{VERSION 14 0 "Windows 7" "14.0" } {USTYLETAB {PSTYLE "Ordered List 1" -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 3 3 2 0 2 0 2 2 -1 1 } {PSTYLE "Ordered List 2" -1 201 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 }{PSTYLE "Ordered List 3" -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 72 2 0 2 2 -1 1 }{PSTYLE "Ordered List 4" -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 2 108 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -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 2 144 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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier New" 1 12 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 "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 "Fixed Width" -1 17 1 {CSTYLE "" -1 -1 "C ourier" 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 "Maple 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 "Line Printe d Output" -1 6 1 {CSTYLE "" -1 -1 "Courier New" 1 12 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 "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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "C ourier New" 1 12 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 "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier New" 1 12 40 120 40 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 "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 "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 "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 "HyperlinkError" -1 206 1 {CSTYLE "" -1 -1 "Courier New" 1 12 255 0 255 1 2 2 1 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier New" 1 12 255 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 "Title" -1 18 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 "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 "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 "Heading 4 " -1 20 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 14 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 16 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 "Hyperlink Warning" -1 207 1 {CSTYLE "" -1 -1 "Courier New" 1 12 0 0 255 1 2 2 1 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified M aple 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 "List 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 }{CSTYLE "Annotation Text" -1 200 "Times" 1 12 0 0 0 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 "2D Math Bold" -1 5 "Times" 1 12 0 0 0 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 "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 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 "Plot Text" -1 28 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Nonterminal" -1 24 "Couri er" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "Ti mes" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic" -1 42 "Ti mes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 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 Italic Bold" -1 40 "Times" 1 12 0 0 0 1 1 2 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 "Help Underlined \+ Italic" -1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier New" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 1 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 Small" -1 7 "Times" 1 1 0 0 0 1 2 2 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 "Output Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Title" -1 27 "Times" 1 10 0 0 0 1 2 1 2 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 "2D Math Symbol 2" -1 16 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small208" -1 201 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small207" -1 202 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" -1 21 "Courie r" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small209" -1 203 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Caption Refe rence" -1 204 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 205 "Courier New" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "Code" -1 206 "Courier New" 1 12 255 