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0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small2022 06" -1 209 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle1 " -1 210 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 0 0 0 1 }{CSTYLE "Help Itali c" -1 42 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Headi ng" -1 26 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Output La bels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Nor mal" -1 30 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Comme nt" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Mapl e Name" -1 35 "Times" 1 12 104 64 92 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2 D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "D ictionary 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 "Times" 1 12 0 0 0 1 1 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 "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 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 "_cstyle3" -1 211 "Courier" 1 14 255 0 0 1 2 1 2 2 1 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 Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 203 "" 0 "" {TEXT 210 15 "NEWTON'S METHOD" } {TEXT 210 0 "" }}{PARA 209 "" 0 "" {TEXT 201 27 "Problem 2 on the work sheet:" }}{PARA 209 "" 0 "" {TEXT 201 57 "Use the Newton's Method to f ind the inflection point for " }{XPPEDIT 2 0 "Typesetting:-mrow(Typese tting:-msup(Typesetting:-mo(\"ⅇ\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.1111111em\"), Type setting:-mrow(Typesetting:-mi(\"cos\", italic = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\"⁡\", mathvariant = \"n ormal\", fence = \"false\", separator = \"false\", stretchy = \"false \", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Type setting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", italic = \"t rue\", mathvariant = \"italic\")), mathvariant = \"normal\")), supersc riptshift = \"0\"), Typesetting:-mo(\",\", mathvariant = \"normal\", f ence = \"false\", separator = \"true\", stretchy = \"false\", symmetri c = \"false\", largeop = \"false\", movablelimits = \"false\", accent \+ = \"false\", lspace = \"0.0em\", rspace = \"0.3333333em\"), Typesettin g:-mo(\" \", mathvariant = \"normal\", fence = \"false\", separator = \+ \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em \", rspace = \"0.0em\"), Typesetting:-mi(\"where\", italic = \"false\" , mathvariant = \"normal\"), Typesetting:-mo(\" \", mathvariant = \"no rmal\", fence = \"false\", separator = \"false\", stretchy = \"false\" , symmetric = \"false\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Types etting:-mi(\"x\", italic = \"false\", mathvariant = \"normal\"), Types etting:-mo(\" \", mathvariant = \"normal\", fence = \"false\", separat or = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \" 0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"is\", italic = \"false \", mathvariant = \"normal\"), Typesetting:-mo(\" \", mathvariant = \" normal\", fence = \"false\", separator = \"false\", stretchy = \"false \", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Type setting:-mo(\"in\", 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:-mo(\" \+ \", mathvariant = \"normal\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspac e = \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn (\"0\", mathvariant = \"normal\"), Typesetting:-mo(\",\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"true\", stretchy = \"fa lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f alse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.3333333em \"), Typesetting:-mo(\" \", mathvariant = \"normal\", fence = \"false \", separator = \"false\", stretchy = \"false\", symmetric = \"false\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"pi\", itali c = \"false\", mathvariant = \"normal\")), mathvariant = \"normal\", o pen = \"[\", close = \"]\"), Typesetting:-mo(\".