^3+x^2+x^2*y)+2*x^2*y^2 = 0;" "6#/,**$)%\"xG\"\"%\"\"
\"F)*$)%\"yGF(F)F)*&F(F),(*$)F,\"\"$F)F)*$)F'\"\"#F)F)*&F3F)F,F)F)F)!
\"\"*(F4F)F2F))F,F4F)F)\"\"!" }{TEXT 276 19 "     at the point  " }
{TEXT 232 1 "P" }{TEXT 276 5 "  =  " }{TEXT 233 2 "( " }{XPPEDIT 18 0 
"(2+sqrt(3))/2;" "6#*&,&\"\"#\"\"\"-%%sqrtG6#\"\"$F&F&F%!\"\"" }{TEXT 
276 5 "  ,  " }{XPPEDIT 18 0 "(2*sqrt(3)+3)/2;" "6#*&,&*&\"\"#\"\"\"-%
%sqrtG6#\"\"$F'F'F+F'F'F&!\"\"" }{TEXT 276 2 "  " }{TEXT 234 1 ")" }
{TEXT 276 1 "." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" 
{TEXT 276 48 "  First,  we enter the equation of the cardioid:" }}
{PARA 0 "" 0 "" {TEXT 276 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eq:=x^4+y^
4-4*(y^3+x^2+x^2*y)+2*x^2*y^2=0;" }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}
{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "/,.*$I
\"xG6\"\"\"%\"\"\"*$I\"yGF&F'F(*$F*\"\"$!\"%*$F%\"\"#F-*&F%F/F*F(F-*&F
%F/F*F/F/\"\"!" }}}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" 
{TEXT 276 77 "   Next, we sketch a graph of the cardioid in the coordi
nate plane using the " }{TEXT 235 6 "Maple " }{TEXT 276 8 "command " }
}{PARA 0 "" 0 "" {TEXT 276 1 " " }{TEXT 236 12 "implicitplot" }{TEXT 
237 1 " " }{TEXT 276 25 "which is located in the  " }{TEXT 238 7 "plot
s p" }{TEXT 276 21 "ackage. This part of " }{TEXT 239 5 "Maple" }{TEXT
 276 47 " can be accessed by first entering the command " }{TEXT 240 
17 "with(plots): .  (" }{TEXT 276 107 "Note that we ended the command \+
with a colon rather than a semicolon---if you terminate it with a semi
colon " }{TEXT 241 5 "Maple" }{TEXT 276 54 " responds with the content
s of the package. (Try it))." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}
{PARA 0 "" 0 "" {TEXT 276 50 "arning, the name changecoords has been r
edefined\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "implicitplot(eq,x=-4..4,y
=-1..4,grid=[100,100],color=black);" }}{PARA 13 "" 1 "" {GLPLOT2D 244 
244 244 {PLOTDATA 2 "6%-%+AXESLABELSG6$Q\"x6\"Q\"yF'-%'CURVESG6f]m7$7$
$!33WXXXXXXD!#<$\"3Nz+'\\bPO,\"F07$$!3Y<*f,1Voa#F0$\"36???????5F07$F37
$$!3-)*pj'QJqa#F0$\"3w`5%fa(=@5F07$7$$!3yIw*[#4ecDF0$\"3sqqqqqqq5F0F97
$F?7$$!3=LE6D]!zb#F0$\"3MwL\\?')[y5F07$7$$!3[=H(HrM`c#F0$\"3L@@@@@@@6F
0FE7$7$$!3#*=H(HrM`c#F0FN7$$!3MBGEJ\\PnDF0$\"3(eHUBO7\\8\"F07$7$$!3a\"
e@.PoId#F0$\"3;srrrrrr6F0FT7$7$$!33\"e@.PoId#F0$\"3#><<<<<<<\"F07$$!3+
2[tTpXvDF0$\"3IOBRp'o/>\"F07$7$$!35/wRI1vzDF0$\"3aAAAAAAA7F0F_o7$Feo7$
$!3O2$p#\\I<#e#F0$\"3w\\k5(Gr^C\"F07$7$$!31;?(RMb`e#F0$\"3;tssssss7F0F
[p7$Fap7$$!3sq#o3A^ve#F0$\"3i_3'[pP!*H\"F07$7$$!3Cccj'ph)*e#F0$\"3wBBB
BBBB8F0Fgp7$F]q7$$!3#4U\"3n]i\"f#F0$\"3c@\"\\#**))3_8F07$7$$!357V+7VD$
f#F0$\"3Outttttt8F0Fcq7$Fiq7$$!3Sx6p#QLWf#F0$\"3.q-,Z\"\\VS\"F07$7$$!3
AG#QHCBbf#F0$\"3)\\UUUUUUU\"F0F_r7$Fer7$$!3/+(GFe>gf#F0$\"3Ws(QDdXeX\"
F07$7$$!3i%3Xq&Qm'f#F0$\"3evuuuuuu9F0F[s7$Fas7$$!3'*=&)*)f5V'f#F0$\"3+
g\\F'z2m]\"F07$7$$!3%[xJhiwmf#F0$\"3>EDDDDDD:F0Fgs7$7$$!3Iv<8Emn'f#F0$
\"3UEDDDDDD:F07$$!3wNS8!\\=df#F0$\"3m3sn!\\nmb\"F07$7$$!3_@t&>$oc&f#F0
$\"3!oddddddd\"F0Fht7$F^u7$$!3=(\\sA6NRf#F0$\"3#yz=+$z01;F07$7$$!3#*
\\9`-UM$f#F0$\"3TFEEEEEE;F0Fdu7$Fju7$$!3=8[$f+O6f#F0$\"3g&zi!RN\"[l\"F
07$7$$!3YK\"yU\\A+f#F0$\"3-ywwwwww;F0F`v7$7$Fgv$\"3yxwwwwww;F07$$!3)p^
))))Qxte#F0$\"3I6R\"RXpHq\"F07$7$$!3q'=vc.>ce#F0$\"3SGFFFFFF<F0F_w7$7$
Ffw$\"3jGFFFFFF<F07$$!3'zG_<&fr#e#F0$\"3m=)3i5h0v\"F07$7$$!3I45dZU:!e#
F0$\"3Yzxxxxxx<F0F^x7$7$Fex$\"3Czxxxxxx<F07$$!393`:W#3sd#F0$\"3mcdYRQi
(z\"F07$7$$!3[%[#Qa6ltDF0$\"3iHGGGGGG=F0F]y7$Fcy7$$!3%ffbE754d#F0$\"3I
([LSc#>W=F07$7$$!3)4nG*)*[8mDF0$\"3W!)yyyyyy=F0Fiy7$F_z7$$!3gSp1ni(Qc#
F0$\"3EGcza9I!*=F07$7$$!3)y*R*=FKwb#F0$\"31JHHHHHH>F0Fez7$F[[l7$$!3[?=
^o(fhb#F0$\"3\"*GPq$p$)f$>F07$7$$!3i&oy\\Er\"[DF0$\"3W\")zzzzzz>F0Fa[l
7$7$Fh[l$\"3o\")zzzzzz>F07$$!3On<i*y6ya#F0$\"3A'\\-uDr7)>F07$7$F.$\"3S
ybepLz#*>F0F`\\l7$7$$!3?jkkkkkkCF0$\"3OnG_N8dht!#=7$$!3%ySD;5e_Z#F0$\"
37vwwwwwwwF_]l7$F`]l7$$!3Wjg)>=&)zZ#F0$\"3gw,9gY8gxF_]l7$7$$!39x'*y1+W
\"\\#F0$\"3A\"=======)F_]lFf]l7$F\\^l7$$!37fXk.9\"y\\#F0$\"3#zFc00*4*Q
)F_]l7$7$$!39IGFd%zn]#F0$\"31&ooooooo)F_]lFb^l7$Fh^l7$$!3=zhSy#)*f^#F0
$\"3&*4p'G_<y+*F_]l7$7$$!3_.G$R\\27_#F0$\"3/!>>>>>>>*F_]lF^_l7$7$Fe_l$
\"3%*)=>>>>>>*F_]l7$$!3$)zf$*[/_KDF0$\"3bp'GPfJhh*F_]l7$7$$!3e(R;\")zd
Y`#F0$\"3-&ppppppp*F_]lF]`l7$Fc`l7$F.$\"3dz+'\\bPO,\"F07$Ff\\l7$$!3hvZ
%*4)=x`#F0$\"3$pU4c>oa-#F07$7$$!3M\")3&)p>yODF0$\"30KIIIIII?F0F]al7$7$
$!3*3)3&)p>yODF0Ffal7$$!3on>3ldiEDF0$\"3SA_2$4S!p?F07$7$$!3SzR!H/mS_#F
0$\"3m#3333333#F0F\\bl7$7$$!3'*yR!H/mS_#F0Febl7$$!32'H$RZL,:DF0$\"3P`[
_#Q(G7@F07$7$$!3;0i],DU5DF0$\"3FLJJJJJJ@F0F[cl7$Facl7$$!3lFsn\"[MH]#F0
$\"3+ht&>9V_:#F07$7$$!3Us[8C&*)e\\#F0$\"3)Q=======#F0Fgcl7$F]dl7$$!3wK
[r2\"Q/\\#F0$\"37:ftez$z>#F07$7$$!3/z&zw2/0[#F0$\"3\\MKKKKKKAF0Fcdl7$F
idl7$$!33v%[GBpvZ#F0$\"39#\\\\C'**RSAF07$7$F[]l$\"33C5w*oD<G#F0F_el7$7
$$!3I#QQQQQQQ#F0$\"3#eOzukzeW&F_]l7$$!3Oa!=uhuKR#F0$\"3CbcccccccF_]l7$
F^fl7$$!3/]ty;q$pR#F0$\"3/.n\\7@VQdF_]l7$7$$!3%*GZ;uD?:CF0$\"35fhhhhhh
hF_]lFdfl7$7$F[gl$\"3AghhhhhhhF_]l7$$!3e%41/>-nU#F0$\"3YiVm_\\^HkF_]l7
$7$$!3ox0v3caOCF0$\"3=lmmmmmmmF_]lFcgl7$Figl7$$!3Y!*>3nnuaCF0$\"3[9#R>
1W)4rF_]l7$7$$!3UD&ykZ5sX#F0$\"3;qrrrrrrrF_]lF_hl7$7$$!3'e_ykZ5sX#F0Fh
hlFj\\l7$Feel7$$!3IuH4k6KkCF0$\"3?aB)*p\\i#G#F07$7$$!3'Q_Jt\")eUY#F0$
\"35&GGGGGGG#F0F_il7$Feil7$$!3QbN\"phZ&[CF0$\"3Po-]`:FBBF07$7$$!3wbvM/
m?XCF0$\"3qNLLLLLLBF0F[jl7$Fajl7$$!3$GCb9nlDV#F0$\"3UtQ4))yyjBF07$7$$!
3k1-<q)*RDCF0$\"3I'QQQQQQQ#F0Fgjl7$F][m7$$!3d&)p#\\A6kT#F0$\"3dj(=&4k>
/CF07$7$$!3Nh'G3?v[S#F0$\"3#pVVVVVVV#F0Fc[m7$Fi[m7$$!3?*=enz:,S#F0$\"3
G;$=u\"o^WCF07$7$$!3w#QQQQQQQ#F0$\"3w@w\"QfEW[#F0F_\\m7$7$$!3V,......B
F0$\"3\"*y.-hOMJRF_]l7$$!3c*\\[7$G_9BF0$\"3xRTTTTTTTF_]l7$F`]m7$$!3TbW
pkVg?BF0$\"31,^\"o-_7D%F_]l7$7$$!3\\j!*foUkTBF0$\"3=WYYYYYYYF_]lFf]m7$
7$F]^m$\"3uWYYYYYYYF_]l7$$!3qS![Jrx6O#F0$\"3490qff))4]F_]l7$7$$!3UH^%=
#f]oBF0$\"3E]^^^^^^^F_]lFe^m7$F[_mFiel7$7$FjelFh\\m7$$!3e&ejty%o$Q#F0$
\"3oR<0([_Z[#F07$7$$!3!y*[o#yXOQ#F0$\"3a([[[[[[[#F0Fc_m7$Fi_m7$$!3wzaW
;eZkBF0$\"3QuHtI>DBDF07$7$$!3/YU6pQBfBF0$\"38QNNNNNNDF0F_`m7$Fe`m7$$!3
gDp-H?JXBF0$\"3'zU,Thz<c#F07$7$$!3_Y$pLgQUL#F0$\"3u)eeeeeee#F0F[am7$Fa
am7$$!343,N!>4iK#F0$\"38oMV!RX.g#F07$7$$!31[rLoxo3BF0$\"3NROOOOOOEF0Fg
am7$F]bm7$$!3ImCn`(zrI#F0$\"3,#*\\,Vq&*QEF07$7$F\\]m$\"3#zvU(>s/ZEF0Fc
bm7$7$$!3a?AAAAAAAF0$\"3!Q*p'\\Ujem#F_]l7$$!3O8JJx*3>D#F0$\"3$)HJJJJJJ
JF_]l7$Fbcm7$$!3#z#HNt'HAF#F0$\"3y\\+)3qfQW$F_]l7$7$$!3yH]Or=E%G#F0$\"
3![jjjjjjj$F_]lFhcm7$7$F_dm$\"3CMOOOOOOOF_]lF[]m7$Fibm7$$!3c\"*yq1S%eG
#F0$\"37%=n;DFhn#F07$7$$!3!oH=?8\"H!G#F0$\"3'**ooooooo#F0Fhdm7$7$$!3O'
H=?8\"H!G#F0Faem7$$!3gMc\"pKySE#F0$\"3_t?I_(GIr#F07$7$$!3k!f<=\")33D#F
0$\"3dSPPPPPPFF0Fgem7$F]fm7$$!3&\\6p0QmDC#F0$\"3e\\0MO))3]FF07$7$F^cm$
\"3=/>Shcf&y#F0Fcfm7$7$$!3mRTTTTTT@F0$\"3%z#Rc`Kf\"e\"F_]l7$$!3v$*3d#R
%*R9#F0$\"3j9;;;;;;;F_]l7$Fbgm7$$!3k$>Sv]ej9#F0$\"3+_%\\W!R1Z;F_]l7$7$
$!3IHo5@vE\"=#F0$\"3))>@@@@@@@F_]lFhgm7$7$$!3')Go5@vE\"=#F0$\"3h>@@@@@
@@F_]l7$$!3)3#>vz%Go@#F0$\"3Q^K#et^Df#F_]l7$7$$!3C&e**)>mF>AF0$\"3&[ii
iiiii#F_]lFihm7$F_imF]cm7$Fifm7$$!3OV7!GKa6A#F0$\"3;!oS2N6sy#F07$7$$!3
^&)4Lhtw?AF0$\"3=\"zyyyyyy#F0Ffim7$F\\jm7$$!3Az@8R@$o>#F0$\"3TmDXO]^AG
F07$7$$!3/D&oD3hr=#F0$\"3yTQQQQQQGF0Fbjm7$Fhjm7$$!3E'\\H^v_H<#F0$\"3sR
f&>Z&4eGF07$7$$!3cyFUz1G`@F0$\"3Q#*))))))))))))GF0F^[n7$Fd[n7$$!3IK3R'
e#\\\\@F0$\"3cD$**p\"z$R*GF07$7$F^gm$\"3Ct#[0iJg!HF0Fj[n7$7$$!3yeggggg
g?F0$\"3!G[.)=Ckaj!#>7$$!3vp!34bm15#F0$\"3m46666666F_]l7$Fj\\nF]gm7$7$
F^gm$\"3pt#[0iJg!HF07$$!3DWn=*>!4C@F0$\"3.@=]vkcGHF07$7$$!3FAHL2Vs;@F0
$\"3+VRRRRRRHF0Fd]n7$Fj]n7$$!3Ym?#[9@!)4#F0$\"3#y%*GqOyF'HF07$7$$!33zz
.OCty?F0$\"3i$**)*)*)*)*)*)HF0F`^n7$Ff^n7$$!3o-fQ]'QD2#F0$\"35'R6&eoN(
*HF07$7$Fe\\n$\"3BW2MTAW8IF0F\\_n7$7$$!3!z(zzzzzz>F0$!3A^E3*yB*e>Fi\\n
7$$!3RAeW=q:3?F0$\"3z&*4555555Fi\\n7$F[`n7$$!3)*GMRRBX`?F0$\"3h'p;[[)
\\8cFi\\n7$7$$!3aV/(=6:x0#F0$\"3AYgggggggFi\\nFa`n7$Fg`nFd\\n7$Fb_n7$$
!33`nA7#)fX?F0$\"3Wyp;NT-JIF07$7$$!3-j!Rq_%[Q?F0$\"3AWSSSSSSIF0F^an7$F
dan7$$!3_'y3Bzpv,#F0$\"3y*HBKU6S1$F07$7$$!3eR\"pQy(H'*>F0$\"3#[4444444
$F0Fjan7$F`bn7$$!3eC7mlGG!*>F0$\"3!RitX9iu4$F07$7$Fg_n$\"3,Pq_7I?5JF0F
fbn7$7$$!3+(*)*)*)*)*)*)*=F0$!3#4#)[!G..v$*Fi\\n7$$!3%pK-8MT?!>F0$!3/0
\"444444*Fi\\n7$Fecn7$$!3E^xp(f#))3>F0$!3-<#o;U:EZ)Fi\\n7$7$$!3)f(Q!p(
ykc>F0$!3jaSSSSSSSFi\\nF[dn7$FadnFf_n7$7$Fg_n$\"3dOq_7I?5JF07$$!3K)ouU
$*Q7'>F0$\"3J*3izt9)HJF07$7$$!3g/&*yPDW^>F0$\"3VXTTTTTTJF0F[en7$Faen7$
$!3.[[2]!>:$>F0$\"3#)RA%3'[uhJF07$7$$!3w54[v$4]!>F0$\"3-'>>>>>>>$F0Fge
n7$F]fn7$$!3$)eER<bn->F0$\"3GA4U.FA%>$F07$7$Facn$\"3!y:[!>ME)>$F0Fcfn7
$7$$!37;=======F0$!3QhO)G.IAf\"F_]l7$$!3Q\"G'QhmnR=F0$!3[:9999999F_]l7
$7$$!3h\"G'QhmnR=F0Fegn7$Facn$!3KA)[!G..v$*Fi\\n7$Fifn7$$!3o$eT*='G5(=
F0$\"3l]SRU%[\\A$F07$7$$!3MFJBflga=F0$\"3lYUUUUUUKF0F_hn7$Fehn7$$!37
\\3o'H0*R=F0$\"3%>9'[;9+cKF07$7$F^gn$\"373U_#[w#yKF0F[in7$7$$!3CNPPPPP
P<F0$!3'f5sXJ(Hw@F_]l7$$!3!4;(4qoLs<F0$!3X?>>>>>>>F_]l7$7$$!37hr4qoLs<
F0F]jnF]gn7$Fain7$$!3<:Jcem^3=F0$\"3A4w;o&))oG$F07$7$$!3hYMh+BV-=F0$\"
3E(HHHHHHH$F0Fdjn7$Fjjn7$$!3')*fM2p+^x\"F0$\"3qP)z(Q'3lJ$F07$7$$!3%4G'
3'3npu\"F0$\"3'yMMMMMMM$F0F`[o7$Ff[o7$$!3Lv(=\"oX'Gu\"F0$\"3m(**\\E6mo
M$F07$7$Ffin$\"3]2\"QK-T>N$F0F\\\\o7$7$$!3Oacccccc;F0$!3?D/MaB$\\p#F_]
l7$$!3eG(Q%)*z8)p\"F0$!3UDCCCCCCCF_]l7$F[]oFein7$Fb\\o7$$!3$)e<))3;*zq
\"F0$\"398>jjbdvLF07$7$$!3aU%**3$yQ(o\"F0$\"3Y)RRRRRRR$F0Fb]o7$Fh]o7$$
!3OKl'3Q!ot;F0$\"3$pWFm4OYS$F07$7$Fg\\o$\"3Qn_(3Vu$>MF0F^^o7$7$$!3Ytvv
vvvv:F0$!31`rBbU=`JF_]l7$$!3>?v^Lfm9;F0$!3RIHHHHHHHF_]l7$F]_oFf\\o7$Fd
^o7$$!3H`*y947$Q;F0$\"3(4Eli'f.LMF07$7$$!3([.:(pM`C;F0$\"33\\WWWWWWMF0
Fd_o7$7$$!35N]rpM`C;F0F]`o7$$!3>ir]:m(>g\"F0$\"3#>%zGW8$3Y$F07$7$Fi^o$
\"3?_#fes<=[$F0Fc`o7$7$$!3e#\\\\\\\\\\\\\\\"F0$!3=9o>e(zib$F_]l7$$!3T?
9f'*\\&*=:F0$!3ONMMMMMMMF_]l7$Fbao7$Fi^o$!3i`rBbU=`JF_]l7$Fi`o7$$!3=H'
f8M2ec\"F0$\"3#[y]%)fI()[$F07$7$$!3)\\0k&o/qd:F0$\"3o*\\\\\\\\\\\\\\$F
0F\\bo7$7$Fcbo$\"3C*\\\\\\\\\\\\\\$F07$$!3f/O!4wDv_\"F0$\"36?3<h'4`^$F
07$7$F^ao$\"3#f=nX7#[RNF0F[co7$F]ao7$$!30;%yrXv&H9F0$!3IiETq6$H%QF_]l7
$7$$!3q69999999F0$!3I@*Qb'zq2RF_]lFeco7$Faco7$$!3[9J4P-C!\\\"F0$\"3@9V
Hf7^UNF07$7$$!3Ox`awn3'[\"F0$\"3I]XXXXXXNF0Fado7$Fgdo7$$!3K*\\L.Q;,X\"
F0$\"3G0YK**)Qzc$F07$7$F\\do$\"3C`*[MX9Ef$F0F]eo7$7$$!3\"3LLLLLLL\"F0$
!3E(zga%*4D?%F_]l7$$!3:!*H\"Q%*z_S\"F0$!3LSRRRRRRRF_]l7$F\\foF[do7$7$F
\\do$\"3!G&*[MX9Ef$F07$$!3$z-'\\\"z'R69F0$\"3!fB1o?WUf$F07$7$$!3o'zB4)
yw39F0$\"3!4gffffff$F0Fffo7$F\\go7$$!3?\"*)H&Gtbp8F0$\"3r^u&Hf*f=OF07$
7$Fheo$\"3z;^W\\U\\TOF0Fbgo7$7$$!3%*\\______7F0$!3OH1uBttcWF_]l7$$!3It
\\iP*pjD\"F0$!3JXWWWWWWWF_]l7$FahoFgeo7$Fhgo7$$!37csu*4!4H8F0$\"3%\\Nt
ai7Qk$F07$7$$!3,><!H[gYK\"F0$\"3_^YYYYYYOF0Fhho7$F^io7$$!3uN4-[1o&G\"F
0$\"3Cb%\\'on=nOF07$7$F]ho$\"3'4OuCWGko$F0Fdio7$7$F]ho$!3#*H1uBttcWF_]
l7$$!3c/*y%fz(*[7F0$!3m.T)f-:mY%F_]l7$7$$!3/prrrrrr6F0$!3]#R(y<k1aYF_]
lFajo7$Fjio7$$!3K^hbgC;V7F0$\"3!e,*)>&z6\"p$F07$7$$!3L>>cOzYK7F0$\"3c-
(pppppp$F0F][p7$Fc[p7$$!3kS%4a#HM)>\"F0$\"3Hst-$z5Or$F07$7$Fhjo$\"3g!e
hqAWxs$F0Fi[p7$Fgjo7$$!33<Od7vA@6F0$!3mX;49[+gZF_]l7$7$$!3;)3444444\"F
0$!3%=(HRbF<5[F_]lFc\\p7$7$Fhjo$\"3:!ehqAWxs$F07$$!3i]D3Ib[`6F0$\"3K;J
Xr*zgt$F07$7$$!3KDbQ&f)fI6F0$\"3u_ZZZZZZPF0Fb]p7$Fh]p7$$!3!RNw$H]U26F0
$\"3q$z;!4szdPF07$7$Fj\\p$\"3cKO0[3ylPF0F^^p7$Fi\\p7$$!3M*>())fg=:5F0$
!3g\\7L)Q8x\"\\F_]l7$7$$!3G25555555F0$!3:;'34fIA#\\F_]lFh^p7$Fd^p7$$!3
'o)G)Rbe*f5F0$\"35F4S7djyPF07$7$$!34+`7)3Vq,\"F0$\"3!H!)zzzzzz$F0Fd_p7
$Fj_p7$$!3V*3y_HIG,\"F0$\"3#)za@,co*z$F07$7$F__p$\"3lkzzZ5)3!QF0F``p7$
7$$!31l#HHHHHH*F_]l$!3CIYK'4qL)\\F_]l7$$!3!f#Ho&*ppS(*F_]l$!3G]
\\\\\\\\\\\\\\F_]l7$7$$!3,FHo&*ppS(*F_]lFbapF^_p7$Ff`p7$$!3#=9p')*)[]i
*F_]l$\"3=X&QLFP(=QF07$7$$!3%REHHHHHH*F_]l$\"3()e\\U!f7A$QF0Fiap7$7$F[
ap$!3oHYK'4qL)\\F_]l7$$!3[`FKv#>=B*F_]l$!3u>!*\\5()o()\\F_]l7$7$$!3Kd%
[[[[[[)F_]l$!3ma5\"RFAj*\\F_]lFhbp7$7$F[apFbbp7$$!3gX6C'R1_7*F_]l$\"3_
Y=Wn@+QQF07$7$$!3J+TX7()GW))F_]l$\"3%R&[[[[[[QF0Fecp7$7$$!3?*4aCr)GW))
F_]lF^dp7$$!3>:(3%z:n5')F_]l$\"3yp[*=z[j&QF07$7$F_cp$\"3#z<5JA84'QF0Fd
dp7$F^cp7$$!3rX^%HEJyS)F_]l$!3M>X=82j(*\\F_]l7$7$$!3g\\wwwwwwwF_]l$!3g
!*zNy]Li\\F_]lF^ep7$7$F_cp$\"3Oy,6BK\"4'QF07$$!3'>9Pd)pJw!)F_]l$\"3aZa
H!ocM(QF07$7$Feep$\"3EKqGs#om)QF0F]fp7$Fdep7$$!3O2;;P)>sl(F_]l$!3'ps[#
\\Brh\\F_]l7$7$$!3@BM\">1kv`(F_]lFbapFgfp7$F]gp7$$!3#e]4-7+X'pF_]l$!3W
&G$Hn;h*)[F_]l7$7$$!3'=%oooooooF_]l$!3/J9&4JG8([F_]lFagp7$Fcfp7$$!3uga
R]7?SvF_]l$\"3gU;M(\\a/*QF07$7$$!3]Vp*yPtSD(F_]l$\"3+0**)*)*)*)*)*QF0F
]hp7$Fchp7$$!3=Lb;#\\)3&)pF_]l$\"3]AtX+]E1RF07$7$Fhgp$\"3*zD*[+Fk4RF0F
ihp7$7$Fhgp$!3gJ9&4JG8([F_]l7$$!3N#\\3(>'>+K'F_]l$!3/9f0v9O(y%F_]l7$7$
$!37MgggggggF_]l$!3.h4]$>NRs%F_]lFfip7$F_ip7$$!3ONS1Dub3kF_]l$\"3))H&o
#fot?RF07$7$$!3CNgggggggF_]l$\"3S`\"*)4tF(HRF0Fbjp7$F\\jp7$$!3zavun&R&
=dF_]l$!3!\\*4[-gBeYF_]l7$7$$!3SE_______F_]l$!3]t,@n_2DXF_]lF^[q7$7$F]
jpF[[q7$$!3Bv;!G$\\JCeF_]l$\"3'G=2SvEZ$RF07$7$Fe[q$\"37TfK!ztw%RF0F[
\\q7$Fd[q7$$!3'oXP4b[p:&F_]l$!3F,o$H))zT]%F_]l7$7$$!3is!R!RVgk\\F_]lFd
hoFe\\q7$F[]q7$$!3dMpAa(GVi%F_]l$!3_s.$3v;?L%F_]l7$7$$!36=WWWWWWWF_]l$
!39)4=Q1:4D%F_]lF_]q7$Fa\\q7$$!3!='p-VL&*H_F_]l$\"3U88:0U3[RF07$7$$!3-
'\\(R<$\\t:&F_]l$\"3;b\\\\\\\\\\\\RF0F[^q7$7$$!3#\\\\(R<$\\t:&F_]lFd^q
7$$!3pKcQ&*G2-YF_]l$\"3E\"yywsY$fRF07$7$Ff]q$\"3/+l2'yFB'RF0Fj^q7$7$$!
3n=WWWWWWWF_]l$!3q)4=Q1:4D%F_]l7$$!3Ez5aP&3E7%F_]l$!3xE&37QT09%F_]l7$7
$$!3-h<`$eg?o$F_]lF_foFi_q7$F_`q7$$!3uFiN5XacOF_]l$!3Ga&[J*3yERF_]l7$7
$$!3#)4OOOOOOOF_]l$!3Ad[5\"[\\O\"RF_]lFc`q7$F`_q7$$!3/EPioU@dRF_]l$\"3
c77,9\"[&pRF07$7$Fj`q$\"3yI8nMzguRF0F_aq7$7$$!3E4OOOOOOOF_]lF\\aq7$$!3
^a-rnhv-KF_]l$!3d#y^A5[`q$F_]l7$7$$!3`,GGGGGGGF_]l$!39#=*GX<PtMF_]lF
\\bq7$Feaq7$$!3_S?n/X)\\H$F_]l$\"3M#GpU!QmyRF07$7$$!3(4!GGGGGGGF_]l$\"
3)fe7s``X)RF0Fhbq7$Fbbq7$$!3!f&fD#[<6z#F_]l$!3o8-hv<ddMF_]l7$7$$!3S`D_
]LmZFF_]lFeaoFdcq7$Fjcq7$$!3S7$H%3V3$Q#F_]l$!3Ph8?/?a2KF_]l7$7$$!3:-t(
[DE&H?F_]lF`_oF^dq7$7$$!3V-t([DE&H?F_]lF`_o7$$!3(o:)*)4$Rd-#F_]l$!3rFG
BB@$e#HF_]l7$7$$!3C$*>??????F_]l$!3#4OKKS&H>HF_]lF[eq7$7$Fcbq$\"3W'e7s
``X)RF07$$!3Dg)RmcJ?h#F_]l$\"3q@t9'H%[')RF07$7$Fbeq$\"3)Hf!)Gt&3#*RF0F
jeq7$Faeq7$$!3%)HV:yLrb;F_]l$!3=:A_Dy/_EF_]l7$7$$!3[U;+S^`09F_]lF^]oFd
fq7$Fjfq7$$!3qC3JoA7P8F_]l$!3'3!R7kn6YBF_]l7$7$$!34&=@@@@@@\"F_]l$!3))
yC#H!y:i@F_]lF^gq7$F`fq7$$!3oI#4[n-Y!>F_]l$\"3UdH\"4/vF*RF07$7$Fegq$\"
33&3kCuUr*RF0Fjgq7$Fdgq7$$!3^)o9iS2p-\"F_]l$!3i![$)ya]\\.#F_]l7$7$$!3m
\"f4^[]/'))Fi\\nF]jnFdhq7$7$$!31$f4^[]/'))Fi\\nF]jn7$$!3rQ%4a(=G4sFi
\\n$!32mS]aq8@<F_]l7$7$$!3#*3U<D#p6<&Fi\\nFegnFaiq7$Fgiq7$$!36wof0%Q,$
\\Fi\\n$!3/YoJ;I`e8F_]l7$7$$!3WpPSSSSSSFi\\n$!39W)*\\R='z1\"F_]lF[jq7$
F`hq7$$!3s;9so(*[o6F_]l$\"3#)>vyMIF(*RF07$7$Fbjq$\"3?L)RB2#o**RF0Fgjq7
$7$Fbjq$!3EW)*\\R='z1\"F_]l7$$!3=5/'Q:p%)\\\"Fi\\n$!3]q)*\\R='z1\"F_]l
7$7$$\"317VSSSSSSFi\\n$!3GJ**\\R='z1\"F_]lFd[r7$F][r7$$!3=7ix9c`*)RFi
\\nF^[r7$7$F[\\rF^[rF`\\r7$7$$\"3AR7777777F_]l$!3!p`AH!y:i@F_]l7$$\"3K
S&4^[]/'))Fi\\nF]jn7$F[]r7$$\"3Wu,ow!)zMiFi\\n$!3qc'39/\"H^:F_]l7$7$$
\"3?.W<D#p6<&Fi\\nFegnF_]r7$Fe]rFj[r7$Fd\\r7$$\"3;sy*GjJQ4%Fi\\n$\"3#3
#paxgm**RF07$7$Fg\\r$\"3i%3kCuUr*RF0Fj]r7$7$$\"3lZ???????F_]l$!3)3TKKS
&H>HF_]l7$$\"3U\\;+S^`09F_]lF^]o7$Fi^r7$$\"3OR7777777F_]lFi\\r7$7$F^_r
Fa^r7$$\"3-.N!3z&oi7F_]l$\"3#ROKQrRo*RF07$7$Fe^r$\"3a#f!)Gt&3#*RF0Fb_r
7$7$$\"3$f&GGGGGGGF_]l$!357#*GX<PtMF_]l7$$\"3GZD_]LmZFF_]lFeao7$Fa`r7$
$\"3*4Dfy<yE6#F_]l$!3W#oGy_!4()HF_]l7$7$$\"3?5t([DE&H?F_]lF`_oFe`r7$7$
$\"3[5t([DE&H?F_]lF`_oFd^r7$Fh_r7$$\"3#yGcjQ>\"o@F_]l$\"3Sl`hk^v!*RF07
$7$F]`rFacqFcar7$F\\`r7$$\"3Ebnu0d*>H$F_]l$!3Cs$eF)R;CPF_]l7$7$$\"3AkO
OOOOOOF_]l$!3k')[5\"[\\O\"RF_]lF[br7$7$F]`r$\"3a&e7s``X)RF07$$\"34UdqX
m9MJF_]l$\"3yu5T6N)3)RF07$7$Fbbr$\"3MI8nMzguRF0Fjbr7$7$$\"3'>ZWWWWWW%F
_]l$!3C>\"=Q1:4D%F_]l7$$\"3!QwJNeg?o$F_]lF_fo7$FicrFabr7$F`cr7$$\"3SwC
#p'*[4<%F_]l$\"3ez+%oT)emRF07$7$$\"3^sWWWWWWWF_]l$\"3;*\\wgyFB'RF0F^dr
7$7$$\"3!3GDDDDDD&F_]l$!3\\)=5sEv]_%F_]l7$$\"3]r!R!RVgk\\F_]lFdho7$7$$
\"31s!R!RVgk\\F_]lFdhoFdcr7$7$F[er$\"3CSfK!ztw%RF07$$\"3!Q\\(R<$\\t:&F
_]lFd^q7$Fjer7$FecrFgdr7$7$F[er$!3%z=5sEv]_%F_]l7$$\"3_0k<(\\[([aF_]l$
!3%yR^B(R3nXF_]l7$7$$\"3_)3111111'F_]l$!3ps4]$>NRs%F_]lFcfr7$7$F[er$\"
3!)RfK!ztw%RF07$$\"3'>qv&)oypH&F_]l$\"3//=u4mrYRF07$7$Fjfr$\"3^_\"*)4t
F(HRF0Fbgr7$Fifr7$$\"3EhEa*Hiin'F_]l$!3V-)zPfH#H[F_]l7$7$$\"3E'*oooooo
oF_]l$!3#)Q9&4JG8([F_]lF\\hr7$Fhgr7$$\"3]LCIR.1#e'F_]l$\"33Lk2dS!p\"RF
07$7$Fchr$\"3mc#*[+Fk4RF0Fhhr7$7$$\"350xwwwwwwF_]l$!3/&*zNy]Li\\F_]l7$
$\"3wGM\">1kv`(F_]lFbap7$FgirFbhr7$7$$\"3+/xwwwwwwF_]l$\"3QJqGs#om)QF0
7$$\"31\\p*yPtSD(F_]lFfhp7$7$Fbjr$\"3a/**)*)*)*)*)*QF07$$\"3;&*ooooooo
F_]lF_ir7$7$F]jrFeir7$$\"35VrCn:r'p(F_]l$!3u*fW5))f>'\\F_]l7$7$$\"3i5&
[[[[[[)F_]l$!3wb5\"RFAj*\\F_]lF][s7$7$F]jr$\"3%4.(Gs#om)QF07$$\"3QL(
\\a@4S2)F_]l$\"3exA#GIiT(QF07$7$Fd[s$\"39w,6BK\"4'QF0F\\\\s7$Fc[s7$$\"
3/-9AL(R9b)F_]l$!3e1!G(zW6\"*\\F_]l7$7$$\"3M=$HHHHHH*F_]l$!3!piCj4qL)
\\F_]lFf\\s7$7$$\"3Y>$HHHHHH*F_]l$\"3lc\\U!f7A$QF07$$\"3J+TX7()GW))F_]
lF^dp7$Fg]sFb\\s7$7$Fc]sF_]s7$$\"3R.`Y?B8P$*F_]l$!3mS\\qT=7x\\F_]l7$7$
$\"38=Ho&*ppS(*F_]lFbapF]^s7$Fc^s7$$\"3]$G\\2#=#e+\"F0$!3)>kYg,]F#\\F_
]l7$7$$\"3$G,,,,,,,\"F0$!3[4'34fIA#\\F_]lFg^s7$7$Fc]s$\"35d\\U!f7A$QF0
7$$\"33_$[w6xb(**F_]l$\"3M9*R%f$>e!QF07$7$F^_s$\"3VizzZ5)3!QF0Ff_s7$F]
_s7$$\"3sY3%3nZ62\"F0$!3'zSoS2')f#[F_]l7$7$$\"3q$4444444\"F0$!3'H'HRbF
<5[F_]lF``s7$7$Fg`s$\"3!*HO0[3ylPF07$$\"3J+`7)3Vq,\"F0$\"3M.)zzzzzz$F0
7$F_as7$F^_s$\"3*>'zzZ5)3!QF07$7$Fg`s$!3_jHRbF<5[F_]l7$$\"3#\\[DutsN8
\"F0$!3!)*)=<NA46ZF_]l7$7$$\"3gurrrrrr6F0$!3szty<k1aYF_]lF\\bs7$7$Fcbs
$\"3$zdhqAWxs$F07$$\"3KDbQ&f)fI6F0F[^p7$F[csF\\as7$Fbbs7$$\"3!eqQYq-U>
\"F0$!3o:S?D!z\\e%F_]l7$7$$\"3[b______7F0$!3%\\hSPKPnX%F_]lF`cs7$7$Fgc
s$\"3'yNuCWGko$F07$$\"3n=>cOzYK7F0$\"3m,(pppppp$F07$7$F`ds$\"37-(ppppp
p$F0Fhbs7$7$Fgcs$!3Q91uBttcWF_]l7$$\"3amBtLdu`7F0$!3C)))))>Xs?X%F_]l7$
7$$\"3=u\\iP*pjD\"F0FdhoF\\es7$Fbes7$$\"3/afoi=%eI\"F0$!3=0$)*GvAEF%F_
]l7$7$$\"3POLLLLLL8F0$!3Qy2YX*4D?%F_]lFfes7$7$$\"3fOLLLLLL8F0$\"3C8^W
\\U\\TOF07$$\"3M=<!H[gYK\"F0$\"33^YYYYYYOF07$7$$\"3c=<!H[gYK\"F0FaioF
\\ds7$7$Fcfs$!3%*y2YX*4D?%F_]l7$$\"33G8+OKIe8F0$!3A)))o5$eX&4%F_]l7$7$
$\"3\\*)H\"Q%*z_S\"F0F_foFdgs7$Fjgs7$$\"3pexi8!42T\"F0$!3guN=O9%z\"RF_
]l7$7$$\"3D<9999999F0$!3*z*)Qb'zq2RF_]lF^hs7$7$Fehs$\"3C\\*[MX9Ef$F07$
$\"3!pzB4)yw39F0$\"3M,'ffffff$F07$F]is7$F]fsFefs7$Fdhs7$$\"3y'Hh@PyoX
\"F0$!3,$on>U\\9q$F_]l7$7$$\"3O)\\\\\\\\\\\\\\\"F0$!3m)y'>e(zib$F_]lFe
is7$7$$\"39)\\\\\\\\\\\\\\\"F0$\"3\"G=nX7#[RNF07$$\"3-y`awn3'[\"F0$\"3
u]XXXXXXNF07$7$$\"3!yPXlx'3'[\"F0FjdoFjhs7$7$FbjsF^js7$$\"3R,$HH&z;0:F
0$!3S0sr'z3#)\\$F_]l7$7$$\"3k?9f'*\\&*=:F0FeaoFa[t7$Fg[t7$$\"3cnNhUlJ
\\:F0$!3]kL>xp3pKF_]l7$7$$\"3Czvvvvvv:F0$!3?CrBbU=`JF_]lF[\\t7$7$$\"3!
)yvvvvvv:F0$\"3wZ#fes<=[$F07$$\"3)\\0k&o/qd:F0Fibo7$7$$\"3?bSco/qd:F0F
eboFajs7$7$$\"3-zvvvvvv:F0$!3kBrBbU=`JF_]l7$$\"3OmOd$4ENf\"F0$!3:xMklh
MSIF_]l7$7$$\"3>?v^Lfm9;F0F`_oFi]t7$F_^t7$$\"3g`6*GF+ej\"F0$!3QlsK\"G4
&*z#F_]l7$7$$\"3!*fcccccc;F0$!3!3RSVNK\\p#F_]lFc^t7$7$$\"37gcccccc;F0$
\"3#QEv3Vu$>MF07$$\"3KN]rpM`C;F0$\"3_\\WWWWWWMF07$7$Fe_tF]`o7$Fe]t$\"3
?[#fes<=[$F07$7$$\"3ofcccccc;F0F\\_t7$$\"3'o*GV3v%on\"F0$!3YcET)*R+^DF
_]l7$7$$\"3eG(Q%)*z8)p\"F0F^]oFb`t7$Fh`t7$$\"3ty*Rb5`nr\"F0$!3m89GvMO&
H#F_]l7$7$$\"3zSPPPPPP<F0$!3Kp?d9tHw@F_]lF\\at7$7$$\"3,TPPPPPP<F0$\"3]
.\"QK-T>N$F07$$\"3wU%**3$yQ(o\"F0$\"3!*)RRRRRRR$F07$F]bt7$Fj^tFb_t7$Fb
at7$$\"3kfg3:>^b<F0$!339R*)HbbK?F_]l7$7$$\"37hr4qoLs<F0F]jnFebt7$F[ct7
$$\"3_D4*[6RFz\"F0$!3A>QiB]<g<F_]l7$7$$\"3!>#=======F0$!3?>O)G.IAf\"F_
]lF_ct7$7$$\"3n@=======F0$\"3y-U_#[w#yKF07$$\"3RYMh+BV-=F0F][o7$7$$\"3
hYMh+BV-=F0F][o7$$\"3ewhuS6xo<F0$\"3evlKm4\"QK$F07$7$$\"3%4G'3'3npu\"F
0Fi[oFgdt7$7$$\"3;\"G'3'3npu\"F0Fi[oFhat7$Fect7$$\"3.@+SQL)*H=F0$!3!4;
0b\"4!z[\"F_]l7$7$$\"3h\"G'QhmnR=F0FegnFeet7$F[ft7$$\"3MPn*yrxV'=F0$!3
_M\"4BG:y>\"F_]l7$7$$\"3a-**)*)*)*)*)*=F0$!3ul$[!G..v$*Fi\\nF_ft7$7$Ff
ft$\"3!H:[!>ME)>$F07$$\"37FJBflga=F0Fhhn7$7$$\"3MFJBflga=F0FhhnF[dt7$7
$$\"3K-**)*)*)*)*)*=F0Fhft7$$\"3ct<,%ya2!>F0$!3IQgx/W@,#*Fi\\n7$7$$\"3
gFBIT8/->F0FhcnFigt7$F_ht7$$\"3b?z@C>GK>F0$!3mg^:<c:@hFi\\n7$7$$\"3avQ
!p(ykc>F0FddnFcht7$Fiht7$$\"3i8jb>#yc'>F0$!3My'*HD!>z:$Fi\\n7$7$$\"3m$
)zzzzzz>F0$!390@3*yB*e>Fi\\nF]it7$7$$\"3A$)zzzzzz>F0$\"3!3.FD,.-6$F07$
$\"3g/&*yPDW^>F0Fden7$F^jt7$$\"3B'4V$HYh8>F0$\"3-]%[atyF=$F07$7$$\"3V6
4[v$4]!>F0F`fnFbjt7$7$Fijt$\"3e&>>>>>>>$F07$Fggt$\"3Y_\"[!>ME)>$F07$7$
Fdit$!3![5#3*yB*e>Fi\\n7$$\"3QUiHZ)>q*>F0$!3#H3>S&3dEm!#@7$7$$\"3RAeW=
q:3?F0F^`nFf[u7$F]\\u7$$\"3mo(z#Q2:F?F0$\"3)eX%\\b'e55$Fi\\n7$7$$\"35V
/(=6:x0#F0Fj`nFa\\u7$7$Fh\\u$\"3!p/111111'Fi\\n7$$\"3gel=q<we?F0$\"3Sm
^#=@ue<'Fi\\n7$7$$\"35kgggggg?F0$\"335T!)=CkajFi\\nF^]u7$7$Fe]u$\"38P2
MTAW8IF07$$\"3-j!Rq_%[Q?F0$\"3mWSSSSSSIF07$7$F^^uFgan7$$\"3![yLu7%4:?F
0$\"37>nj)**[)oIF07$7$$\"3eR\"pQy(H'*>F0$\"3Q%4444444$F0Fd^u7$7$$\"3!)
R\"pQy(H'*>F0FcbnFiit7$Fd]u7$$\"3en7GK2:'3#F0$\"3B))3TJ\"pX^*Fi\\n7$7$
$\"3vp!34bm15#F0F]]nFd_u7$Fj_u7$$\"3U?fkY3G9@F0$\"3%H^7M?%p!G\"F_]l7$7
$$\"3*\\9999999#F0$\"3g#*Rc`Kf\"e\"F_]lF^`u7$7$Fe`u$\"39m#[0iJg!HF07$$
\"3sAHL2Vs;@F0$\"3WVRRRRRRHF07$7$$\"3FAHL2Vs;@F0F]^n7$$\"3A/UcA0c&4#F0
$\"3/c^<^C0oHF07$7$$\"33zz.OCty?F0$\"3;$**)*)*)*)*)*)HF0Ffau7$7$F]buFi
^nFj]u7$Fd`u7$$\"3-tepF@8V@F0$\"3q93!>?Cag\"F_]l7$7$$\"3>%*3d#R%*R9#F0
FegmFdbu7$Fjbu7$$\"3!4]AZgy!o@F0$\"3?'*[`D#fX&>F_]l7$7$$\"3IHo5@vE\"=#
F0FghmF^cu7$Fdcu7$$\"3WUCcpew$>#F0$\"3gndLDV1*H#F_]l7$7$$\"3C&e**)>mF>
AF0FbimFhcu7$F^du7$$\"3va$4dmn,A#F0$\"3\"*p!oWg.\"REF_]l7$7$$\"3(eAAAA
AAA#F0$\"3_rq'\\Ujem#F_]lFbdu7$7$Fidu$\"3'[*=Shcf&y#F07$$\"3i%)4Lhtw?A
F0F_jm7$Faeu7$$\"3G*))><i<)>AF0$\"3%>v#>j;Q*y#F07$7$$\"3/D&oD3hr=#F0F[
[nFeeu7$F[fu7$$\"3=zUW$z,C;#F0$\"3Ye+P1;xvGF07$7$$\"3-zFUz1G`@F0$\"3%>
*))))))))))))GF0F_fu7$7$FffuFg[nFj`u7$Fhdu7$$\"3n^XJ)*\\.VAF0$\"3_#4O2
GL7+$F_]l7$7$$\"3O8JJx*3>D#F0FecmF]gu7$Fcgu7$$\"3+g#*H/9+mAF0$\"3%4<#Q
[PuiLF_]l7$7$$\"3MH]Or=E%G#F0FedmFggu7$7$$\"3yH]Or=E%G#F0Fadm7$$\"3UPc
`2HO*G#F0$\"3o=`?e[y@PF_]l7$7$$\"3w1......BF0$\"3]q/-hOMJRF_]lFdhu7$7$
F[iu$\"3/\\Fu>s/ZEF07$$\"3O'H=?8\"H!G#F0Faem7$Fciu7$$\"3)==UU]5zE#F0$
\"31o76h&=)3FF07$7$$\"3k!f<=\")33D#F0F`fmFgiu7$7$$\"33\"f<=\")33D#F0F`
fmF^eu7$Fjhu7$$\"3eoyqYyX6BF0$\"3%*y$HM*>u)3%F_]l7$7$$\"3c*\\[7$G_9BF0
$\"3LSTTTTTTTF_]lFeju7$F[[v7$$\"3'y6)o%pn:L#F0$\"3WELg[f5oWF_]l7$7$$\"
3\\j!*foUkTBF0Fc^mFa[v7$7$Fh[vF_^m7$$\"3w'HP_$*4=N#F0$\"3!RY@-XUm%[F_]
l7$7$$\"3)*G^%=#f]oBF0F^_mF\\\\v7$Fb\\v7$$\"3!)pM\"[.@@P#F0$\"3=')3#He
[ZA&F_]l7$7$$\"3k(QQQQQQQ#F0$\"3sv%zukzeW&F_]lFf\\v7$7$F]]v$\"3A5w\"Qf
EW[#F07$$\"3!y*[o#yXOQ#F0F\\`m7$Fe]v7$$\"3!3Vp?1rNQ#F0$\"3/'3a4c:][#F0
7$7$$\"3/YU6pQBfBF0Fh`mFi]v7$7$$\"3gXU6pQBfBF0Fh`m7$$\"3Irk>X2&)[BF0$
\"3=OZ]43AdDF07$7$$\"3_Y$pLgQUL#F0FdamFf^v7$F\\_v7$$\"3r$\\\"\\\"GW:J#
F0$\"37(RD)*RU5j#F07$7$$\"3^[rLoxo3BF0F`bmF`_v7$7$$\"3&*[rLoxo3BF0F`bm
7$F[iu$\"3g[Fu>s/ZEF07$F\\]v7$$\"3e@R:1Z7\"R#F0$\"34oN4Uh-6cF_]l7$7$$
\"3![0=uhuKR#F0FaflFa`v7$Fg`v7$$\"3VzJqjjF3CF0$\"3S57Y(yy)3gF_]l7$7$$
\"3%*GZ;uD?:CF0FaglF[av7$Faav7$$\"3&zA=55!HDCF0$\"3PkEHMMf2kF_]l7$7$$
\"3ox0v3caOCF0F\\hlFeav7$F[bv7$$\"3^%QP$=')4UCF0$\"3kQ%)412f2oF_]l7$7$
$\"3UD&ykZ5sX#F0$\"3ErrrrrrrrF_]lF_bv7$7$FfbvFhhl7$$\"3OkH#pGI'eCF0$\"
3#*o!*[#G=$4sF_]l7$7$$\"3aokkkkkkCF0$\"3o6I_N8dhtF_]lF\\cv7$7$Fccv$\"3
)*35w*oD<G#F07$$\"3'Q_Jt\")eUY#F0Fhil7$F[dv7$$\"3io!30``TY#F0$\"3/&ykm
OOJG#F07$7$$\"3KbvM/m?XCF0FdjlF_dv7$Fedv7$$\"3J0Ti?:SRCF0$\"3%HJZLU6\"
\\BF07$7$$\"3k1-<q)*RDCF0F`[mFidv7$F_ev7$$\"3&R\"***p6xDT#F0$\"3#H[<hs
\"Q;CF07$7$$\"3!=mG3?v[S#F0F\\\\mFcev7$FievFb]v7$7$Fccv$\"3e5I_N8dhtF_
]l7$$\"3IMA#y<dLZ#F0$\"3RP\">%>dKAwF_]l7$7$$\"3G3ai,\"e_Z#F0Fc]lFafv7$
Fgfv7$$\"3e)o-_6oo[#F0$\"3A/=%e'G$H/)F_]l7$7$$\"3ex'*y1+W\"\\#F0$\"35!
=======)F_]lF[gv7$Fagv7$$\"3[hkvyA'**\\#F0$\"3%=B\"o[[9m%)F_]l7$7$$\"3
9IGFd%zn]#F0F[_lFggv7$F]hv7$$\"3LyikJ^d7DF0$\"3#*z.<B]O#*))F_]l7$7$$\"
3_.G$R\\27_#F0Fg_lFahv7$7$$\"33.G$R\\27_#F0F[`l7$$\"3)R-@A.TY_#F0$\"3>
E(G'\\O+A$*F_]l7$7$$\"3e(R;\")zdY`#F0Ff`lF^iv7$Fdiv7$$\"339.fjQ4ODF0$
\"3uk6ieRZb(*F_]l7$7$$\"3U\\XXXXXXDF0$\"35.,'\\bPO,\"F0Fhiv7$7$F_jv$\"
3)Rb&epLz#*>F07$$\"3X!)3&)p>yODF0Ffal7$7$$\"3*3)3&)p>yODF0Ffal7$$\"3**
Rc!H\\y``#F0$\"3Q+h9j0gO?F07$7$$\"3'*yR!H/mS_#F0FeblF^[w7$Fd[w7$$\"3o!
>C0ma,_#F0$\"3'ob*))30i'4#F07$7$$\"3;0i],DU5DF0FdclFh[w7$F^\\w7$$\"32<
%**pl]K]#F0$\"3?\"f(fh0pd@F07$7$$\"3Us[8C&*)e\\#F0F`dlFb\\w7$Fh\\w7$$
\"37I;v6!=Y[#F0$\"3x3DQ:5%)>AF07$7$$\"3/z&zw2/0[#F0F\\elF\\]w7$Fb]wFhc
v7$F^jv7$$\"3C1&)=#y!oYDF0$\"3)pHVAiN%>5F07$7$$\"3Y<*f,1Voa#F0F6Fg]w7$
F]^w7$$\"3]UKFl^RbDF0$\"3#yQ?L=%\\k5F07$7$$\"3mJw*[#4ecDF0FBFa^w7$Fg^w
7$$\"3CeNOF#GMc#F0$\"3\"3**=+dy*46F07$7$$\"3[=H(HrM`c#F0FNF[_w7$7$$\"3
#*=H(HrM`c#F0FN7$$\"3ArnBZcsqDF0$\"3I$G.JtAf:\"F07$7$$\"3a\"e@.PoId#F0
F]oFh_w7$7$$\"33\"e@.PoId#F0$\"3qrrrrrrr6F07$$\"35aT`YSBxDF0$\"3Qpu/M+
O-7F07$7$$\"35/wRI1vzDF0FhoFg`w7$F]aw7$$\"3sJOX$H,He#F0$\"3qYyAbIK\\7F
07$7$$\"31;?(RMb`e#F0FdpFaaw7$Fgaw7$$\"3-)*H&*\\nn(e#F0$\"3K$z?aWVoH\"
F07$7$$\"3occj'ph)*e#F0F`qF[bw7$7$$\"3Cccj'ph)*e#F0F`q7$$\"3g+;)fX6:f#
F0$\"3#y'zl/=&\\M\"F07$7$$\"357V+7VD$f#F0$\"3eutttttt8F0Fhbw7$7$F_cwF
\\r7$$\"3kl3UY#eVf#F0$\"3Ux%Q6hxOR\"F07$7$$\"3AG#QHCBbf#F0$\"3vCCCCCCC
9F0Fecw7$7$F\\dwFhr7$$\"3'H_4')zrhf#F0$\"3&phD:>\\IW\"F07$7$$\"3=%3Xq&
Qm'f#F0$\"3Ovuuuuuu9F0Fbdw7$7$$\"3i%3Xq&Qm'f#F0Fds7$$\"3eAmV5'3pf#F0$
\"3uI(QYt$4$\\\"F07$7$$\"3%[xJhiwmf#F0FftFaew7$7$FhewF`t7$$\"3Ss!)*3\"
p_'f#F0$\"3fu`NZt$Qa\"F07$7$$\"3_@t&>$oc&f#F0$\"3-xvvvvvv:F0F\\fw7$7$F
cfwFau7$$\"3U@^k1l)\\f#F0$\"31?&=0:0`f\"F07$7$$\"3O]9`-UM$f#F0$\"3jFEE
EEEE;F0Fifw7$7$$\"3#*\\9`-UM$f#F0F]v7$$\"3mxeMp&[Af#F0$\"3I)fN=T@vk\"F
07$7$$\"3YK\"yU\\A+f#F0$\"3Cywwwwww;F0Fhgw7$7$F_hwFiv7$$\"3+U+gp`F)e#F
0$\"3.'z\"=7(40q\"F07$7$$\"3q'=vc.>ce#F0F\\xFehw7$7$F\\iwFhw7$$\"3OrTo
j*HIe#F0$\"3_lUQTJHa<F07$7$$\"3I45dZU:!e#F0$\"3-zxxxxxx<F0F`iw7$Ffiw7$
$\"3+jSdReZwDF0$\"3%Q8e%>X*)3=F07$7$$\"3#\\[#Qa6ltDF0$\"31IGGGGGG=F0F
\\jw7$7$$\"3[%[#Qa6ltDF0Ffy7$$\"3'=,C&GldoDF0$\"3[m%p$RmLk=F07$7$$\"3)
4nG*)*[8mDF0FbzF[[x7$Fa[x7$$\"3+fT-)=&HfDF0$\"3BDpoFDk?>F07$7$$\"3M)*R
*=FKwb#F0$\"3%3$HHHHHH>F0Fe[x7$F[\\x7$$\"3=*ee7;%f[DF0$\"3/d/#*>d$y(>F
07$7$$\"31'oy\\Er\"[DF0F^\\lFa\\x7$7$Fh\\x$\"3!>)zzzzzz>F0Fdjv-%&COLOR
G6&%$RGBG$\"\"!!\"\"Fb]xFb]x" 1 2 2 1 10 1 2 6 1 4 2 1.0 45.0 45.0 1 0
 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 
276 13 "  Now we tell" }{TEXT 242 6 " Maple" }{TEXT 276 11 " to treat \+
 " }{TEXT 243 1 "y" }{TEXT 276 20 "  as a function of  " }{TEXT 244 1 
"x" }{TEXT 276 2 " ." }}{EXCHG {PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "y:=f(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
-I\"fG6\"6#I\"xGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "eq;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "/,.*$I\"xG6\"\"\"%\"\"\"*$-I\"fGF&6#F%F
'F(*$F*\"\"$!\"%*$F%\"\"#F/*&F%F1F*F(F/*&F%F1F*F1F1\"\"!" }}}{PARA 0 "
" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 54 "  Observe that M
aple has replaced each occurrence of  " }{TEXT 245 1 "y" }{TEXT 276 
52 "  by  f (x) .                                       " }}{PARA 0 ""
 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 50 "  To differentiat
e this equation with respect to  " }{TEXT 246 1 "x" }{TEXT 276 13 ", w
e use the " }{TEXT 247 5 "diff " }{TEXT 276 8 "command." }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "de
q:=diff(eq,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "/,2*$I\"xG6\"\"\"$\"\"
%*&-I\"fGF&6#F%F'-I%diffG%*protectedG6$F*F%\"\"\"F(*&F*\"\"#F-F1!#7F%!
\")*&F%F1F*F1F5*&F%F3F-F1!\"%*&F%F1F*F3F(*(F%F3F*F1F-F1F(\"\"!" }}}
{PARA 0 "" 0 "" {TEXT 276 18 "  Here Maple uses " }{XPPEDIT 18 0 "diff
(f(x), x);" "6#-%%diffG6$-%\"fG6#%\"xGF)" }{TEXT 276 46 " to denote f \+
'( x ), the derivative of f( x )." }}{PARA 0 "" 0 "" {TEXT 276 20 "  W
e now solve for  " }{XPPEDIT 18 0 "diff(f(x), x);" "6#-%%diffG6$-%\"fG
6#%\"xGF)" }{TEXT 276 2 " :" }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Diff(f(x),x)=solve(deq,diff(
f(x),x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "/-I%DiffG6$%*protectedGI(_s
yslibG6\"6$-I\"fGF(6#I\"xGF(F-,$*(F-\"\"\",**$F-\"\"#F0!\"#F0F*F4*$F*F
3F0F0,**$F*\"\"$F0F5!\"$F2!\"\"*&F-F3F*F0F0F:F:" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT 276 111 " The single Maple command \"implicitdiff\" combine
s the above computations but uses \"y\" rather than \"f(x)\"." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "y:='y';" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "I\"yG6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 276 53 "(Previo
usly,we had replaced y by f(x); the command \"" }{TEXT 248 6 "y:='y'" 
}{TEXT 276 17 " \"undoes this.) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
 1 0 3 "eq;" }}{PARA 11 "" 1 "" {XPPMATH 20 "/,.*$I\"xG6\"\"\"%\"\"\"*
$I\"yGF&F'F(*$F*\"\"$!\"%*$F%\"\"#F-*&F%F/F*F(F-*&F%F/F*F/F/\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "dydx:=implicitdiff(eq,y,x);"
 }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(I\"xG6\"\"\"\",**$F$\"\"#F&!\"#F&
I\"yGF%F**$F+F)F&F&,**$F+\"\"$F&F,!\"$F(!\"\"*&F$F)F+F&F&F1F1" }}}
{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 12 "  The p
oint " }{TEXT 249 1 "P" }{TEXT 276 18 " has coordinates  " }{TEXT 250 
1 "x" }{TEXT 276 3 " = " }{XPPEDIT 18 0 "(2+sqrt(3))/2;" "6#*&,&\"\"#
\"\"\"-%%sqrtG6#\"\"$F&F&F%!\"\"" }{TEXT 276 8 "   and  " }{TEXT 251 
1 "y" }{TEXT 276 5 "  =  " }{XPPEDIT 18 0 "(2*sqrt(3)+3)/2;" "6#*&,&*&
\"\"#\"\"\"-%%sqrtG6#\"\"$F'F'F+F'F'F&!\"\"" }{TEXT 276 24 " ,  so in \+
order to find " }{TEXT 252 1 "m" }{TEXT 276 30 ", the slope of the tan
gent at " }{TEXT 253 2 "P," }{TEXT 276 17 " we must replace " }{TEXT 
254 0 "" }{TEXT 276 10 " y  by    " }{XPPEDIT 18 0 "(2*sqrt(3)+3)/2;" 
"6#*&,&*&\"\"#\"\"\"-%%sqrtG6#\"\"$F'F'F+F'F'F&!\"\"" }{TEXT 276 8 "  \+
and   " }{TEXT 255 1 "x" }{TEXT 276 9 "   by    " }{XPPEDIT 18 0 "(2+s
qrt(3))/2;" "6#*&,&\"\"#\"\"\"-%%sqrtG6#\"\"$F&F&F%!\"\"" }{TEXT 276 
28 "   in the formula for dy/dx." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "subs(y=(2*sqrt(3)+3)/2,x=(2+
sqrt(3))/2,dydx);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(,&\"\"\"F%*$\"
\"$#F%\"\"#F(F%,**$F$F)F%!\"&F%F&!\"#*$,&F&F%#F'F)F%F)F%F%,**$F/F'F%F.
!\"$F+!\"\"*&F$F)F/F%F%F4F4" }}}{PARA 0 "" 0 "" {TEXT 276 0 "" }}
{PARA 0 "" 0 "" {TEXT 276 59 "  Simplifying this complicated fraction,
 we find the slope " }{TEXT 256 1 "m" }{TEXT 276 37 " of the tangent l
ine to the graph at " }{TEXT 257 1 "P" }{TEXT 276 7 " to be:" }}{PARA 
0 "" 0 "" {TEXT 276 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 276 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "m:=simplify(%);" }}{PARA 11 "" 1 ""
 {XPPMATH 20 "!\"\"" }}}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 
"" {TEXT 276 47 "  In order to get a decimal representation for " }
{TEXT 258 1 "m" }{TEXT 276 52 " accurate to ten significant digits, we
 may use the " }{TEXT 259 5 "evalf" }{TEXT 276 10 "  command." }}
{PARA 11 "" 0 "" {TEXT 277 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 9 "evalf(m);" }}{PARA 11 "" 0 "" {TEXT 277 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "$!\"\"\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 276 0 "" }}
{PARA 0 "" 0 "" {TEXT 276 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 276 37 
" The equation of the tangent is  y = " }{TEXT 260 1 "m" }{TEXT 276 5 
"(x - " }{XPPEDIT 18 0 "(2+sqrt(3))/2;" "6#*&,&\"\"#\"\"\"-%%sqrtG6#\"
\"$F&F&F%!\"\"" }{TEXT 276 5 " ) + " }{XPPEDIT 18 0 "(2*sqrt(3)+3)/2;"
 "6#*&,&*&\"\"#\"\"\"-%%sqrtG6#\"\"$F'F'F+F'F'F&!\"\"" }{TEXT 276 80 "
 .  We can plot the cardioid and its tangent on the same set of axes a
s follows:" }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 63 "A:=implicitplot(eq,x=-4..4,y=-1..4,grid=[100,100],
color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "B:=plot(m*
(x-(2+sqrt(3))/2)+(2*sqrt(3)+3)/2,x=-4..4,y=-1..5):" }}}{EXCHG {PARA 
211 "" 0 "" {TEXT 276 0 "" }{TEXT 203 57 "NOTE THAT THE ABOVE COMMANDS
 END WITH \":\"AND NOT \";\"." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "display([A,B]);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6&-%+AXESLABELSG6'Q\"x6\"Q\"yF'-%%FONTG6$%*HELVETICAG\"#5
%+HORIZONTALGF.-%'CURVESG6g]m7$7$$!33WXXXXXXD!#<$\"3Nz+'\\bPO,\"F67$$!
3Y<*f,1Voa#F6$\"36???????5F67$F97$$!3-)*pj'QJqa#F6$\"3w`5%fa(=@5F67$7$
$!3yIw*[#4ecDF6$\"3sqqqqqqq5F6F?7$FE7$$!3=LE6D]!zb#F6$\"3MwL\\?')[y5F6
7$7$$!3[=H(HrM`c#F6$\"3L@@@@@@@6F6FK7$7$$!3#*=H(HrM`c#F6FT7$$!3MBGEJ
\\PnDF6$\"3(eHUBO7\\8\"F67$7$$!3a\"e@.PoId#F6$\"3;srrrrrr6F6FZ7$7$$!33
\"e@.PoId#F6$\"3#><<<<<<<\"F67$$!3+2[tTpXvDF6$\"3IOBRp'o/>\"F67$7$$!35
/wRI1vzDF6$\"3aAAAAAAA7F6Feo7$F[p7$$!3O2$p#\\I<#e#F6$\"3w\\k5(Gr^C\"F6
7$7$$!31;?(RMb`e#F6$\"3;tssssss7F6Fap7$Fgp7$$!3sq#o3A^ve#F6$\"3i_3'[pP
!*H\"F67$7$$!3Cccj'ph)*e#F6$\"3wBBBBBBB8F6F]q7$Fcq7$$!3#4U\"3n]i\"f#F6
$\"3c@\"\\#**))3_8F67$7$$!357V+7VD$f#F6$\"3Outttttt8F6Fiq7$F_r7$$!3Sx6
p#QLWf#F6$\"3.q-,Z\"\\VS\"F67$7$$!3AG#QHCBbf#F6$\"3)\\UUUUUUU\"F6Fer7$
F[s7$$!3/+(GFe>gf#F6$\"3Ws(QDdXeX\"F67$7$$!3i%3Xq&Qm'f#F6$\"3evuuuuuu9
F6Fas7$Fgs7$$!3'*=&)*)f5V'f#F6$\"3+g\\F'z2m]\"F67$7$$!3%[xJhiwmf#F6$\"
3>EDDDDDD:F6F]t7$7$$!3Iv<8Emn'f#F6$\"3UEDDDDDD:F67$$!3wNS8!\\=df#F6$\"
3m3sn!\\nmb\"F67$7$$!3_@t&>$oc&f#F6$\"3!oddddddd\"F6F^u7$Fdu7$$!3=(\\s
A6NRf#F6$\"3#yz=+$z01;F67$7$$!3#*\\9`-UM$f#F6$\"3TFEEEEEE;F6Fju7$F`v7$
$!3=8[$f+O6f#F6$\"3g&zi!RN\"[l\"F67$7$$!3YK\"yU\\A+f#F6$\"3-ywwwwww;F6
Ffv7$7$F]w$\"3yxwwwwww;F67$$!3)p^))))Qxte#F6$\"3I6R\"RXpHq\"F67$7$$!3q
'=vc.>ce#F6$\"3SGFFFFFF<F6Few7$7$F\\x$\"3jGFFFFFF<F67$$!3'zG_<&fr#e#F6
$\"3m=)3i5h0v\"F67$7$$!3I45dZU:!e#F6$\"3Yzxxxxxx<F6Fdx7$7$F[y$\"3Czxxx
xxx<F67$$!393`:W#3sd#F6$\"3mcdYRQi(z\"F67$7$$!3[%[#Qa6ltDF6$\"3iHGGGGG
G=F6Fcy7$Fiy7$$!3%ffbE754d#F6$\"3I([LSc#>W=F67$7$$!3)4nG*)*[8mDF6$\"3W
!)yyyyyy=F6F_z7$Fez7$$!3gSp1ni(Qc#F6$\"3EGcza9I!*=F67$7$$!3)y*R*=FKwb#
F6$\"31JHHHHHH>F6F[[l7$Fa[l7$$!3[?=^o(fhb#F6$\"3\"*GPq$p$)f$>F67$7$$!3
i&oy\\Er\"[DF6$\"3W\")zzzzzz>F6Fg[l7$7$F^\\l$\"3o\")zzzzzz>F67$$!3On<i
*y6ya#F6$\"3A'\\-uDr7)>F67$7$F4$\"3SybepLz#*>F6Ff\\l7$7$$!3?jkkkkkkCF6
$\"3OnG_N8dht!#=7$$!3%ySD;5e_Z#F6$\"37vwwwwwwwFe]l7$Ff]l7$$!3Wjg)>=&)z
Z#F6$\"3gw,9gY8gxFe]l7$7$$!39x'*y1+W\"\\#F6$\"3A\"=======)Fe]lF\\^l7$F
b^l7$$!37fXk.9\"y\\#F6$\"3#zFc00*4*Q)Fe]l7$7$$!39IGFd%zn]#F6$\"31&oooo
ooo)Fe]lFh^l7$F^_l7$$!3=zhSy#)*f^#F6$\"3&*4p'G_<y+*Fe]l7$7$$!3_.G$R\\2
7_#F6$\"3/!>>>>>>>*Fe]lFd_l7$7$F[`l$\"3%*)=>>>>>>*Fe]l7$$!3$)zf$*[/_KD
F6$\"3bp'GPfJhh*Fe]l7$7$$!3e(R;\")zdY`#F6$\"3-&ppppppp*Fe]lFc`l7$Fi`l7
$F4$\"3dz+'\\bPO,\"F67$F\\]l7$$!3hvZ%*4)=x`#F6$\"3$pU4c>oa-#F67$7$$!3M
\")3&)p>yODF6$\"30KIIIIII?F6Fcal7$7$$!3*3)3&)p>yODF6F\\bl7$$!3on>3ldiE
DF6$\"3SA_2$4S!p?F67$7$$!3SzR!H/mS_#F6$\"3m#3333333#F6Fbbl7$7$$!3'*yR!
H/mS_#F6F[cl7$$!32'H$RZL,:DF6$\"3P`[_#Q(G7@F67$7$$!3;0i],DU5DF6$\"3FLJ
JJJJJ@F6Facl7$Fgcl7$$!3lFsn\"[MH]#F6$\"3+ht&>9V_:#F67$7$$!3Us[8C&*)e
\\#F6$\"3)Q=======#F6F]dl7$Fcdl7$$!3wK[r2\"Q/\\#F6$\"37:ftez$z>#F67$7$
$!3/z&zw2/0[#F6$\"3\\MKKKKKKAF6Fidl7$F_el7$$!33v%[GBpvZ#F6$\"39#\\\\C'
**RSAF67$7$Fa]l$\"33C5w*oD<G#F6Feel7$7$$!3I#QQQQQQQ#F6$\"3#eOzukzeW&Fe
]l7$$!3Oa!=uhuKR#F6$\"3CbcccccccFe]l7$Fdfl7$$!3/]ty;q$pR#F6$\"3/.n\\7@
VQdFe]l7$7$$!3%*GZ;uD?:CF6$\"35fhhhhhhhFe]lFjfl7$7$Fagl$\"3AghhhhhhhFe
]l7$$!3e%41/>-nU#F6$\"3YiVm_\\^HkFe]l7$7$$!3ox0v3caOCF6$\"3=lmmmmmmmFe
]lFigl7$F_hl7$$!3Y!*>3nnuaCF6$\"3[9#R>1W)4rFe]l7$7$$!3UD&ykZ5sX#F6$\"3
;qrrrrrrrFe]lFehl7$7$$!3'e_ykZ5sX#F6F^ilF`]l7$F[fl7$$!3IuH4k6KkCF6$\"3
?aB)*p\\i#G#F67$7$$!3'Q_Jt\")eUY#F6$\"35&GGGGGGG#F6Feil7$F[jl7$$!3QbN
\"phZ&[CF6$\"3Po-]`:FBBF67$7$$!3wbvM/m?XCF6$\"3qNLLLLLLBF6Fajl7$Fgjl7$
$!3$GCb9nlDV#F6$\"3UtQ4))yyjBF67$7$$!3k1-<q)*RDCF6$\"3I'QQQQQQQ#F6F][m
7$Fc[m7$$!3d&)p#\\A6kT#F6$\"3dj(=&4k>/CF67$7$$!3Nh'G3?v[S#F6$\"3#pVVVV
VVV#F6Fi[m7$F_\\m7$$!3?*=enz:,S#F6$\"3G;$=u\"o^WCF67$7$$!3w#QQQQQQQ#F6
$\"3w@w\"QfEW[#F6Fe\\m7$7$$!3V,......BF6$\"3\"*y.-hOMJRFe]l7$$!3c*\\[7
$G_9BF6$\"3xRTTTTTTTFe]l7$Ff]m7$$!3TbWpkVg?BF6$\"31,^\"o-_7D%Fe]l7$7$$
!3\\j!*foUkTBF6$\"3=WYYYYYYYFe]lF\\^m7$7$Fc^m$\"3uWYYYYYYYFe]l7$$!3qS!
[Jrx6O#F6$\"3490qff))4]Fe]l7$7$$!3UH^%=#f]oBF6$\"3E]^^^^^^^Fe]lF[_m7$F
a_mF_fl7$7$F`flF^]m7$$!3e&ejty%o$Q#F6$\"3oR<0([_Z[#F67$7$$!3!y*[o#yXOQ
#F6$\"3a([[[[[[[#F6Fi_m7$F_`m7$$!3wzaW;eZkBF6$\"3QuHtI>DBDF67$7$$!3/YU
6pQBfBF6$\"38QNNNNNNDF6Fe`m7$F[am7$$!3gDp-H?JXBF6$\"3'zU,Thz<c#F67$7$$
!3_Y$pLgQUL#F6$\"3u)eeeeeee#F6Faam7$Fgam7$$!343,N!>4iK#F6$\"38oMV!RX.g
#F67$7$$!31[rLoxo3BF6$\"3NROOOOOOEF6F]bm7$Fcbm7$$!3ImCn`(zrI#F6$\"3,#*
\\,Vq&*QEF67$7$Fb]m$\"3#zvU(>s/ZEF6Fibm7$7$$!3a?AAAAAAAF6$\"3!Q*p'\\Uj
em#Fe]l7$$!3O8JJx*3>D#F6$\"3$)HJJJJJJJFe]l7$Fhcm7$$!3#z#HNt'HAF#F6$\"3
y\\+)3qfQW$Fe]l7$7$$!3yH]Or=E%G#F6$\"3![jjjjjjj$Fe]lF^dm7$7$Fedm$\"3CM
OOOOOOOFe]lFa]m7$F_cm7$$!3c\"*yq1S%eG#F6$\"37%=n;DFhn#F67$7$$!3!oH=?8
\"H!G#F6$\"3'**ooooooo#F6F^em7$7$$!3O'H=?8\"H!G#F6Fgem7$$!3gMc\"pKySE#
F6$\"3_t?I_(GIr#F67$7$$!3k!f<=\")33D#F6$\"3dSPPPPPPFF6F]fm7$Fcfm7$$!3&
\\6p0QmDC#F6$\"3e\\0MO))3]FF67$7$Fdcm$\"3=/>Shcf&y#F6Fifm7$7$$!3mRTTTT
TT@F6$\"3%z#Rc`Kf\"e\"Fe]l7$$!3v$*3d#R%*R9#F6$\"3j9;;;;;;;Fe]l7$Fhgm7$
$!3k$>Sv]ej9#F6$\"3+_%\\W!R1Z;Fe]l7$7$$!3IHo5@vE\"=#F6$\"3))>@@@@@@@Fe
]lF^hm7$7$$!3')Go5@vE\"=#F6$\"3h>@@@@@@@Fe]l7$$!3)3#>vz%Go@#F6$\"3Q^K#
et^Df#Fe]l7$7$$!3C&e**)>mF>AF6$\"3&[iiiiiii#Fe]lF_im7$FeimFccm7$F_gm7$
$!3OV7!GKa6A#F6$\"3;!oS2N6sy#F67$7$$!3^&)4Lhtw?AF6$\"3=\"zyyyyyy#F6F
\\jm7$Fbjm7$$!3Az@8R@$o>#F6$\"3TmDXO]^AGF67$7$$!3/D&oD3hr=#F6$\"3yTQQQ
QQQGF6Fhjm7$F^[n7$$!3E'\\H^v_H<#F6$\"3sRf&>Z&4eGF67$7$$!3cyFUz1G`@F6$
\"3Q#*))))))))))))GF6Fd[n7$Fj[n7$$!3IK3R'e#\\\\@F6$\"3cD$**p\"z$R*GF67
$7$Fdgm$\"3Ct#[0iJg!HF6F`\\n7$7$$!3yegggggg?F6$\"3!G[.)=Ckaj!#>7$$!3vp
!34bm15#F6$\"3m46666666Fe]l7$F`]nFcgm7$7$Fdgm$\"3pt#[0iJg!HF67$$!3DWn=
*>!4C@F6$\"3.@=]vkcGHF67$7$$!3FAHL2Vs;@F6$\"3+VRRRRRRHF6Fj]n7$F`^n7$$!
3Ym?#[9@!)4#F6$\"3#y%*GqOyF'HF67$7$$!33zz.OCty?F6$\"3i$**)*)*)*)*)*)HF
6Ff^n7$F\\_n7$$!3o-fQ]'QD2#F6$\"35'R6&eoN(*HF67$7$F[]n$\"3BW2MTAW8IF6F
b_n7$7$$!3!z(zzzzzz>F6$!3A^E3*yB*e>F_]n7$$!3RAeW=q:3?F6$\"3z&*4555555F
_]n7$Fa`n7$$!3)*GMRRBX`?F6$\"3h'p;[[)\\8cF_]n7$7$$!3aV/(=6:x0#F6$\"3AY
gggggggF_]nFg`n7$F]anFj\\n7$Fh_n7$$!33`nA7#)fX?F6$\"3Wyp;NT-JIF67$7$$!
3-j!Rq_%[Q?F6$\"3AWSSSSSSIF6Fdan7$Fjan7$$!3_'y3Bzpv,#F6$\"3y*HBKU6S1$F
67$7$$!3eR\"pQy(H'*>F6$\"3#[4444444$F6F`bn7$Ffbn7$$!3eC7mlGG!*>F6$\"3!
RitX9iu4$F67$7$F]`n$\"3,Pq_7I?5JF6F\\cn7$7$$!3+(*)*)*)*)*)*)*=F6$!3#4#
)[!G..v$*F_]n7$$!3%pK-8MT?!>F6$!3/0\"444444*F_]n7$F[dn7$$!3E^xp(f#))3>
F6$!3-<#o;U:EZ)F_]n7$7$$!3)f(Q!p(ykc>F6$!3jaSSSSSSSF_]nFadn7$FgdnF\\`n
7$7$F]`n$\"3dOq_7I?5JF67$$!3K)ouU$*Q7'>F6$\"3J*3izt9)HJF67$7$$!3g/&*yP
DW^>F6$\"3VXTTTTTTJF6Faen7$Fgen7$$!3.[[2]!>:$>F6$\"3#)RA%3'[uhJF67$7$$
!3w54[v$4]!>F6$\"3-'>>>>>>>$F6F]fn7$Fcfn7$$!3$)eER<bn->F6$\"3GA4U.FA%>
$F67$7$Fgcn$\"3!y:[!>ME)>$F6Fifn7$7$$!37;=======F6$!3QhO)G.IAf\"Fe]l7$
$!3Q\"G'QhmnR=F6$!3[:9999999Fe]l7$7$$!3h\"G'QhmnR=F6F[hn7$Fgcn$!3KA)[!
G..v$*F_]n7$F_gn7$$!3o$eT*='G5(=F6$\"3l]SRU%[\\A$F67$7$$!3MFJBflga=F6$
\"3lYUUUUUUKF6Fehn7$F[in7$$!37\\3o'H0*R=F6$\"3%>9'[;9+cKF67$7$Fdgn$\"3
73U_#[w#yKF6Fain7$7$$!3CNPPPPPP<F6$!3'f5sXJ(Hw@Fe]l7$$!3!4;(4qoLs<F6$!
3X?>>>>>>>Fe]l7$7$$!37hr4qoLs<F6FcjnFcgn7$Fgin7$$!3<:Jcem^3=F6$\"3A4w;
o&))oG$F67$7$$!3hYMh+BV-=F6$\"3E(HHHHHHH$F6Fjjn7$F`[o7$$!3')*fM2p+^x\"
F6$\"3qP)z(Q'3lJ$F67$7$$!3%4G'3'3npu\"F6$\"3'yMMMMMMM$F6Ff[o7$F\\\\o7$
$!3Lv(=\"oX'Gu\"F6$\"3m(**\\E6moM$F67$7$F\\jn$\"3]2\"QK-T>N$F6Fb\\o7$7
$$!3Oacccccc;F6$!3?D/MaB$\\p#Fe]l7$$!3eG(Q%)*z8)p\"F6$!3UDCCCCCCCFe]l7
$Fa]oF[jn7$Fh\\o7$$!3$)e<))3;*zq\"F6$\"398>jjbdvLF67$7$$!3aU%**3$yQ(o
\"F6$\"3Y)RRRRRRR$F6Fh]o7$F^^o7$$!3OKl'3Q!ot;F6$\"3$pWFm4OYS$F67$7$F]]
o$\"3Qn_(3Vu$>MF6Fd^o7$7$$!3Ytvvvvvv:F6$!31`rBbU=`JFe]l7$$!3>?v^Lfm9;F
6$!3RIHHHHHHHFe]l7$Fc_oF\\]o7$Fj^o7$$!3H`*y947$Q;F6$\"3(4Eli'f.LMF67$7
$$!3([.:(pM`C;F6$\"33\\WWWWWWMF6Fj_o7$7$$!35N]rpM`C;F6Fc`o7$$!3>ir]:m(
>g\"F6$\"3#>%zGW8$3Y$F67$7$F__o$\"3?_#fes<=[$F6Fi`o7$7$$!3e#
\\\\\\\\\\\\\\\"F6$!3=9o>e(zib$Fe]l7$$!3T?9f'*\\&*=:F6$!3ONMMMMMMMFe]l
7$Fhao7$F__o$!3i`rBbU=`JFe]l7$F_ao7$$!3=H'f8M2ec\"F6$\"3#[y]%)fI()[$F6
7$7$$!3)\\0k&o/qd:F6$\"3o*\\\\\\\\\\\\\\$F6Fbbo7$7$Fibo$\"3C*
\\\\\\\\\\\\\\$F67$$!3f/O!4wDv_\"F6$\"36?3<h'4`^$F67$7$Fdao$\"3#f=nX7#
[RNF6Faco7$Fcao7$$!30;%yrXv&H9F6$!3IiETq6$H%QFe]l7$7$$!3q69999999F6$!3
I@*Qb'zq2RFe]lF[do7$Fgco7$$!3[9J4P-C!\\\"F6$\"3@9VHf7^UNF67$7$$!3Ox`aw
n3'[\"F6$\"3I]XXXXXXNF6Fgdo7$F]eo7$$!3K*\\L.Q;,X\"F6$\"3G0YK**)Qzc$F67
$7$Fbdo$\"3C`*[MX9Ef$F6Fceo7$7$$!3\"3LLLLLLL\"F6$!3E(zga%*4D?%Fe]l7$$!
3:!*H\"Q%*z_S\"F6$!3LSRRRRRRRFe]l7$FbfoFado7$7$Fbdo$\"3!G&*[MX9Ef$F67$
$!3$z-'\\\"z'R69F6$\"3!fB1o?WUf$F67$7$$!3o'zB4)yw39F6$\"3!4gffffff$F6F
\\go7$Fbgo7$$!3?\"*)H&Gtbp8F6$\"3r^u&Hf*f=OF67$7$F^fo$\"3z;^W\\U\\TOF6
Fhgo7$7$$!3%*\\______7F6$!3OH1uBttcWFe]l7$$!3It\\iP*pjD\"F6$!3JXWWWWWW
WFe]l7$FghoF]fo7$F^ho7$$!37csu*4!4H8F6$\"3%\\Ntai7Qk$F67$7$$!3,><!H[gY
K\"F6$\"3_^YYYYYYOF6F^io7$Fdio7$$!3uN4-[1o&G\"F6$\"3Cb%\\'on=nOF67$7$F
cho$\"3'4OuCWGko$F6Fjio7$7$Fcho$!3#*H1uBttcWFe]l7$$!3c/*y%fz(*[7F6$!3m
.T)f-:mY%Fe]l7$7$$!3/prrrrrr6F6$!3]#R(y<k1aYFe]lFgjo7$F`jo7$$!3K^hbgC;
V7F6$\"3!e,*)>&z6\"p$F67$7$$!3L>>cOzYK7F6$\"3c-(pppppp$F6Fc[p7$Fi[p7$$
!3kS%4a#HM)>\"F6$\"3Hst-$z5Or$F67$7$F^[p$\"3g!ehqAWxs$F6F_\\p7$F][p7$$
!33<Od7vA@6F6$!3mX;49[+gZFe]l7$7$$!3;)3444444\"F6$!3%=(HRbF<5[Fe]lFi
\\p7$7$F^[p$\"3:!ehqAWxs$F67$$!3i]D3Ib[`6F6$\"3K;JXr*zgt$F67$7$$!3KDbQ
&f)fI6F6$\"3u_ZZZZZZPF6Fh]p7$F^^p7$$!3!RNw$H]U26F6$\"3q$z;!4szdPF67$7$
F`]p$\"3cKO0[3ylPF6Fd^p7$F_]p7$$!3M*>())fg=:5F6$!3g\\7L)Q8x\"\\Fe]l7$7
$$!3G25555555F6$!3:;'34fIA#\\Fe]lF^_p7$Fj^p7$$!3'o)G)Rbe*f5F6$\"35F4S7
djyPF67$7$$!34+`7)3Vq,\"F6$\"3!H!)zzzzzz$F6Fj_p7$F``p7$$!3V*3y_HIG,\"F
6$\"3#)za@,co*z$F67$7$Fe_p$\"3lkzzZ5)3!QF6Ff`p7$7$$!31l#HHHHHH*Fe]l$!3
CIYK'4qL)\\Fe]l7$$!3!f#Ho&*ppS(*Fe]l$!3G]\\\\\\\\\\\\\\Fe]l7$7$$!3,FHo
&*ppS(*Fe]lFhapFd_p7$F\\ap7$$!3#=9p')*)[]i*Fe]l$\"3=X&QLFP(=QF67$7$$!3
%REHHHHHH*Fe]l$\"3()e\\U!f7A$QF6F_bp7$7$Faap$!3oHYK'4qL)\\Fe]l7$$!3[`F
Kv#>=B*Fe]l$!3u>!*\\5()o()\\Fe]l7$7$$!3Kd%[[[[[[)Fe]l$!3ma5\"RFAj*\\Fe
]lF^cp7$7$FaapFhbp7$$!3gX6C'R1_7*Fe]l$\"3_Y=Wn@+QQF67$7$$!3J+TX7()GW))
Fe]l$\"3%R&[[[[[[QF6F[dp7$7$$!3?*4aCr)GW))Fe]lFddp7$$!3>:(3%z:n5')Fe]l
$\"3yp[*=z[j&QF67$7$Fecp$\"3#z<5JA84'QF6Fjdp7$Fdcp7$$!3rX^%HEJyS)Fe]l$
!3M>X=82j(*\\Fe]l7$7$$!3g\\wwwwwwwFe]l$!3g!*zNy]Li\\Fe]lFdep7$7$Fecp$
\"3Oy,6BK\"4'QF67$$!3'>9Pd)pJw!)Fe]l$\"3aZaH!ocM(QF67$7$F[fp$\"3EKqGs#
om)QF6Fcfp7$Fjep7$$!3O2;;P)>sl(Fe]l$!3'ps[#\\Brh\\Fe]l7$7$$!3@BM\">1kv
`(Fe]lFhapF]gp7$Fcgp7$$!3#e]4-7+X'pFe]l$!3W&G$Hn;h*)[Fe]l7$7$$!3'=%ooo
ooooFe]l$!3/J9&4JG8([Fe]lFggp7$Fifp7$$!3ugaR]7?SvFe]l$\"3gU;M(\\a/*QF6
7$7$$!3]Vp*yPtSD(Fe]l$\"3+0**)*)*)*)*)*QF6Fchp7$Fihp7$$!3=Lb;#\\)3&)pF
e]l$\"3]AtX+]E1RF67$7$F^hp$\"3*zD*[+Fk4RF6F_ip7$7$F^hp$!3gJ9&4JG8([Fe]
l7$$!3N#\\3(>'>+K'Fe]l$!3/9f0v9O(y%Fe]l7$7$$!37MgggggggFe]l$!3.h4]$>NR
s%Fe]lF\\jp7$Feip7$$!3ONS1Dub3kFe]l$\"3))H&o#fot?RF67$7$$!3CNgggggggFe
]l$\"3S`\"*)4tF(HRF6Fhjp7$Fbjp7$$!3zavun&R&=dFe]l$!3!\\*4[-gBeYFe]l7$7
$$!3SE_______Fe]l$!3]t,@n_2DXFe]lFd[q7$7$FcjpFa[q7$$!3Bv;!G$\\JCeFe]l$
\"3'G=2SvEZ$RF67$7$F[\\q$\"37TfK!ztw%RF6Fa\\q7$Fj[q7$$!3'oXP4b[p:&Fe]l
$!3F,o$H))zT]%Fe]l7$7$$!3is!R!RVgk\\Fe]lFjhoF[]q7$Fa]q7$$!3dMpAa(GVi%F
e]l$!3_s.$3v;?L%Fe]l7$7$$!36=WWWWWWWFe]l$!39)4=Q1:4D%Fe]lFe]q7$Fg\\q7$
$!3!='p-VL&*H_Fe]l$\"3U88:0U3[RF67$7$$!3-'\\(R<$\\t:&Fe]l$\"3;b
\\\\\\\\\\\\RF6Fa^q7$7$$!3#\\\\(R<$\\t:&Fe]lFj^q7$$!3pKcQ&*G2-YFe]l$\"
3E\"yywsY$fRF67$7$F\\^q$\"3/+l2'yFB'RF6F`_q7$7$$!3n=WWWWWWWFe]l$!3q)4=
Q1:4D%Fe]l7$$!3Ez5aP&3E7%Fe]l$!3xE&37QT09%Fe]l7$7$$!3-h<`$eg?o$Fe]lFef
oF_`q7$Fe`q7$$!3uFiN5XacOFe]l$!3Ga&[J*3yERFe]l7$7$$!3#)4OOOOOOOFe]l$!3
Ad[5\"[\\O\"RFe]lFi`q7$Ff_q7$$!3/EPioU@dRFe]l$\"3c77,9\"[&pRF67$7$F`aq
$\"3yI8nMzguRF6Feaq7$7$$!3E4OOOOOOOFe]lFbaq7$$!3^a-rnhv-KFe]l$!3d#y^A5
[`q$Fe]l7$7$$!3`,GGGGGGGFe]l$!39#=*GX<PtMFe]lFbbq7$F[bq7$$!3_S?n/X)\\H
$Fe]l$\"3M#GpU!QmyRF67$7$$!3(4!GGGGGGGFe]l$\"3)fe7s``X)RF6F^cq7$Fhbq7$
$!3!f&fD#[<6z#Fe]l$!3o8-hv<ddMFe]l7$7$$!3S`D_]LmZFFe]lF[boFjcq7$F`dq7$
$!3S7$H%3V3$Q#Fe]l$!3Ph8?/?a2KFe]l7$7$$!3:-t([DE&H?Fe]lFf_oFddq7$7$$!3
V-t([DE&H?Fe]lFf_o7$$!3(o:)*)4$Rd-#Fe]l$!3rFGBB@$e#HFe]l7$7$$!3C$*>???
???Fe]l$!3#4OKKS&H>HFe]lFaeq7$7$Fibq$\"3W'e7s``X)RF67$$!3Dg)RmcJ?h#Fe]
l$\"3q@t9'H%[')RF67$7$Fheq$\"3)Hf!)Gt&3#*RF6F`fq7$Fgeq7$$!3%)HV:yLrb;F
e]l$!3=:A_Dy/_EFe]l7$7$$!3[U;+S^`09Fe]lFd]oFjfq7$F`gq7$$!3qC3JoA7P8Fe]
l$!3'3!R7kn6YBFe]l7$7$$!34&=@@@@@@\"Fe]l$!3))yC#H!y:i@Fe]lFdgq7$Fffq7$
$!3oI#4[n-Y!>Fe]l$\"3UdH\"4/vF*RF67$7$F[hq$\"33&3kCuUr*RF6F`hq7$Fjgq7$
$!3^)o9iS2p-\"Fe]l$!3i![$)ya]\\.#Fe]l7$7$$!3m\"f4^[]/'))F_]nFcjnFjhq7$
7$$!31$f4^[]/'))F_]nFcjn7$$!3rQ%4a(=G4sF_]n$!32mS]aq8@<Fe]l7$7$$!3#*3U
<D#p6<&F_]nF[hnFgiq7$F]jq7$$!36wof0%Q,$\\F_]n$!3/YoJ;I`e8Fe]l7$7$$!3Wp
PSSSSSSF_]n$!39W)*\\R='z1\"Fe]lFajq7$Ffhq7$$!3s;9so(*[o6Fe]l$\"3#)>vyM
IF(*RF67$7$Fhjq$\"3?L)RB2#o**RF6F][r7$7$Fhjq$!3EW)*\\R='z1\"Fe]l7$$!3=
5/'Q:p%)\\\"F_]n$!3]q)*\\R='z1\"Fe]l7$7$$\"317VSSSSSSF_]n$!3GJ**\\R='z
1\"Fe]lFj[r7$Fc[r7$$!3=7ix9c`*)RF_]nFd[r7$7$Fa\\rFd[rFf\\r7$7$$\"3AR77
77777Fe]l$!3!p`AH!y:i@Fe]l7$$\"3KS&4^[]/'))F_]nFcjn7$Fa]r7$$\"3Wu,ow!)
zMiF_]n$!3qc'39/\"H^:Fe]l7$7$$\"3?.W<D#p6<&F_]nF[hnFe]r7$F[^rF`\\r7$Fj
\\r7$$\"3;sy*GjJQ4%F_]n$\"3#3#paxgm**RF67$7$F]]r$\"3i%3kCuUr*RF6F`^r7$
7$$\"3lZ???????Fe]l$!3)3TKKS&H>HFe]l7$$\"3U\\;+S^`09Fe]lFd]o7$F__r7$$
\"3OR7777777Fe]lF_]r7$7$Fd_rFg^r7$$\"3-.N!3z&oi7Fe]l$\"3#ROKQrRo*RF67$
7$F[_r$\"3a#f!)Gt&3#*RF6Fh_r7$7$$\"3$f&GGGGGGGFe]l$!357#*GX<PtMFe]l7$$
\"3GZD_]LmZFFe]lF[bo7$Fg`r7$$\"3*4Dfy<yE6#Fe]l$!3W#oGy_!4()HFe]l7$7$$
\"3?5t([DE&H?Fe]lFf_oF[ar7$7$$\"3[5t([DE&H?Fe]lFf_oFj^r7$F^`r7$$\"3#yG
cjQ>\"o@Fe]l$\"3Sl`hk^v!*RF67$7$Fc`rFgcqFiar7$Fb`r7$$\"3Ebnu0d*>H$Fe]l
$!3Cs$eF)R;CPFe]l7$7$$\"3AkOOOOOOOFe]l$!3k')[5\"[\\O\"RFe]lFabr7$7$Fc`
r$\"3a&e7s``X)RF67$$\"34UdqXm9MJFe]l$\"3yu5T6N)3)RF67$7$Fhbr$\"3MI8nMz
guRF6F`cr7$7$$\"3'>ZWWWWWW%Fe]l$!3C>\"=Q1:4D%Fe]l7$$\"3!QwJNeg?o$Fe]lF
efo7$F_drFgbr7$Ffcr7$$\"3SwC#p'*[4<%Fe]l$\"3ez+%oT)emRF67$7$$\"3^sWWWW
WWWFe]l$\"3;*\\wgyFB'RF6Fddr7$7$$\"3!3GDDDDDD&Fe]l$!3\\)=5sEv]_%Fe]l7$
$\"3]r!R!RVgk\\Fe]lFjho7$7$$\"31s!R!RVgk\\Fe]lFjhoFjcr7$7$Faer$\"3CSfK
!ztw%RF67$$\"3!Q\\(R<$\\t:&Fe]lFj^q7$F`fr7$F[drF]er7$7$Faer$!3%z=5sEv]
_%Fe]l7$$\"3_0k<(\\[([aFe]l$!3%yR^B(R3nXFe]l7$7$$\"3_)3111111'Fe]l$!3p
s4]$>NRs%Fe]lFifr7$7$Faer$\"3!)RfK!ztw%RF67$$\"3'>qv&)oypH&Fe]l$\"3//=
u4mrYRF67$7$F`gr$\"3^_\"*)4tF(HRF6Fhgr7$F_gr7$$\"3EhEa*Hiin'Fe]l$!3V-)
zPfH#H[Fe]l7$7$$\"3E'*oooooooFe]l$!3#)Q9&4JG8([Fe]lFbhr7$F^hr7$$\"3]LC
IR.1#e'Fe]l$\"33Lk2dS!p\"RF67$7$Fihr$\"3mc#*[+Fk4RF6F^ir7$7$$\"350xwww
wwwFe]l$!3/&*zNy]Li\\Fe]l7$$\"3wGM\">1kv`(Fe]lFhap7$F]jrFhhr7$7$$\"3+/
xwwwwwwFe]l$\"3QJqGs#om)QF67$$\"31\\p*yPtSD(Fe]lF\\ip7$7$Fhjr$\"3a/**)
*)*)*)*)*QF67$$\"3;&*oooooooFe]lFeir7$7$FcjrF[jr7$$\"35VrCn:r'p(Fe]l$!
3u*fW5))f>'\\Fe]l7$7$$\"3i5&[[[[[[)Fe]l$!3wb5\"RFAj*\\Fe]lFc[s7$7$Fcjr
$\"3%4.(Gs#om)QF67$$\"3QL(\\a@4S2)Fe]l$\"3exA#GIiT(QF67$7$Fj[s$\"39w,6
BK\"4'QF6Fb\\s7$Fi[s7$$\"3/-9AL(R9b)Fe]l$!3e1!G(zW6\"*\\Fe]l7$7$$\"3M=
$HHHHHH*Fe]l$!3!piCj4qL)\\Fe]lF\\]s7$7$$\"3Y>$HHHHHH*Fe]l$\"3lc\\U!f7A
$QF67$$\"3J+TX7()GW))Fe]lFddp7$F]^sFh\\s7$7$Fi]sFe]s7$$\"3R.`Y?B8P$*Fe
]l$!3mS\\qT=7x\\Fe]l7$7$$\"38=Ho&*ppS(*Fe]lFhapFc^s7$Fi^s7$$\"3]$G\\2#
=#e+\"F6$!3)>kYg,]F#\\Fe]l7$7$$\"3$G,,,,,,,\"F6$!3[4'34fIA#\\Fe]lF]_s7
$7$Fi]s$\"35d\\U!f7A$QF67$$\"33_$[w6xb(**Fe]l$\"3M9*R%f$>e!QF67$7$Fd_s
$\"3VizzZ5)3!QF6F\\`s7$Fc_s7$$\"3sY3%3nZ62\"F6$!3'zSoS2')f#[Fe]l7$7$$
\"3q$4444444\"F6$!3'H'HRbF<5[Fe]lFf`s7$7$F]as$\"3!*HO0[3ylPF67$$\"3J+`
7)3Vq,\"F6$\"3M.)zzzzzz$F67$Feas7$Fd_s$\"3*>'zzZ5)3!QF67$7$F]as$!3_jHR
bF<5[Fe]l7$$\"3#\\[DutsN8\"F6$!3!)*)=<NA46ZFe]l7$7$$\"3gurrrrrr6F6$!3s
zty<k1aYFe]lFbbs7$7$Fibs$\"3$zdhqAWxs$F67$$\"3KDbQ&f)fI6F6Fa^p7$FacsFb
as7$Fhbs7$$\"3!eqQYq-U>\"F6$!3o:S?D!z\\e%Fe]l7$7$$\"3[b______7F6$!3%
\\hSPKPnX%Fe]lFfcs7$7$F]ds$\"3'yNuCWGko$F67$$\"3n=>cOzYK7F6$\"3m,(pppp
pp$F67$7$Ffds$\"37-(pppppp$F6F^cs7$7$F]ds$!3Q91uBttcWFe]l7$$\"3amBtLdu
`7F6$!3C)))))>Xs?X%Fe]l7$7$$\"3=u\\iP*pjD\"F6FjhoFbes7$Fhes7$$\"3/afoi
=%eI\"F6$!3=0$)*GvAEF%Fe]l7$7$$\"3POLLLLLL8F6$!3Qy2YX*4D?%Fe]lF\\fs7$7
$$\"3fOLLLLLL8F6$\"3C8^W\\U\\TOF67$$\"3M=<!H[gYK\"F6$\"33^YYYYYYOF67$7
$$\"3c=<!H[gYK\"F6FgioFbds7$7$Fifs$!3%*y2YX*4D?%Fe]l7$$\"33G8+OKIe8F6$
!3A)))o5$eX&4%Fe]l7$7$$\"3\\*)H\"Q%*z_S\"F6FefoFjgs7$F`hs7$$\"3pexi8!4
2T\"F6$!3guN=O9%z\"RFe]l7$7$$\"3D<9999999F6$!3*z*)Qb'zq2RFe]lFdhs7$7$F
[is$\"3C\\*[MX9Ef$F67$$\"3!pzB4)yw39F6$\"3M,'ffffff$F67$Fcis7$FcfsF[gs
7$Fjhs7$$\"3y'Hh@PyoX\"F6$!3,$on>U\\9q$Fe]l7$7$$\"3O)\\\\\\\\\\\\\\\"F
6$!3m)y'>e(zib$Fe]lF[js7$7$$\"39)\\\\\\\\\\\\\\\"F6$\"3\"G=nX7#[RNF67$
$\"3-y`awn3'[\"F6$\"3u]XXXXXXNF67$7$$\"3!yPXlx'3'[\"F6F`eoF`is7$7$Fhjs
Fdjs7$$\"3R,$HH&z;0:F6$!3S0sr'z3#)\\$Fe]l7$7$$\"3k?9f'*\\&*=:F6F[boFg[
t7$F]\\t7$$\"3cnNhUlJ\\:F6$!3]kL>xp3pKFe]l7$7$$\"3Czvvvvvv:F6$!3?CrBbU
=`JFe]lFa\\t7$7$$\"3!)yvvvvvv:F6$\"3wZ#fes<=[$F67$$\"3)\\0k&o/qd:F6F_c
o7$7$$\"3?bSco/qd:F6F[coFgjs7$7$$\"3-zvvvvvv:F6$!3kBrBbU=`JFe]l7$$\"3O
mOd$4ENf\"F6$!3:xMklhMSIFe]l7$7$$\"3>?v^Lfm9;F6Ff_oF_^t7$Fe^t7$$\"3g`6
*GF+ej\"F6$!3QlsK\"G4&*z#Fe]l7$7$$\"3!*fcccccc;F6$!3!3RSVNK\\p#Fe]lFi^
t7$7$$\"37gcccccc;F6$\"3#QEv3Vu$>MF67$$\"3KN]rpM`C;F6$\"3_\\WWWWWWMF67
$7$F[`tFc`o7$F[^t$\"3?[#fes<=[$F67$7$$\"3ofcccccc;F6Fb_t7$$\"3'o*GV3v%
on\"F6$!3YcET)*R+^DFe]l7$7$$\"3eG(Q%)*z8)p\"F6Fd]oFh`t7$F^at7$$\"3ty*R
b5`nr\"F6$!3m89GvMO&H#Fe]l7$7$$\"3zSPPPPPP<F6$!3Kp?d9tHw@Fe]lFbat7$7$$
\"3,TPPPPPP<F6$\"3].\"QK-T>N$F67$$\"3wU%**3$yQ(o\"F6$\"3!*)RRRRRRR$F67
$Fcbt7$F`_tFh_t7$Fhat7$$\"3kfg3:>^b<F6$!339R*)HbbK?Fe]l7$7$$\"37hr4qoL
s<F6FcjnF[ct7$Fact7$$\"3_D4*[6RFz\"F6$!3A>QiB]<g<Fe]l7$7$$\"3!>#======
=F6$!3?>O)G.IAf\"Fe]lFect7$7$$\"3n@=======F6$\"3y-U_#[w#yKF67$$\"3RYMh
+BV-=F6Fc[o7$7$$\"3hYMh+BV-=F6Fc[o7$$\"3ewhuS6xo<F6$\"3evlKm4\"QK$F67$
7$$\"3%4G'3'3npu\"F6F_\\oF]et7$7$$\"3;\"G'3'3npu\"F6F_\\oF^bt7$F[dt7$$
\"3.@+SQL)*H=F6$!3!4;0b\"4!z[\"Fe]l7$7$$\"3h\"G'QhmnR=F6F[hnF[ft7$Faft
7$$\"3MPn*yrxV'=F6$!3_M\"4BG:y>\"Fe]l7$7$$\"3a-**)*)*)*)*)*=F6$!3ul$[!
G..v$*F_]nFeft7$7$F\\gt$\"3!H:[!>ME)>$F67$$\"37FJBflga=F6F^in7$7$$\"3M
FJBflga=F6F^inFadt7$7$$\"3K-**)*)*)*)*)*=F6F^gt7$$\"3ct<,%ya2!>F6$!3IQ
gx/W@,#*F_]n7$7$$\"3gFBIT8/->F6F^dnF_ht7$Feht7$$\"3b?z@C>GK>F6$!3mg^:<
c:@hF_]n7$7$$\"3avQ!p(ykc>F6FjdnFiht7$F_it7$$\"3i8jb>#yc'>F6$!3My'*HD!
>z:$F_]n7$7$$\"3m$)zzzzzz>F6$!390@3*yB*e>F_]nFcit7$7$$\"3A$)zzzzzz>F6$
\"3!3.FD,.-6$F67$$\"3g/&*yPDW^>F6Fjen7$Fdjt7$$\"3B'4V$HYh8>F6$\"3-]%[a
tyF=$F67$7$$\"3V64[v$4]!>F6FffnFhjt7$7$F_[u$\"3e&>>>>>>>$F67$F]ht$\"3Y
_\"[!>ME)>$F67$7$Fjit$!3![5#3*yB*e>F_]n7$$\"3QUiHZ)>q*>F6$!3#H3>S&3dEm
!#@7$7$$\"3RAeW=q:3?F6Fd`nF\\\\u7$Fc\\u7$$\"3mo(z#Q2:F?F6$\"3)eX%\\b'e
55$F_]n7$7$$\"35V/(=6:x0#F6F`anFg\\u7$7$F^]u$\"3!p/111111'F_]n7$$\"3ge
l=q<we?F6$\"3Sm^#=@ue<'F_]n7$7$$\"35kgggggg?F6$\"335T!)=CkajF_]nFd]u7$
7$F[^u$\"38P2MTAW8IF67$$\"3-j!Rq_%[Q?F6$\"3mWSSSSSSIF67$7$Fd^uF]bn7$$
\"3![yLu7%4:?F6$\"37>nj)**[)oIF67$7$$\"3eR\"pQy(H'*>F6$\"3Q%4444444$F6
Fj^u7$7$$\"3!)R\"pQy(H'*>F6FibnF_jt7$Fj]u7$$\"3en7GK2:'3#F6$\"3B))3TJ
\"pX^*F_]n7$7$$\"3vp!34bm15#F6Fc]nFj_u7$F``u7$$\"3U?fkY3G9@F6$\"3%H^7M
?%p!G\"Fe]l7$7$$\"3*\\9999999#F6$\"3g#*Rc`Kf\"e\"Fe]lFd`u7$7$F[au$\"39
m#[0iJg!HF67$$\"3sAHL2Vs;@F6$\"3WVRRRRRRHF67$7$$\"3FAHL2Vs;@F6Fc^n7$$
\"3A/UcA0c&4#F6$\"3/c^<^C0oHF67$7$$\"33zz.OCty?F6$\"3;$**)*)*)*)*)*)HF
6F\\bu7$7$FcbuF__nF`^u7$Fj`u7$$\"3-tepF@8V@F6$\"3q93!>?Cag\"Fe]l7$7$$
\"3>%*3d#R%*R9#F6F[hmFjbu7$F`cu7$$\"3!4]AZgy!o@F6$\"3?'*[`D#fX&>Fe]l7$
7$$\"3IHo5@vE\"=#F6F]imFdcu7$Fjcu7$$\"3WUCcpew$>#F6$\"3gndLDV1*H#Fe]l7
$7$$\"3C&e**)>mF>AF6FhimF^du7$Fddu7$$\"3va$4dmn,A#F6$\"3\"*p!oWg.\"REF
e]l7$7$$\"3(eAAAAAAA#F6$\"3_rq'\\Ujem#Fe]lFhdu7$7$F_eu$\"3'[*=Shcf&y#F
67$$\"3i%)4Lhtw?AF6Fejm7$Fgeu7$$\"3G*))><i<)>AF6$\"3%>v#>j;Q*y#F67$7$$
\"3/D&oD3hr=#F6Fa[nF[fu7$Fafu7$$\"3=zUW$z,C;#F6$\"3Ye+P1;xvGF67$7$$\"3
-zFUz1G`@F6$\"3%>*))))))))))))GF6Fefu7$7$F\\guF]\\nF`au7$F^eu7$$\"3n^X
J)*\\.VAF6$\"3_#4O2GL7+$Fe]l7$7$$\"3O8JJx*3>D#F6F[dmFcgu7$Figu7$$\"3+g
#*H/9+mAF6$\"3%4<#Q[PuiLFe]l7$7$$\"3MH]Or=E%G#F6F[emF]hu7$7$$\"3yH]Or=
E%G#F6Fgdm7$$\"3UPc`2HO*G#F6$\"3o=`?e[y@PFe]l7$7$$\"3w1......BF6$\"3]q
/-hOMJRFe]lFjhu7$7$Faiu$\"3/\\Fu>s/ZEF67$$\"3O'H=?8\"H!G#F6Fgem7$Fiiu7
$$\"3)==UU]5zE#F6$\"31o76h&=)3FF67$7$$\"3k!f<=\")33D#F6FffmF]ju7$7$$\"
33\"f<=\")33D#F6FffmFdeu7$F`iu7$$\"3eoyqYyX6BF6$\"3%*y$HM*>u)3%Fe]l7$7
$$\"3c*\\[7$G_9BF6$\"3LSTTTTTTTFe]lF[[v7$Fa[v7$$\"3'y6)o%pn:L#F6$\"3WE
Lg[f5oWFe]l7$7$$\"3\\j!*foUkTBF6Fi^mFg[v7$7$F^\\vFe^m7$$\"3w'HP_$*4=N#
F6$\"3!RY@-XUm%[Fe]l7$7$$\"3)*G^%=#f]oBF6Fd_mFb\\v7$Fh\\v7$$\"3!)pM\"[
.@@P#F6$\"3=')3#He[ZA&Fe]l7$7$$\"3k(QQQQQQQ#F6$\"3sv%zukzeW&Fe]lF\\]v7
$7$Fc]v$\"3A5w\"QfEW[#F67$$\"3!y*[o#yXOQ#F6Fb`m7$F[^v7$$\"3!3Vp?1rNQ#F
6$\"3/'3a4c:][#F67$7$$\"3/YU6pQBfBF6F^amF_^v7$7$$\"3gXU6pQBfBF6F^am7$$
\"3Irk>X2&)[BF6$\"3=OZ]43AdDF67$7$$\"3_Y$pLgQUL#F6FjamF\\_v7$Fb_v7$$\"
3r$\\\"\\\"GW:J#F6$\"37(RD)*RU5j#F67$7$$\"3^[rLoxo3BF6FfbmFf_v7$7$$\"3
&*[rLoxo3BF6Ffbm7$Faiu$\"3g[Fu>s/ZEF67$Fb]v7$$\"3e@R:1Z7\"R#F6$\"34oN4
Uh-6cFe]l7$7$$\"3![0=uhuKR#F6FgflFg`v7$F]av7$$\"3VzJqjjF3CF6$\"3S57Y(y
y)3gFe]l7$7$$\"3%*GZ;uD?:CF6FgglFaav7$Fgav7$$\"3&zA=55!HDCF6$\"3PkEHMM
f2kFe]l7$7$$\"3ox0v3caOCF6FbhlF[bv7$Fabv7$$\"3^%QP$=')4UCF6$\"3kQ%)412
f2oFe]l7$7$$\"3UD&ykZ5sX#F6$\"3ErrrrrrrrFe]lFebv7$7$F\\cvF^il7$$\"3OkH
#pGI'eCF6$\"3#*o!*[#G=$4sFe]l7$7$$\"3aokkkkkkCF6$\"3o6I_N8dhtFe]lFbcv7
$7$Ficv$\"3)*35w*oD<G#F67$$\"3'Q_Jt\")eUY#F6F^jl7$Fadv7$$\"3io!30``TY#
F6$\"3/&ykmOOJG#F67$7$$\"3KbvM/m?XCF6FjjlFedv7$F[ev7$$\"3J0Ti?:SRCF6$
\"3%HJZLU6\"\\BF67$7$$\"3k1-<q)*RDCF6Ff[mF_ev7$Feev7$$\"3&R\"***p6xDT#
F6$\"3#H[<hs\"Q;CF67$7$$\"3!=mG3?v[S#F6Fb\\mFiev7$F_fvFh]v7$7$Ficv$\"3
e5I_N8dhtFe]l7$$\"3IMA#y<dLZ#F6$\"3RP\">%>dKAwFe]l7$7$$\"3G3ai,\"e_Z#F
6Fi]lFgfv7$F]gv7$$\"3e)o-_6oo[#F6$\"3A/=%e'G$H/)Fe]l7$7$$\"3ex'*y1+W\"
\\#F6$\"35!=======)Fe]lFagv7$Fggv7$$\"3[hkvyA'**\\#F6$\"3%=B\"o[[9m%)F
e]l7$7$$\"39IGFd%zn]#F6Fa_lF]hv7$Fchv7$$\"3LyikJ^d7DF6$\"3#*z.<B]O#*))
Fe]l7$7$$\"3_.G$R\\27_#F6F]`lFghv7$7$$\"33.G$R\\27_#F6Fa`l7$$\"3)R-@A.
TY_#F6$\"3>E(G'\\O+A$*Fe]l7$7$$\"3e(R;\")zdY`#F6F\\alFdiv7$Fjiv7$$\"33
9.fjQ4ODF6$\"3uk6ieRZb(*Fe]l7$7$$\"3U\\XXXXXXDF6$\"35.,'\\bPO,\"F6F^jv
7$7$Fejv$\"3)Rb&epLz#*>F67$$\"3X!)3&)p>yODF6F\\bl7$7$$\"3*3)3&)p>yODF6
F\\bl7$$\"3**Rc!H\\y``#F6$\"3Q+h9j0gO?F67$7$$\"3'*yR!H/mS_#F6F[clFd[w7
$Fj[w7$$\"3o!>C0ma,_#F6$\"3'ob*))30i'4#F67$7$$\"3;0i],DU5DF6FjclF^\\w7
$Fd\\w7$$\"32<%**pl]K]#F6$\"3?\"f(fh0pd@F67$7$$\"3Us[8C&*)e\\#F6FfdlFh
\\w7$F^]w7$$\"37I;v6!=Y[#F6$\"3x3DQ:5%)>AF67$7$$\"3/z&zw2/0[#F6FbelFb]
w7$Fh]wF^dv7$Fdjv7$$\"3C1&)=#y!oYDF6$\"3)pHVAiN%>5F67$7$$\"3Y<*f,1Voa#
F6F<F]^w7$Fc^w7$$\"3]UKFl^RbDF6$\"3#yQ?L=%\\k5F67$7$$\"3mJw*[#4ecDF6FH
Fg^w7$F]_w7$$\"3CeNOF#GMc#F6$\"3\"3**=+dy*46F67$7$$\"3[=H(HrM`c#F6FTFa
_w7$7$$\"3#*=H(HrM`c#F6FT7$$\"3ArnBZcsqDF6$\"3I$G.JtAf:\"F67$7$$\"3a\"
e@.PoId#F6FcoF^`w7$7$$\"33\"e@.PoId#F6$\"3qrrrrrrr6F67$$\"35aT`YSBxDF6
$\"3Qpu/M+O-7F67$7$$\"35/wRI1vzDF6F^pF]aw7$Fcaw7$$\"3sJOX$H,He#F6$\"3q
YyAbIK\\7F67$7$$\"31;?(RMb`e#F6FjpFgaw7$F]bw7$$\"3-)*H&*\\nn(e#F6$\"3K
$z?aWVoH\"F67$7$$\"3occj'ph)*e#F6FfqFabw7$7$$\"3Cccj'ph)*e#F6Ffq7$$\"3
g+;)fX6:f#F6$\"3#y'zl/=&\\M\"F67$7$$\"357V+7VD$f#F6$\"3eutttttt8F6F^cw
7$7$FecwFbr7$$\"3kl3UY#eVf#F6$\"3Ux%Q6hxOR\"F67$7$$\"3AG#QHCBbf#F6$\"3
vCCCCCCC9F6F[dw7$7$FbdwF^s7$$\"3'H_4')zrhf#F6$\"3&phD:>\\IW\"F67$7$$\"
3=%3Xq&Qm'f#F6$\"3Ovuuuuuu9F6Fhdw7$7$$\"3i%3Xq&Qm'f#F6Fjs7$$\"3eAmV5'3
pf#F6$\"3uI(QYt$4$\\\"F67$7$$\"3%[xJhiwmf#F6F\\uFgew7$7$F^fwFft7$$\"3S
s!)*3\"p_'f#F6$\"3fu`NZt$Qa\"F67$7$$\"3_@t&>$oc&f#F6$\"3-xvvvvvv:F6Fbf
w7$7$FifwFgu7$$\"3U@^k1l)\\f#F6$\"31?&=0:0`f\"F67$7$$\"3O]9`-UM$f#F6$
\"3jFEEEEEE;F6F_gw7$7$$\"3#*\\9`-UM$f#F6Fcv7$$\"3mxeMp&[Af#F6$\"3I)fN=
T@vk\"F67$7$$\"3YK\"yU\\A+f#F6$\"3Cywwwwww;F6F^hw7$7$FehwF_w7$$\"3+U+g
p`F)e#F6$\"3.'z\"=7(40q\"F67$7$$\"3q'=vc.>ce#F6FbxF[iw7$7$FbiwF^x7$$\"
3OrToj*HIe#F6$\"3_lUQTJHa<F67$7$$\"3I45dZU:!e#F6$\"3-zxxxxxx<F6Ffiw7$F
\\jw7$$\"3+jSdReZwDF6$\"3%Q8e%>X*)3=F67$7$$\"3#\\[#Qa6ltDF6$\"31IGGGGG
G=F6Fbjw7$7$$\"3[%[#Qa6ltDF6F\\z7$$\"3'=,C&GldoDF6$\"3[m%p$RmLk=F67$7$
$\"3)4nG*)*[8mDF6FhzFa[x7$Fg[x7$$\"3+fT-)=&HfDF6$\"3BDpoFDk?>F67$7$$\"
3M)*R*=FKwb#F6$\"3%3$HHHHHH>F6F[\\x7$Fa\\x7$$\"3=*ee7;%f[DF6$\"3/d/#*>
d$y(>F67$7$$\"31'oy\\Er\"[DF6Fd\\lFg\\x7$7$F^]x$\"3!>)zzzzzz>F6Fjjv-%&
COLORG6&%$RGBG$\"\"!!\"\"Fh]xFh]x-F06$7S7$$!\"%Fi]x$\"3+;LN6i2)4*F67$$
!3ommmmFiDQF6$\"38$)*>!y*)pB*)F67$$!35LLLo!)*Qn$F6$\"37\\mozU(>x)F67$$
!3nmmmwxE.NF6$\"3B#)*>!))RM,')F67$$!3YmmmOk]JLF6$\"3Z#)*>![EeH%)F67$$!
3_LLL[9cgJF6$\"3m[mofwje#)F67$$!3smmmhN2-IF6$\"3H#)*>Ix\\,5)F67$$!3!**
****\\`oz$GF6$\"3\"fJ`juWg$zF67$$!3!omm;)3DoEF6$\"3E$)*>I4Fjw(F67$$!3?
+++:v2*\\#F6$\"3w:LNEP:(f(F67$$!3BLLL8>1DBF6$\"3C\\moC\"QJU(F67$$!3kmm
mw))yr@F6$\"3m#)*>!)3l)psF67$$!3;+++S(R#**>F6$\"3;;LN^fJ(4(F67$$!30+++
+@)f#=F6$\"31;LN6$eS#pF67$$!3-+++gi,f;F6$\"3g:LNrC4dnF67$$!3qmmm\"G&R2
:F6$\"3r#)*>I\\rag'F67$$!3XLLLtK5F8F6$\"3!*\\mo%[z^U'F67$$!3eLLL$HsV<
\"F6$\"3g\\mo/&[CF'F67$$!3+-++]&)4n**Fe]l$\"3k;LNmgy%4'F67$$!37PLLL\\[
%R)Fe]l$\"3<]mo/Z_PfF67$$!3G)*****\\&y!pmFe]l$\"3%eJ`j1%)\\w&F67$$!3Y*
*****\\O3E]Fe]l$\"3S;LNwXo+cF67$$!3NKLLL3z6LFe]l$\"3p\\mo%Hb#HaF67$$!3
sLLL$)[`P<Fe]l$\"3Q\\mo*pH=F&F67$$!3gSnmmmr[R!#?$\"3v#)*>!G\\--^F67$$
\"3yELL$=2Vs\"Fe]l$\"3L$)*>I\\Xc#\\F67$$\"3)e*****\\`pfKFe]l$\"3U;LNwm
5sZF67$$\"36HLLLm&z\"\\Fe]l$\"35$)*>![0G1YF67$$\"3>(******z-6j'Fe]l$\"
3H;LNJf'\\V%F67$$\"3q\"******4#32$)Fe]l$\"3%oJ`8+otE%F67$$\"3r$*****
\\#y'G**Fe]l$\"3k;LN'Q3_5%F67$$\"3G******H%=H<\"F6$\"3s;LN\"yd^#RF67$$
\"35mmm1>qM8F6$\"3#*\\mo/VPjPF67$$\"3%)*******HSu]\"F6$\"3;;LN6fj!f$F6
7$$\"3'HLL$ep'Rm\"F6$\"3/$)*>ID4TV$F67$$\"3')******R>4N=F6$\"39;LNrU)H
E$F67$$\"3#emm;@2h*>F6$\"3>]mo***o>5$F67$$\"3]*****\\c9W;#F6$\"3];LNY;
mLHF67$$\"3Lmmmmd'*GBF6$\"3o\\moW/6pFF67$$\"3j*****\\iN7]#F6$\"3Q;LN'e
Sof#F67$$\"3aLLLt>:nEF6$\"3Z#)*>!QU#4V#F67$$\"35LLL.a#o$GF6$\"3!H)*>!3
3DhAF67$$\"3ammm^Q40IF6$\"3Y\\mofB)H4#F67$$\"3y******z]rfJF6$\"3A;LNJ6
OQ>F67$$\"3gmmmc%GpL$F6$\"3U\\moax9h<F67$$\"3/LLL8-V&\\$F6$\"3)H)*>!)*
fk-;F67$$\"3=+++XhUkOF6$\"3#eJ`j1]OV\"F67$$\"3=+++:o<EQF6$\"3%eJ`jR**=
F\"F67$$\"\"%Fi]x$\"3+;LN6i2)4\"F6-Fe]x6&Fg]x$F-Fj]xFh]xFh]x-%%VIEWG6$
;$!#SFj]x$\"#SFj]x;$!#5Fj]x$\"#]Fj]x" 1 2 2 1 10 1 2 6 1 4 2 1.0 45.0 
45.0 1 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 
1 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}{PARA 0 "" 0 "" 
{TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" 
{TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" 
{TEXT 276 3 "   " }{TEXT 261 9 "Exercises" }}{PARA 0 "" 0 "" {TEXT 
276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 37 " 1.  Given the equation      \+
        " }{XPPEDIT 18 0 "x*cos(Pi*y) = (x+y)^2;" "6#/*&%\"xG\"\"\"-%$
cosG6#*&%#PiGF&%\"yGF&F&*$),&F%F&F,F&\"\"#F&" }{TEXT 276 1 " " }}
{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 48 "   (a) \+
  Plot a graph of the equation  for   -8 " }{TEXT 262 1 "<" }{TEXT 
276 2 "  " }{TEXT 263 1 "x" }{TEXT 276 2 "  " }{TEXT 264 1 "<" }{TEXT 
276 10 " 8 ,   -5 " }{TEXT 265 1 "<" }{TEXT 276 2 "  " }{TEXT 266 1 "y
" }{TEXT 276 2 "  " }{TEXT 267 1 "<" }{TEXT 276 5 " 6  ." }}{PARA 0 ""
 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 36 "   (b)   Verify t
hat the point  P = " }{TEXT 268 2 "( " }{XPPEDIT 18 0 "(23+sqrt(129))/
12;" "6#*&,&\"#B\"\"\"-%%sqrtG6#\"$H\"F&F&\"#7!\"\"" }{TEXT 276 5 "  ,
  " }{TEXT 203 1 " " }{XPPEDIT 18 0 "-5/3;" "6#,$*&\"\"&\"\"\"\"\"$!\"
\"F(" }{TEXT 203 2 "  " }{TEXT 269 1 ")" }{TEXT 276 34 "  is on the gr
aph of the equation." }{MPLTEXT 1 0 1 " " }}{PARA 0 "" 0 "" {TEXT 276 
0 "" }}{PARA 0 "" 0 "" {TEXT 276 13 "   (c)   Use " }{TEXT 270 5 "Mapl
e" }{TEXT 276 10 " to find  " }{XPPEDIT 18 0 "dy/dx;" "6#*&%#dyG\"\"\"
%#dxG!\"\"" }{TEXT 276 3 "  ." }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" 
{TEXT 276 62 "   (d)   Find the slope of the tangent line to the curve
 at P." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 276 
75 "   (e) Plot the graph of the curve and the tangent on the same set
 of axes." }}{PARA 0 "" 0 "" {TEXT 276 0 "" }}{PARA 0 "" 0 "" {TEXT 
276 24 "2.)  Given the equation " }}{PARA 0 "" 0 "" {TEXT 276 16 "    \+
            " }{XPPEDIT 18 0 "y^4-4*y^2 = x^4-9*x^2;" "6#/,&*$)%\"yG\"
\"%\"\"\"F)*&F(F)*$)F'\"\"#F)F)!\"\",&*$)%\"xGF(F)F)*&\"\"*F)*$)F2F-F)
F)F." }{TEXT 276 23 ",    P=(3,2) ,      -5 " }{TEXT 271 2 "< " }{TEXT
 276 2 "x " }{TEXT 272 1 "<" }{TEXT 276 8 "5 ,  -5 " }{TEXT 273 1 "<" 
}{TEXT 276 3 " y " }{TEXT 274 1 "<" }{TEXT 276 1 " " }{TEXT 203 2 "5,"
 }}{PARA 13 "" 0 "" {TEXT 278 0 "" }}{PARA 0 "" 0 "" {TEXT 276 39 "   \+
   do a), b), c) , d), e.) and also:" }}{PARA 0 "" 0 "" {TEXT 276 108 
"     (f)  Solve the equation for y. There will be four solutions, eac
h a function of x. Determine which part" }}{PARA 0 "" 0 "" {TEXT 276 
283 "          of the graph of the equation is the graph of each of th
ese four equations.  Plot all four solutions on the same              \+
                      graph in different colors.    (If you print out \+
on a non-color printer make a seperate graph for each of the four func
tions.) " }}{PARA 0 "" 0 "" {TEXT 276 2 "  " }}{PARA 13 "" 0 "" {TEXT 
278 0 "" }}{PARA 0 "" 0 "" {TEXT 276 6 "      " }}}
{MARK "0 0 0" 0 }{VIEWOPTS 0 0 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 
33 1 1 }