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small206" -1 207 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small205" -1 208 "Times " 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small210213 " -1 209 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Inert Ou tput" -1 210 "Times" 1 12 144 144 144 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE " 2D Math Italic Small" -1 211 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small210211" -1 212 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small210212" -1 213 "Times" 1 1 0 0 0 1 1 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 "Help Underlined Bold" -1 41 "Tim es" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "Copyright" -1 34 "Times " 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small21121 4" -1 214 "Times" 1 1 0 0 0 1 1 2 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 "Help Und erlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Prom pt" -1 1 "Courier" 1 12 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 "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math Italic S mall211" -1 215 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D M ath Italic Small210" -1 216 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "Header and Footer" -1 217 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 218 "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 "Help Bold" -1 39 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "Equation Label" -1 219 "Times" 1 12 0 0 0 1 2 1 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 "Popup" -1 31 "Times" 1 12 0 128 128 1 1 2 1 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 "Caption Text" -1 220 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Fixed" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 208 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 "" -1 209 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 "" -1 210 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 "" -1 211 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 8 4 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 221 20 "Golden Search Method" } }}{EXCHG {PARA 19 "" 0 "" {TEXT 222 37 "\251 2011 Sri Harsha Garapati, Autar Kaw" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 222 28 "University of Sou th Florida " }}}{EXCHG {PARA 19 "" 0 "" {TEXT 222 24 "United States of America" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 222 15 "kaw@eng.usf.edu" }} }{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 218 146 "NOTE: This worksheet demonstrates the use of Maple to i llustrate Golden Interval search method, a technique used in solving o ptimization problems." }}}{EXCHG {PARA 210 "" 0 "" {TEXT 218 0 "" }}} {EXCHG {PARA 211 "" 0 "" {TEXT 218 17 "Problem Statement" }}}{EXCHG {PARA 3 "" 0 "" {TEXT 218 189 "The cross-sectional area of a gutter wi th equal base and edge length of 2 is given by, A=4*sin(theta)*(1+cos( theta)). Use an initial interval of (0,pi/2).Use an intial interval ep silon=0.2." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 223 6 "Inputs" }}{EXCHG {PARA 3 "" 0 "" {TEXT 218 123 "The following simulation approximates t he optimal angle (theta) to maximize the area of a gutter given with a edge length 2" }}{PARA 3 "" 0 "" {TEXT 218 98 " a) Cross-section al area of the gutter, A b) lower limit of the range , a \+ " }}{PARA 3 "" 0 "" {TEXT 218 86 " c) Upper limit of the ra nge , b d) Interval range, epsilon" }}{PARA 3 "" 0 "" {TEXT 218 4 " " }{TEXT 218 0 "" }{TEXT 218 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 0 1 "Typesetting:-mrow(Typesetting:-mi(\"re start\", bold = \"false\", italic = \"true\", mathvariant = \"italic\" ), Typesetting:-mo(\";\", bold = \"false\", mathvariant = \"normal\", \+ fence = \"false\", separator = \"true\", stretchy = \"false\", symmetr ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em\"), Typesetti ng:-mo(\" \", bold = \"false\", mathvariant = \"normal\", fence = \"fa lse\", separator = \"false\", stretchy = \"false\", symmetric = \"fals e\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mspace(heigh t = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"new line\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", de pth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mi(\"A\", bold = \"false\", italic = \"true\", mathvariant = \"italic\"), Typesettin g:-mo(\"≔\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typese tting:-mi(\"θ\", bold = \"false\", italic = \"false\", mathvaria nt = \"normal\"), Typesetting:-mo(\"→\", bold = \"false\", mathv ariant = \"normal\", fence = \"false\", separator = \"false\", stretch y = \"false\", symmetric = \"false\", largeop = \"false\", movablelimi ts = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0 em\"), Typesetting:-mn(\"4\", bold = \"false\", mathvariant = \"normal \"), Typesetting:-mo(\"⋅\", bold = \"false\", mathvariant = \"nor mal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\" , accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typeset ting:-mi(\"sin\", bold = \"false\", italic = \"false\", mathvariant = \+ \"normal\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\" θ\", bold = \"false\", italic = \"false\", mathvariant = \"norma l\")), bold = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\" ⋅\", bold = \"false\", mathvariant = \"normal\", fence = \"false \", separator = \"false\", stretchy = \"false\", symmetric = \"false\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced(Typesett ing:-mrow(Typesetting:-mn(\"1\", bold = \"false\", mathvariant = \"nor mal\"), Typesetting:-mo(\"+\", bold = \"false\", mathvariant = \"norma l\", fence = \"false\", separator = \"false\", stretchy = \"false\", s ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+ accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\" ), Typesetting:-mi(\"cos\", bold = \"false\", italic = \"false\", math variant = \"normal\"), Typesetting:-mfenced(Typesetting:-mrow(Typesett ing:-mi(\"θ\", bold = \"false\", italic = \"false\", mathvariant = \"normal\")), bold = \"false\", mathvariant = \"normal\")), bold = \+ \"false\", mathvariant = \"normal\"), Typesetting:-mo(\";\", bold = \" false\", mathvariant = \"normal\", fence = \"false\", separator = \"tr ue\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\" , movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", r space = \"0.2777778em\"), Typesetting:-mspace(height = \"0.0ex\", widt h = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesettin g:-mi(\"xl\", bold = \"false\", italic = \"true\", mathvariant = \"ita lic\"), Typesetting:-mo(\"≔\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fa lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f alse\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.277 7778em\"), Typesetting:-mn(\"0\", bold = \"false\", mathvariant = \"no rmal\"), Typesetting:-mo(\";\", bold = \"false\", mathvariant = \"norm al\", fence = \"false\", separator = \"true\", stretchy = \"false\", s ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+ accent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em\"), Typ esetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0e x\", linebreak = \"newline\"), Typesetting:-mi(\"xu\", bold = \"false \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"&c oloneq;\", bold = \"false\", mathvariant = \"normal\", fence = \"false \", separator = \"false\", stretchy = \"false\", symmetric = \"false\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mi( \"evalf\", bold = \"false\", italic = \"true\", mathvariant = \"italic \"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac(Typeset ting:-mrow(Typesetting:-mi(\"π\", bold = \"false\", italic = \"fals e\", mathvariant = \"normal\")), Typesetting:-mrow(Typesetting:-mn(\"2 .0\", bold = \"false\", mathvariant = \"normal\")), linethickness = \" 1\", denomalign = \"center\", numalign = \"center\", bevelled = \"fals e\")), bold = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\" ;\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", se parator = \"true\", stretchy = \"false\", symmetric = \"false\", large op = \"false\", movablelimits = \"false\", accent = \"false\", lspace \+ = \"0.0em\", rspace = \"0.2777778em\"), Typesetting:-mspace(height = \+ \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline \"), Typesetting:-mi(\"ϵ\", bold = \"false\", italic = \"fa lse\", mathvariant = \"normal\"), Typesetting:-mo(\"≔\", bold \+ = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \+ \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.277 7778em\", rspace = \"0.2777778em\"), Typesetting:-mn(\"0.05\", bold = \+ \"false\", mathvariant = \"normal\"), Typesetting:-mo(\";\", bold = \" false\", mathvariant = \"normal\", fence = \"false\", separator = \"tr ue\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\" , movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", r space = \"0.2777778em\"), Typesetting:-mspace(height = \"0.0ex\", widt h = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesettin g:-mi(\"\", bold = \"false\", italic = \"true\", mathvariant = \"itali c\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6D-I#miG F$6&Q(restartF'/%%boldGQ&falseF'/%'italicGQ%trueF'/%,mathvariantGQ'ita licF'-I#moGF$6.Q\";F'F//F6Q'normalF'/%&fenceGF1/%*separatorGF4/%)stret chyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimitsGF1/%'accentGF1/%'ls paceGQ&0.0emF'/%'rspaceGQ,0.2777778emF'-F96.Q\"~F'F/F/FAF1FBFDFFFHF JFL/FPFN-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFN/%&depthGFfn/%*lin ebreakGQ(newlineF'FW-F,6&Q\"AF'F/F2F5-F96.Q*≔F'F/FFUFBFDFFF HFJ/FMFQFO-F,6&Q(θF'F//F3F1F<-F96.Q(→F'F/FFUFBFDFFFHFJF LFV-I#mnGF$6%Q\"4F'F/F<-F96.Q'⋅F'F/FFUFBFDFFFHFJFLFV-F,6&Q$sin F'F/FhoF<-I(mfencedGF$6%-F#6#FeoF/FFUFBFDFFFHFJ/FMQ,0.2222222emF'/FPFfq-F,6&Q$cosF'F/FhoF " 0 "" {XPPEDIT 0 1 "`assign`(range1, `+`(`*`(100, ` *`(epsilon))));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF '62-I#miGF$6&Q'range1F'/%%boldGQ&falseF'/%'italicGQ%trueF'/%,mathvaria ntGQ'italicF'-I#moGF$6.Q*≔F'F//F6Q'normalF'/%&fenceGF1/%*separ atorGF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimitsGF1/% 'accentGF1/%'lspaceGQ,0.2777778emF'/%'rspaceGFN-I#mnGF$6%Q$100F'F/F<-F 96.Q'⋅F'F/FF@FBFDFFFHFJ/FMQ&0.0emF'/FPFY-F,6&Q-ϵF'F //F3F1F<-F96.Q\";F'F/F/FAF4FBFDFFFHFJFXFO-F96.Q\"~F'F/FF@FBFDFFF HFJFXFZF]oF]o-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFY/%&depthGFeo/ %*linebreakGQ(newlineF'F]o-F,6&Q*iterationF'F/F2F5F8-FR6%Q\"0F'F/F " 0 "" {XPPEDIT 19 1 "while `>`(range1, epsilon) do `assign`(iteration, `+`(i teration, 1)); `assign`(d, evalf(`*`(`*`(`+`(sqrt(5), `-`(1)), `/`(1, \+ 2)), `*`(`+`(xu, `-`(xl)))))); `assign`(x1, `+`(xl, d)); `assign`(x2, \+ `+`(xu, `-`(d))); `assign`(val1, A(x1)); `assign`(val2, A(x2)); `assig n`(interval, [xl, xu]); `assign`(range1, `+`(xu, `-`(xl))); `assign`(o ptimization[point], `*`(`+`(xu, xl), `/`(1, 2))); printf(\"Iteration # %g\\n\", iteration); printf(\"Interval=\"); print(interval); printf(\" Optimization Point #%g\\n\\n\", optimization[point]); if `>`(val1, val 2) then `assign`(xl, x2); `assign`(x2, x1); `assign`(xu, xu); `assign` (d, evalf(`*`(`*`(`+`(sqrt(5), `-`(1)), `/`(1, 2)), `*`(`+`(xu, `-`(xl )))))); `assign`(x1, `+`(xl, d)) else `assign`(xl, xl); `assign`(xu, x 1); `assign`(x1, x2); `assign`(d, evalf(`*`(`*`(`+`(sqrt(5), `-`(1)), \+ `/`(1, 2)), `*`(`+`(xl, `-`(xu)))))); `assign`(x2, `+`(xu, `-`(d))) en d if end do:" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6[ y-I#miGF$6&Q!F'/%%boldGQ&falseF'/%'italicGQ%trueF'/%,mathvariantGQ'ita licF'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGF=/%* linebreakGQ(newlineF'-F96&F;F>FA/FDQ%autoF'-I#moGF$62Q&whileF'/%'famil yGQ,Courier~NewF'/F0F4/%+foregroundGQ*[255,0,0]F'/%0font_style_nameGQ, Maple~InputF'/F6Q%boldF'/%+fontweightGFY/%&fenceGF1/%*separatorGF1/%)s tretchyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimitsGF1/%'accentGF1/ %'lspaceGF@/%'rspaceGF@-FK60Q\"~F'FNFRFU/F6Q'normalF'FfnFhnFjnF\\oF^oF `oFboFdoFfo-I(mfencedGF$6)-F#6%-F,6(Q'range1F'FNF2FRFUF5-FK60Q\">F'FNF RFUF[pFfnFhnFjnF\\oF^oF`oFbo/FeoQ,0.2777778emF'/FgoFip-F,6(Q-&varepsil on;F'FN/F3F1FRFUF[pFNFQFRFUFXFZFho-FK62Q#doF'FNFQFRFUFXFZFfnFhnFjnF\\o F^oF`oFboFdoFfoFhoF8Fho-F,6(Q*iterationF'FNF2FRFUF5-FK60Q*≔F'F NFRFUF[pFfnFhnFjnF\\oF^oF`oFboFhpFjpFbq-FK60Q\"+F'FNFRFUF[pFfnFhnFjnF \\oF^oF`oFbo/FeoQ,0.2222222emF'/FgoF\\r-I#mnGF$6'Q\"1F'FNFRFUF[p-FK60Q \";F'FNFRFUF[pFfn/FinF4FjnF\\oF^oF`oFboFdoFjpF8Fho-F,6(Q\"dF'FNF2FRFUF 5Feq-F,6(Q&evalfF'FNF2FRFUF5-F^p6'-F#6%-I&mfracGF$6)-F#6&-F,6(Q%sqrtF' FNF^qFRFUF[p-F^p6'-F#6#-F_r6'Q\"5F'FNFRFUF[pFNFRFUF[p-FK60Q(−F'F NFRFUF[pFfnFhnFjnF\\oF^oF`oFboF[rF]rF^r-F#6#-F_r6'Q\"2F'FNFRFUF[p/%.li nethicknessGFar/%+denomalignGQ'centerF'/%)numalignGF[u/%)bevelledGF1FR -FK60Q'⋅F'FNFRFUF[pFfnFhnFjnF\\oF^oF`oFboFdoFfo-F^p6'-F#6%-F,6(Q# xuF'FNF2FRFUF5F_t-F,6(Q#xlF'FNF2FRFUF5FNFRFUF[pFNFRFUF[pFbrF8Fho-F,6(Q #x1F'FNF2FRFUF5FeqFjuFhqFfrFbrF8Fho-F,6(Q#x2F'FNF2FRFUF5FeqFguF_tFfrFb rF8Fho-F,6(Q%val1F'FNF2FRFUF5Feq-F,6(Q\"AF'FNF2FRFUF5-F^p6'-F#6#F]vFNF RFUF[pFbrF8Fho-F,6(Q%val2F'FNF2FRFUF5FeqFfv-F^p6'-F#6#F`vFNFRFUF[pFbrF 8Fho-F,6(Q)intervalF'FNF2FRFUF5Feq-F^p6)-F#6&Fju-FK60Q\",F'FNFRFUF[pFf nFerFjnF\\oF^oF`oFboFdo/FgoQ,0.3333333emF'FhoFguFNFRFUF[p/%%openGQ\"[F '/%&closeGQ\"]F'FbrF8FhoFbpFeqFguF_tFjuFbrF8Fho-I%msubGF$6%-F,6(Q-opti mizationF'FNF2FRFUF5-F#6#-F,6(Q&pointF'FNF2FRFUF5/%/subscriptshiftGQ\" 0F'Feq-Fas6)-F#6%FguFhqFjuFbtFgtFitF\\uF^uFRFbrF8Fho-F,6(Q'printfF'FNF 2FRFUF5-F^p6'-F#6&F+-I#msGF$6#Q0Iteration~#%g\\nF'F[xFbqFNFRFUF[pFbrF8 FhoFhy-F^p6)-F#6%F+-F`z6#Q*Interval=F'F+FNFQFRFUFXFZFbrF8Fho-F,6(Q&pri ntF'FNF2FRFUF5-F^p6)-F#6#FdwFNFQFRFUFXFZFbrF8FhoFhy-F^p6'-F#6&F+-F`z6# Q;Optimization~Point~#%g\\n\\nF'F[xFfxFNFRFUF[pFbrF8FFF8FFFFFFFho-FK62 Q#ifF'FNFQFRFUFXFZFfnFhnFjnF\\oF^oF`oFboFdoFfoFho-F^p6)-F#6%FcvFepF]wF NFQFRFUFXFZFho-FK62Q%thenF'FNFQFRFUFXFZFfnFhnFjnF\\oF^oF`oFboFdoFfoF8F hoFhoFhoFhoFjuFeqF`vFbrF8FhoFhoFhoFhoF`vFeqF]vFbrF8FhoFhoFhoFhoFguFeqF guFbrF8FhoFhoFhoFhoFfrFeqFirF\\sFbrF8FhoFhoFhoFhoF]vFeqFjuFhqFfrFbrF8F ho-FK62Q%elseF'FNFQFRFUFXFZFfnFhnFjnF\\oF^oF`oFboFdoFfoF8FhoFhoFhoFhoF juFeqFjuFbrF8FhoFhoFhoFhoFguFeqF]vFbrF8FhoFhoFhoFhoF]vFeqF`vFbrF8FhoFh oFhoFhoFfrFeqFir-F^p6'-F#6%F`sF`u-F^p6'-F#6%FjuF_tFguFNFRFUF[pFNFRFUF[ pFbrF8FhoFhoFhoFhoF`vFeqFgu-FK60Q*&uminus0;F'FNFRFUF[pFfnFhnFjnF\\oF^o F`oFboF[rF]rFfrFbrF8Fho-FK62Q$endF'FNFQFRFUFXFZFfnFhnFjnF\\oF^oF`oFboF doFfoFhoFh[l-FK60Q\":F'FNFRFUF[pFfnFhnFjnF\\oF^oF`oFboFhpFjpFhoFhoFhoF 8FFF8F`]lFhoF_qFc]lF8Fho" }}{PARA 6 "" 1 "" {TEXT 224 12 "Iteration #1 " }{TEXT 224 10 "\nInterval=" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!$ \"+Fjzq:!\"*" }}{PARA 6 "" 1 "" {TEXT 224 28 "Optimization Point #0.78 5398" }{TEXT 224 1 "\n" }{TEXT 224 13 "\nIteration #2" }{TEXT 224 10 " \nInterval=" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+v!3***f!#5$\"+Fjzq: !\"*" }}{PARA 6 "" 1 "" {TEXT 224 27 "Optimization Point #1.08539" } {TEXT 224 1 "\n" }{TEXT 224 13 "\nIteration #3" }{TEXT 224 10 "\nInter val=" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+v!3***f!#5$\"+:;)**>\"!\"* " }}{PARA 6 "" 1 "" {TEXT 224 28 "Optimization Point #0.899986" }{TEXT 224 1 "\n" }{TEXT 224 13 "\nIteration #4" }{TEXT 224 10 "\nInterval=" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+J!p;H)!#5$\"+:;)**>\"!\"*" }} {PARA 6 "" 1 "" {TEXT 224 27 "Optimization Point #1.01457" }{TEXT 224 1 "\n" }{TEXT 224 13 "\nIteration #5" }{TEXT 224 10 "\nInterval=" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+&>b!3(*!#5$\"+:;)**>\"!\"*" }} {PARA 6 "" 1 "" {TEXT 224 27 "Optimization Point #1.08539" }{TEXT 224 1 "\n" }{TEXT 224 13 "\nIteration #6" }{TEXT 224 10 "\nInterval=" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+&>b!3(*!#5$\"+OTW76!\"*" }}{PARA 6 "" 1 "" {TEXT 224 27 "Optimization Point #1.04162" }{TEXT 224 1 "\n" }{TEXT 224 13 "\nIteration #7" }{TEXT 224 10 "\nInterval=" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+dm!\\-\"!\"*$\"+OTW76F%" }}{PARA 6 "" 1 "" {TEXT 224 27 "Optimization Point #1.06868" }{TEXT 224 1 "\n" }{TEXT 224 13 "\nIteration #8" }{TEXT 224 10 "\nInterval=" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+dm!\\-\"!\"*$\"+%z2!z5F%" }}{PARA 6 "" 1 "" {TEXT 224 27 "Optimization Point #1.05196" }{TEXT 224 1 "\n" }{TEXT 224 13 " \nIteration #9" }{TEXT 224 10 "\nInterval=" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"+dm!\\-\"!\"*$\"+)*HMe5F%" }}{PARA 6 "" 1 "" {TEXT 224 27 "Optimization Point #1.04162" }{TEXT 224 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }