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{SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 6 "Error:" }{TEXT -1 19 "  di
vision by zero\n" }}{PARA 0 "" 0 "" {TEXT -1 109 "In mathematics, divi
sion by zero is not allowed.  In Maple, an attempt to divide by zero p
roduces this error." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sin(0)
/0;" }}{PARA 8 "" 1 "" {TEXT -1 23 "Error, division by zero" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 111 "In some cases \+
when a division by zero results from evaluating some expression at a c
ertain value of a variable " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 
66 ", what is really wanted instead is the limit of the expression as \+
" }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 55 " approaches this value.  \+
This may be obtained by using " }{MPLTEXT 0 21 5 "limit" }{TEXT -1 1 "
." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(sin(x)/x, x=0);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 109 "Sometimes a division by zero can \+
result when Maple fails to recognize early enough that some quantity i
s 0.  " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "series(p/((1-sin(x
-p)^2 - cos(x+p)^2)), p = 0,3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#+)%
\"pG*&\"\"\"F&,(\"\"\"F(*$)-%$sinG6#%\"xG\"\"#F&!\"\"*$)-%$cosGF-F/F&F
0!\"\"\"\"\",$*&*&F+F(F3F(F&*&,(F0F(F)F(F1F(\"\"\"F'\"\"\"F5\"\"%\"\"#
-%\"OG6#F(\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify
(%);" }}{PARA 8 "" 1 "" {TEXT -1 42 "Error, (in simplify/trig) divisio
n by zero" }}}{PARA 0 "" 0 "" {TEXT -1 20 "When this occurs in " }
{MPLTEXT 0 21 6 "series" }{TEXT -1 142 " and related commands, you may
 be able to fix the problem by changing the environment variable Testz
ero, whose value is the procedure used in " }{MPLTEXT 0 21 6 "series" 
}{TEXT -1 76 " to determine when the leading coefficient is 0.  By def
ault this just uses " }{MPLTEXT 0 21 6 "normal" }{TEXT -1 1 "." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eval(Testzero);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#R6#%\"OG6\"F&F&-%&evalbG6#/-RF&F&6$%(builtinG%)
rememberGE\\s1*&%\"OG\"\"\"%$/XXG!\"\"F1,$*&F3F3,(!\"\"\"\"\"*$)%\"OG
\"\"#F3F:*$)%\"OGF>F3F:F5F9F6,$*&*&-%$sinG6#%\"xGF:-%$cosGFGF:F3*$),(F
9F:*$)FEF>F3F:*$)FIF>F3F:\"\"#F3F5\"\"%FBFEFE,$*&F3F3,(F:F:F;F9F?F9F5F
9F7FIFIFVFVF7F7,(F:F:FNF9FPF9FW,$*&*&F=F:FAF:F3*$)F8\"\"#F3F5FSFX*&F3F
3FMF5Fhn*&-FF6#F4F3F4F5Fin,$*&*&F=F3FAF3F3*&F8\"\"\"FV\"\"\"F5!\"%FX,$
FhnF9FcoFUF6FjnFjn\"$W\"F&F&F&%'normalG6#9$\"\"!F&F&F&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eval(normal);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#R6\"F$6$%(builtinG%)rememberGE\\s1*&%\"OG\"\"\"%$/XXG!
\"\"F),$*&F+F+,(!\"\"\"\"\"*$)%\"OG\"\"#F+F2*$)%\"OGF6F+F2F-F1F.,$*&*&
-%$sinG6#%\"xGF2-%$cosGF?F2F+*$),(F1F2*$)F=F6F+F2*$)FAF6F+F2\"\"#F+F-
\"\"%F:F=F=,$*&F+F+,(F2F2F3F1F7F1F-F1F/FAFAFNFNF/F/,(F2F2FFF1FHF1FO,$*
&*&F5F2F9F2F+*$)F0\"\"#F+F-FKFP*&F+F+FEF-FV*&-F>6#F,F+F,F-FW,$*&*&F5F+
F9F+F+*&F0\"\"\"FN\"\"\"F-!\"%FP,$FVF1F[oFMF.FXFX\"$W\"F$F$F$%'normalG
" }}}{PARA 0 "" 0 "" {TEXT -1 16 "You can replace " }{MPLTEXT 0 21 6 "
normal" }{TEXT -1 4 " by " }{MPLTEXT 0 21 8 "simplify" }{TEXT -1 24 " \+
to get a stronger test." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "T
estzero:= proc(O) evalb(simplify(O)=0) end:" }}}{PARA 0 "" 0 "" {TEXT 
-1 6 "Since " }{MPLTEXT 0 21 6 "series" }{TEXT -1 9 " has the " }
{MPLTEXT 0 21 8 "remember" }{TEXT -1 29 " option, if you try the same \+
" }{MPLTEXT 0 21 6 "series" }{TEXT -1 131 " command again it will just
 remember the value it computed before.  To get it to try again, you c
an make it forget the past values." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "readlib(forget)(series);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 49 "series(p/((1-sin(x-p)^2 - cos(x+p)^2)), p = 0,3);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#+'%\"pG,$*&\"\"\"F'*&-%$sinG6#%\"xG
\"\"\"-%$cosGF+\"\"\"!\"\"#\"\"\"\"\"%\"\"!-%\"OG6#F3\"\"#" }}}}{SECT 
0 {PARA 0 "" 0 "" {TEXT 26 9 "See also:" }{TEXT -1 1 " " }{HYPERLNK 
17 "limit" 2 "limit" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "series" 2 "ser
ies" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "Testzero" 2 "envvar" "" }
{TEXT -1 2 ", " }{HYPERLNK 17 "normal" 2 "normal" "" }{TEXT -1 2 ", " 
}{HYPERLNK 17 "simplify" 2 "simplify" "" }{TEXT -1 2 ", " }{HYPERLNK 
17 "forget" 2 "forget" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 22 "Mapl
e Advisor Database" }{TEXT -1 18 "   R. Israel, 1997" }}}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}{MARK "2 0 1" 18 }{VIEWOPTS 1 1 0 1 1 1803 }