\", mathvariant = \"no rmal\", fence = \"false\", separator = \"false\", stretchy = \"false\" , symmetric = \"false\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"));" "-I %mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6/-I%msupGF$6%-I#mo GF$6-Q/ⅇF'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*s eparatorGF7/%)stretchyGF7/%*symmetricGF7/%(largeopGF7/%.movablelimitsG F7/%'accentGF7/%'lspaceGQ&0.0emF'/%'rspaceGQ,0.1111111emF'-F#6%-I#miGF $6%Q$cosF'/%'italicGF7F2-F/6-Q0⁡F'F2F5F8F:FF@FBFD/FHF F-I(mfencedGF$6$-F#6#-FM6%Q\"xF'/FQQ%trueF'/F3Q'italicF'F2/%1superscri ptshiftGQ\"0F'-F/6-Q\",F'F2F5/F9FinF:FF@FBFD/FHQ,0.3333333emF'-F/6- Q\"~F'F2F5F8F:FF@FBFDFU-FM6%Q&whereF'FPF2Feo-FM6%FgnFPF2Feo-FM6%Q#i sF'FPF2Feo-F/6.Q#inF'/%%boldGF7F2F5F8F:FF@FBFDFUFeo-FW6&-F#6&-I#mnG F$6$Q\"0F'F2F_oFeo-FM6%Q#piF'FPF2F2/%%openGQ\"[F'/%&closeGQ\"]F'-F/6-Q \".F'F2F5F8F:FF@FBFDFU" }}{PARA 209 "" 0 "" {MPLTEXT 1 211 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mi(\"g\", italic = \"tru e\", mathvariant = \"italic\"), Typesetting:-mo(\"≔\", mathvar iant = \"normal\", fence = \"false\", separator = \"false\", stretchy \+ = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspace = \+ \"0.2777778em\"), Typesetting:-mi(\"x\", italic = \"true\", mathvarian t = \"italic\"), Typesetting:-mo(\"→\", mathvariant = \"normal\" , fence = \"false\", separator = \"false\", stretchy = \"false\", symm etric = \"false\", largeop = \"false\", movablelimits = \"false\", acc ent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting: -mi(\"exp\", italic = \"false\", mathvariant = \"normal\"), Typesettin g:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"cos\", italic = \"false \", mathvariant = \"normal\"), Typesetting:-mfenced(Typesetting:-mrow( Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), \+ mathvariant = \"normal\")), mathvariant = \"normal\"), Typesetting:-mo (\";\", mathvariant = \"normal\", fence = \"false\", separator = \"tru e\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rs pace = \"0.2777778em\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI (_syslibGF'6)-I#miGF$6%Q\"gF'/%'italicGQ%trueF'/%,mathvariantGQ'italic F'-I#moGF$6-Q*≔F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF =/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accen tGF=/%'lspaceGQ,0.2777778emF'/%'rspaceGFL-F,6%Q\"xF'F/F2-F66-Q(→ F'F9F;F>F@FBFDFFFH/FKQ&0.0emF'/FNFV-F,6%Q$expF'/F0F=F9-I(mfencedGF$6$- F#6$-F,6%Q$cosF'FenF9-Fgn6$-F#6#FOF9F9-F66-Q\";F'F9F;/F?F1F@FBFDFFFHFU FM" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arr owGF%F%-I$expGF%6#-I$cosGF%F#F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mi(\"diff\", italic = \" true\", mathvariant = \"italic\"), Typesetting:-mfenced(Typesetting:-m row(Typesetting:-mi(\"g\", italic = \"true\", mathvariant = \"italic\" ), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", itali c = \"true\", mathvariant = \"italic\")), mathvariant = \"normal\"), T ypesetting:-mo(\",\", mathvariant = \"normal\", fence = \"false\", sep arator = \"true\", stretchy = \"false\", symmetric = \"false\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.3333333em\"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), mathvariant = \"normal\"), Type setting:-mo(\";\", mathvariant = \"normal\", fence = \"false\", separa tor = \"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \" 0.0em\", rspace = \"0.2777778em\"));" "-I%mrowG6#/I+modulenameG6\"I,Ty pesettingGI(_syslibGF'6%-I#miGF$6%Q%diffF'/%'italicGQ%trueF'/%,mathvar iantGQ'italicF'-I(mfencedGF$6$-F#6&-F,6%Q\"gF'F/F2-F66$-F#6#-F,6%Q\"xF 'F/F2/F3Q'normalF'-I#moGF$6-Q\",F'FD/%&fenceGQ&falseF'/%*separatorGF1/ %)stretchyGFL/%*symmetricGFL/%(largeopGFL/%.movablelimitsGFL/%'accentG FL/%'lspaceGQ&0.0emF'/%'rspaceGQ,0.3333333emF'FAFD-FG6-Q\";F'FDFJFMFOF QFSFUFWFY/FgnQ,0.2777778emF'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&-I$s inG6$%*protectedGI(_syslibG6\"6#I\"xGF)\"\"\"-I$expGF&6#-I$cosGF&F*F,! \"\"" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typ esetting:-mi(\"diff\", italic = \"true\", mathvariant = \"italic\"), T ypesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo(\"&uminus0;\", m athvariant = \"normal\", fence = \"false\", separator = \"false\", str etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable limits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspa ce = \"0.2222222em\"), Typesetting:-mi(\"sin\", italic = \"false\", ma thvariant = \"normal\"), Typesetting:-mfenced(Typesetting:-mrow(Typese tting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), mathva riant = \"normal\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \" false\", symmetric = \"false\", largeop = \"false\", movablelimits = \+ \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\") , Typesetting:-msup(Typesetting:-mo(\"ⅇ\", mathvariant = \+ \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fal se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa lse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.1111111em \"), Typesetting:-mrow(Typesetting:-mi(\"cos\", italic = \"false\", ma thvariant = \"normal\"), Typesetting:-mo(\"⁡\", mathvari ant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits \+ = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em \"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", ita lic = \"true\", mathvariant = \"italic\")), mathvariant = \"normal\")) , superscriptshift = \"0\"), Typesetting:-mo(\",\", mathvariant = \"no rmal\", fence = \"false\", separator = \"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\" , accent = \"false\", lspace = \"0.0em\", rspace = \"0.3333333em\"), T ypesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), m athvariant = \"normal\"), Typesetting:-mo(\";\", mathvariant = \"norma l\", fence = \"false\", separator = \"true\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em\"));" "- I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q%diff F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I(mfencedGF$6$-F#6)-I#mo GF$6-Q*&uminus0;F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGFB/%)str etchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/%' lspaceGQ,0.2222222emF'/%'rspaceGFQ-F,6%Q$sinF'/F0FBF>-F66$-F#6#-F,6%Q \"xF'F/F2F>-F;6-Q1⁢F'F>F@FCFEFGFIFKFM/FPQ&0.0emF'/FSF]o -I%msupGF$6%-F;6-Q/ⅇF'F>F@FCFEFGFIFKFMF\\o/FSQ,0.1111111e mF'-F#6%-F,6%Q$cosF'FWF>-F;6-Q0⁡F'F>F@FCFEFGFIFKFMF\\oF^ oFX/%1superscriptshiftGQ\"0F'-F;6-Q\",F'F>F@/FDF1FEFGFIFKFMF\\o/FSQ,0. 3333333emF'FfnF>-F;6-Q\";F'F>F@FepFEFGFIFKFMF\\o/FSQ,0.2777778emF'" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*&-I$cosG6$%*protectedGI(_syslibG6\"6# I\"xGF)\"\"\"-I$expGF&6#F$F,!\"\"*&)-I$sinGF&F*\"\"#F,F-F,F," }}} {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting: -mi(\"f\", italic = \"true\", mathvariant = \"italic\"), Typesetting:- mo(\"≔\", mathvariant = \"normal\", fence = \"false\", separat or = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \" 0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mi(\"x\", itali c = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"→\", \+ mathvariant = \"normal\", fence = \"false\", separator = \"false\", st retchy = \"false\", symmetric = \"false\", largeop = \"false\", movabl elimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \+ \"0.0em\"), Typesetting:-mrow(Typesetting:-mo(\"&uminus0;\", mathvaria nt = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0 .2222222em\"), Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-m row(Typesetting:-mi(\"cos\", italic = \"false\", mathvariant = \"norma l\"), Typesetting:-mo(\"⁡\", mathvariant = \"normal\", f ence = \"false\", separator = \"false\", stretchy = \"false\", symmetr ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mf enced(Typesetting:-mrow(Typesetting:-mi(\"x\", italic = \"true\", math variant = \"italic\")), mathvariant = \"normal\")), Typesetting:-mo(\" ⁢\", mathvariant = \"normal\", fence = \"false\", separ ator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+ \"0.0em\", rspace = \"0.0em\"), Typesetting:-msup(Typesetting:-mo(\"&E xponentialE;\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0 .0em\", rspace = \"0.1111111em\"), Typesetting:-mrow(Typesetting:-mi( \"cos\", italic = \"false\", mathvariant = \"normal\"), Typesetting:-m o(\"⁡\", mathvariant = \"normal\", fence = \"false\", se parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced(Typesetting:-m row(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\" )), mathvariant = \"normal\")), superscriptshift = \"0\")), Typesettin g:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", separator = \+ \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.222 2222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-ms up(Typesetting:-mrow(Typesetting:-mi(\"sin\", italic = \"false\", math variant = \"normal\"), Typesetting:-mo(\"⁡\", mathvarian t = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\" ), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", itali c = \"true\", mathvariant = \"italic\")), mathvariant = \"normal\")), \+ Typesetting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \+ \"0\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\" , fence = \"false\", separator = \"false\", stretchy = \"false\", symm etric = \"false\", largeop = \"false\", movablelimits = \"false\", acc ent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting: -msup(Typesetting:-mo(\"ⅇ\", mathvariant = \"normal\", fe nce = \"false\", separator = \"false\", stretchy = \"false\", symmetri c = \"false\", largeop = \"false\", movablelimits = \"false\", accent \+ = \"false\", lspace = \"0.0em\", rspace = \"0.1111111em\"), Typesettin g:-mrow(Typesetting:-mi(\"cos\", italic = \"false\", mathvariant = \"n ormal\"), Typesetting:-mo(\"⁡\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin g:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), mathvariant = \"normal\")), superscriptsh ift = \"0\")), Typesetting:-mi(\"\")), Typesetting:-mo(\";\", mathvari ant = \"normal\", fence = \"false\", separator = \"true\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.27777 78em\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6(-I# miGF$6%Q\"fF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q*&c oloneq;F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/ %*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ, 0.2777778emF'/%'rspaceGFL-F,6%Q\"xF'F/F2-F66-Q(→F'F9F;F>F@FBFDFF FH/FKQ&0.0emF'/FNFV-F#6'-F66-Q*&uminus0;F'F9F;F>F@FBFDFFFH/FKQ,0.22222 22emF'/FNFhn-F#6&-F,6#Q!F'-F#6%-F,6%Q$cosF'/F0F=F9-F66-Q0&ApplyFunctio n;F'F9F;F>F@FBFDFFFHFUFW-I(mfencedGF$6$-F#6#FOF9-F66-Q1&InvisibleTimes ;F'F9F;F>F@FBFDFFFHFUFW-I%msupGF$6%-F66-Q/ⅇF'F9F;F>F@FBFD FFFHFU/FNQ,0.1111111emF'F_o/%1superscriptshiftGQ\"0F'-F66-Q\"+F'F9F;F> F@FBFDFFFHFgnFin-F#6%-Fap6%-F#6%-F,6%Q$sinF'FdoF9FeoFho-I#mnGF$6$Q\"2F 'F9FhpF]pF`pF\\o-F66-Q\";F'F9F;/F?F1F@FBFDFFFHFUFM" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&-I$cosG6$%* protectedGI(_syslibGF%F#\"\"\"-I$expGF-6#F+F0!\"\"*&)-I$sinGF-F#\"\"#F 0F1F0F0F%F%F%" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 211 26 "plot(f (x),x=0..4,y=-5..5);" }{MPLTEXT 1 211 0 "" }}{PARA 13 "" 1 "" {TEXT 212 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6'-%'CURVESG6$7W7$$\"\"!! \"\"$!1X!f%G=G=F!#:7$$\"2mmmmT:(z@!#=$!1h3*Gi*p:F!#:7$$\"1LLLL3VfV!#<$ !2MOmz]izq#!#;7$$\"*DY\"Rl!#5$!0)G*Q$*)4&p#!#97$$\"1mmmm;')=()!#<$!2D* )eV8crn#!#;7$$\",D\"z>^7!#6$!2W*=*HmFSj#!#;7$$\"2MLL$e'40j\"!#<$!2k!z= (R-id#!#;7$$\"2nmmm6hO[#!#<$!2XI2!RT&fR#!#;7$$\"2mmmm\"yYUL!#<$!2')y&* >$)*z_@!#;7$$\"1LLLeF>(>%!#;$!1^_1q:5i=!#:7$$\"2kmm;>K'*)\\!#<$!0)[^qq \">c\"!#97$$\"1*****\\Kd,\"e!#;$!2b2U1rqLB\"!#;7$$\"1mmm\"fX(em!#;$!0$ ez;,L')))!#:7$$\"1*****\\U7Y](!#;$!1n\"HL7%=Lb!#;7$$\"1MLLL/pu$)!#;$!2 '3UP!pe@H#!#<7$$\"1nmm;c0T\"*!#;$\"1F4?Ej*=4$!#<7$$\"*8!Q+5!\")$\"2k!* [h#HL!*G!#<7$$\"*&*3q3\"!\")$\"1Na)HSt92&!#;7$$\"*(=\\q6!\")$\"/#4DCu* on!#97$$\"2nmm\"fBIY7!#;$\"1$[l*)3v8(z!#;7$$\"2LLLLO[kL\"!#;$\"1c8VD'Q Y+*!#;7$$\"2KLLL&Q\"GT\"!#;$\"1`*yX?xFd*!#;7$$\",D2X;]\"!#5$\"11e])pTQ #**!#;7$$\"2JLLLvv-e\"!#;$\"1'H'>aMm)***!#;7$$\",D2Ylm\"!#5$\"1dWtWR/u )*!#;7$$\",v\"ep[ *!#;7$$\"2LLLeDBJ\">!#;$\"0fQ\"e2jU()!#:7$$\"2mmm;kD!)*>!#;$\"1nB#fnT6 @)!#;7$$\"2jmm\"f`@'3#!#;$\"1'>8`L]`j(!#;7$$\",vw%)H;#!#5$\"1uTB!RkP8( !#;7$$\"2lmm;$y*eC#!#;$\"19X#G]>tg'!#;7$$\"*9b:L#!\")$\"1e[qW*eG4'!#;7 $$\"2'*****\\5a`T#!#;$\"1W#>!o!oyi&!#;7$$\"2(****\\7RV'\\#!#;$\"0TeSz! 4?_!#:7$$\"2'*****\\@fke#!#;$\"2Mh^)Q.V?[!#<7$$\"1LLL`4NnE!#:$\"2;y2Fc r8^%!#<7$$\"*:?Pv#!\")$\"1W=YE1'\\B%!#;7$$\"2lmm\"zM)>$G!#;$\"2lj(*et[ E.%!#<7$$\"*(fa " 0 "" {MPLTEXT 1 211 39 "pl ot(\{f(x),D(f)(1)*(x-1)+f(1)\},x=0..4);" }{MPLTEXT 1 211 0 "" }}{PARA 13 "" 1 "" {TEXT 212 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6(-%'CUR VESG6$7S7$$\"\"!!\"\"$!2O#[G\\e#\\Z#!#;7$$\"1mmmm;')=()!#<$!1a(*e6;.MA !#:7$$\"2MLL$e'40j\"!#<$!2PwDM#3VC?!#;7$$\"2nmmm6hO[#!#<$!2oCtc\"Gr)y \"!#;7$$\"2mmmm\"yYUL!#<$!2,?bfJK9b\"!#;7$$\"1LLLeF>(>%!#;$!2K0L!p&z_J \"!#;7$$\"2kmm;>K'*)\\!#<$!0W!)HuNj4\"!#97$$\"1*****\\Kd,\"e!#;$!1*)HC G4K'p)!#;7$$\"1mmm\"fX(em!#;$!1Z*)HN&[r&)[m]!#=7$$\"*8!Q+5!\")$\"2Ox')y!pL!*G!#<7$$\"*&*3q3\"!\")$\"1C4\" 3h7QG&!#;7$$\"*(=\\q6!\")$\"1)=T3&*p.f(!#;7$$\"2nmm\"fBIY7!#;$\"1()3t( )\\%\\o*!#;7$$\"2LLLLO[kL\"!#;$\"2OxA)H(fv@\"!#;7$$\"2KLLL&Q\"GT\"!#;$ 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\"*9b:L#!\")$\"1e[qW*eG4'!#;7$$\"2'*****\\5a`T#!#;$\"1W#>!o!oyi&!#;7$$ \"2(****\\7RV'\\#!#;$\"0TeSz!4?_!#:7$$\"2'*****\\@fke#!#;$\"2Mh^)Q.V?[ !#<7$$\"1LLL`4NnE!#:$\"2;y2Fcr8^%!#<7$$\"*:?Pv#!\")$\"1W=YE1'\\B%!#;7$ $\"2lmm\"zM)>$G!#;$\"2lj(*et[E.%!#<7$$\"*(fa!#<$\"1ij9.e@R!)!#;$\"2' \\_'eM%yg>!#<-%%VIEWG6$;$\"\"!!\"\"$\"#S!\"\"%(DEFAULTG-%+AXESLABELSG6 '-I#miG6#/I+modulenameG6\"I,TypesettingGI(_syslibG6\"6'Q\"x6\"/%'famil yGQ!6\"/%%sizeGQ#106\"/%'italicGQ%true6\"/%,mathvariantGQ'italic6\"Q!6 \"-%%FONTG6%%!G%!G\"#5%+HORIZONTALG%+HORIZONTALG-%*AXESSTYLEG6#%'NORMA LG-%(SCALINGG6#%.UNCONSTRAINEDG" 1 2 2 1 10 1 2 6 0 4 2 1.0 45.0 45.0 0 0 "Curve 1" "Curve 2" }}{TEXT 212 0 "" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 201 66 "The procedure now calls for us to obtain the x- interc ept of the" }{TEXT 201 0 "" }}{PARA 209 "" 0 "" {TEXT 201 47 "linear a pproximation as the next approximation." }{TEXT 201 0 "" }}{PARA 209 " " 0 "" {TEXT 201 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 211 35 "x1 := f solve(D(f)(1)*(x-1)+f(1),x);" }{MPLTEXT 1 211 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+%[!od*)!#5" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 201 0 " " }}{PARA 202 "> " 0 "" {MPLTEXT 1 211 73 "plot(\{f(x),D(f)(x1)*(x-x1) +f(x1),D(f)(1)*(x-1)+f(1)\},x=0..4,thickness=2);" }{MPLTEXT 1 211 0 "" }}{PARA 13 "" 1 "" {TEXT 212 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6*-%'CURVESG6$7S7$$\"\"!!\"\"$!2O#[G\\e#\\Z#!#;7$$\"1mmmm;')=()!#<$!1 a(*e6;.MA!#:7$$\"2MLL$e'40j\"!#<$!2PwDM#3VC?!#;7$$\"2nmmm6hO[#!#<$!2oC tc\"Gr)y\"!#;7$$\"2mmmm\"yYUL!#<$!2,?bfJK9b\"!#;7$$\"1LLLeF>(>%!#;$!2K 0L!p&z_J\"!#;7$$\"2kmm;>K'*)\\!#<$!0W!)HuNj4\"!#97$$\"1*****\\Kd,\"e!# ;$!1*)HCG4K'p)!#;7$$\"1mmm\"fX(em!#;$!1Z*)HN&[r&)[m]!#=7$$\"*8!Q+5!\")$\"2Ox')y!pL!*G!#<7$$\"*&*3q3\"!\")$ \"1C4\"3h7QG&!#;7$$\"*(=\\q6!\")$\"1)=T3&*p.f(!#;7$$\"2nmm\"fBIY7!#;$ \"1()3t()\\%\\o*!#;7$$\"2LLLLO[kL\"!#;$\"2OxA)H(fv@\"!#;7$$\"2KLLL&Q\" GT\"!#;$\"2$)*>Y]1bG9!#;7$$\",D2X;]\"!#5$\"2`1S)\\K)Rn\"!#;7$$\"2JLLLv 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variantGQ'italic6\"Q!6\"-%%FONTG6%%!G%!G\"#5%+HORIZONTALG%+HORIZONTALG -%*THICKNESSG6#\"\"#-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%.UNCONSTRAIN EDG" 1 2 2 1 10 2 2 6 0 4 2 1.0 45.0 45.0 0 0 "Curve 1" "Curve 2" "Cur ve 3" }}{TEXT 212 0 "" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 201 69 "As be fore, the procedure now calls for us to obtain the x- intercept" } {TEXT 201 0 "" }}{PARA 209 "" 0 "" {TEXT 201 66 "of the linear approxi mation as the next approximation. Rather than" }{TEXT 201 0 "" }} {PARA 209 "" 0 "" {TEXT 201 65 "explain each step we will simply apply the Maple V commands to do" }{TEXT 201 0 "" }}{PARA 209 "" 0 "" {TEXT 201 67 "this until two successive approximations differ by no more th an ten" }{TEXT 201 0 "" }}{PARA 209 "" 0 "" {TEXT 201 7 "digits." } {TEXT 201 0 "" }}{PARA 209 "" 0 "" {TEXT 201 0 "" }}{PARA 202 "> " 0 " " {MPLTEXT 1 211 38 "x2 := fsolve(D(f)(x1)*(x-x1)+f(x1),x);" }{MPLTEXT 1 211 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+2w+X!*!#5" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 211 38 "x3 := fsolve(D(f)(x2)*(x-x2)+f( x2),x);" }{MPLTEXT 1 211 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+>*ob /*!#5" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 211 38 "x4 := fsolve(D (f)(x3)*(x-x3)+f(x3),x);" }{MPLTEXT 1 211 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+S*ob/*!#5" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 211 38 "x5 := fsolve(D(f)(x4)*(x-x4)+f(x4),x);" }{MPLTEXT 1 211 0 "" } }{PARA 11 "" 1 "" {XPPMATH 20 "$\"+W*ob/*!#5" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 211 38 "x6 := fsolve(D(f)(x5)*(x-x5)+f(x5),x);" } {MPLTEXT 1 211 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+V*ob/*!#5" }}} {EXCHG {PARA 209 "" 0 "" {TEXT 201 0 "" }}{PARA 209 "" 0 "" {TEXT 201 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 211 30 "f(x2);f(x3);f(x4);f(x5); f(x6);" }{MPLTEXT 1 211 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!'!3$=! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!\"(!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!\"\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F#" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F#" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }