{VERSION 2 3 "DEC ALPHA UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "alpha:=16*arctan(1/5 )-4*arctan(1/239);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG,&-%'ar ctanG6##\"\"\"\"\"&\"#;-F'6##F*\"$R#!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expand(cos(alpha));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expand(sin(alpha ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(alpha);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #$\"+`EfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "K:=10:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 221 "for k from 0 to K do \n S :=series(arctan(x),x,2*k+1);\n P:=convert(S,polynom);\n approx[2*k+1 ,rat]:=16*subs(x=1/5,P)-4*subs(x=1/239,P);\n l:=floor(log[10](5^(2*k+ 3)));\n approx[2*k+1,float]:=evalf(approx[2*k+1,rat],l)\nod:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "for k from 0 to K do\n [2*k +1,approx[2*k+1,rat],approx[2*k+1,float]]\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\" \"$#\"%/Q\"%&>\"$\"$=$!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"&# \"+KqRf`\"+v)*[1<$\"%TJ!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"( #\"2%oRLrT#z#Q\"2vVt=5b%=7$\"'iTJ!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"*#\"8w4a#>!=4r[Gl(\"8DJ?=%Rf&3yfV#$\"(#fTJ!\"'" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7%\"#6#\"?O#=)[I!eoeAStQ&yK\"?vVt_&QIm3/#>RTh-hS)=IR;$\"+`EfTJ!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"#:#\"MCd@sgjYNXpH+Hk[tJ%>i1c*\"MDcwfiT01_\"f&HA\"47 #)[H`K/$$\",Ol#fTJ!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"#<#\"T;Wu !45*yG*\\ot!pe\"Qz!o1W\\JKk#o\"TDJ?L!f#\"en_gj!=L0\"3kQ)))ot ePGC\"[v#=iFAWFWJ$\"enDcwMc_d]+:$o.S-)=Y78jU#*)**=-:]0\"$\"/)*e`EfTJ!# 8" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7%\"#@#\"\\oc'*H@**HrJ&\\k^pJoI.% >D2EMzsHOb:(>'G**)\"\\ov=<^u8Zy=[om(HLzlS:*e>I'fPGBjqo^iG$\"1#z*e`EfTJ !#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }