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A study was made on the amount of convertedsugar in a certain process at various temperatures. Thedata were coded and recorded as follows:Estimate the linear regression line.

T, (x) Converted ugar, y !esidual" #." $.$"%$&$'' #.$#&%*

"." '.# $.$"+%*#$+ '.'#*&+"&". #.% $.$"#$*%*% #."+&+%".* .# $.$"%*+& .'#$&+'*+".& .% $.$"$* .&'#'$$'".% #. $.$%' #.#''&''#".+ #.+ $.$&$&%" #.%'%'%&".' "$. $.$%%"# "$."'&&'#".# .* $.$'$"$ .'#$"". . $.$#%"+*# ."'"*+

"$.% $.$*$$"*+' "$.&+#+*

!esumen

stadísticas de la regresión

Coeciente d $.'$'$+&&Coeciente d $.&##+*!- austad $.&&&*"#"Error t/pico $.+*+$'&01servacion ""

A23455 6E 7A!5A28AGrados de libert

!egresi9n "!esiduos

Total "$

Coefcientes

5ntercepci9n +.&"*+*+*+7aria1le " ".#$$$"

An;lisis de los residuales

Observación onóstico para

" #.''' #.&$*+*+*+* #.%#&%&%&%

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& #.'+%&%&%%% #.&+*+*+&+ ."'''*' .*$#"#"## .$$" .+'

"$ .#%$$$"" "$.$*"#"#

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".$*&%&%&% *".#"#"#"# #.+$.%%*+*+*+ &$.$$$ #.

$.'''* %$ .$.'$#"#"# %.$$$" .*$.'"$$$ +#."#"#"# .%

$.*' ''.'''* .#

$.+%$$$ #+.*+*+*+& "$.$.&+#"#"# %.&%&%&%% "$.%Residual

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uperior !"$% Superior !"#nerior !"$%#uperior !"$%#

#.%$%*"## #.%$%*"## &.*"%#% #.%$%*"##*."'*%%$ *."'*%%$ $.&&&+*"+ *."'*%%$

Convert

y calc

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!esidual

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d ugar, y

VariabVariable X 1 Curv

Gráfco de

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e X 1 Gráfco de los residuale de regresión ajustada

D

ron9stico para D

probabilidad normal

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e han o1tenido los siguientes datos de presi9n de saturaci9n del etanol para diferena. uponiendo Fue no se conoce la funcionalidad entre T (x) y s (y), austar un mod1. Auste los par;metros de lecuaci9n e Antoinec. Auste los par;metros de la ecuaci9n de Antoine modicadad. Auste los par;metros de la ecuaci9n 65!

Gmm

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!- austad $.#$##""Error t/pico $.$%%*''+#01servacione '

A23455 6E 7A!5A28AGrados de libert a de cuadra edio de los cuadr F lor crítico de

!egresi9n " ".+'$"*# ".+'$"*'%* %&&.#%"*' 2.66!"##6!esiduos % $.$"%***&* $.$$*$+++#+

Total + ".+#+&%#"

Coefcientes Error típico Estadístico t Probabilidad Inerior !"#

5ntercepci9n .$%#+*&*& $.*&" '.$"$%$% $.$$$$%*% .#"%++&'7aria1le " ".#+'" $.$#$$ *.*&"'$'* .+#%E$$+ ".++$'$"

a. olinomica

x x y ycalc error% +% %%. %+.&$&'+"$% $.%$&'+"*$ $$ '$ '".+&#%'"&* ".+&#%'"*% "% ' .*+&#%'"&* &.+*%'"&&$ "+$$ ""'.% "".'$&'+"$% .$&'+"&% $% "%&." "%*.%&#%'"& $.%%'"&#+%$ %$$ "$.' "*.+"&#%'"& ."&#%'%% *$% &". &$.$+"$&'+ ".#'*#$%

!esumen


Coeciente d $.&Coeciente d $.#&%'!- austad $.''+#+Error t/pico *.$*"$01servacione '

A23455 6E 7A!5A28A

Grados de libert a de cuadra edio de los cuadr F lor crítico de!egresi9n '$&$."%'+ "*%$.$'##$% "*"'.'+"'+ 2.2$%!"##6!esiduos & &".$*%*# "$.%##$%&

Total + '$#"."'"


5ntercepci9n ''.%"&#%' ".%%%"#% *.%+$#%&$" $.$#*'+ "'.++'&%&7aria1le " &.$$&$&'+ "."*&' *.%%&$%$"" $.$*%+#" '."'%%7aria1le $."+%*#" $.$"*'% .$%$+'$&&' $.$$$#%# $.$#''"$%"

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a*. Exponencial

x y lny ycalc error% %%. &.$*%+&*# %+.%##'# $.+#

*$ '$ &.&%& '.%%""" .%%""*% ' &.%'&'"$# .#""%''% &.'"$'##&&$ ""'.% &.'++&*#** ""'."#%#++# $.&"#%#+*&% "%&." %.$*'+$"'& "%$.++#+'*"&+ *.&*"*+#"%$ "$.' %.%$'$"%" ".%"%"&$' ".#"%"&%% &". %.#%&& &%.'''#*" &.$'''#*

!esumen


Coeciente d $.#+'"#Coeciente d $.'*&%'!- austad $.+#"'Error t/pico $.$"""01servacione '


!egresi9n " ".+#"''$$& ".+#"''$$&&' "#'#.'%"% 1.2&'!"##%!esiduos % $.$$&&'%'' $.$$$#%"%*

Total + ".+#+&%#"


5ntercepci9n .#$*#"& $.$&++%%+ +$.%&"$&' .*##E$$# .+#%+%'7aria1le " $.$&$"%+ $.$$""*$#& &*.*&&%+'""%' ".**+E$$' $.$&+"$#+

e selecciona el modelo polin9mico

1. Ecuaci9n de ClausiusClapeyron

Gmm

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!esumen


Coeciente d $.$#&'%Coeciente d $.#"'$**

!- austad $.'#$&&Error t/pico $.$&$%'01servacione '


!egresi9n " ".+#*"+$%& ".+#*"+$%** ''.'*%#% '.6(!"##!esiduos % $.$$*$#%' $.$$$+"'$%&"

Total + ".+#+&%#"

Coefcientes Error típico Estadístico t Probabilidad Inerior !"#5ntercepci9n $."$'%%% $.*#&% +#.&*%%#+%$# ".+"+E$$# ".*%+%%+7aria1le " &'#."''& ".#'$*$+ %.''*$+$ &.#+%"E$$# %$*&.**'%%

c. Ecuaci9n de Antoine

A L C"#."" *#$&."%$*###% &".+#

Gmm

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".&+&+$$& $.$$*$&'* $.$$$#%"'$&+ $.$$"&''".+$'%&$% $.$$#&&% $.$$"$%&"&"* $.$$'%"$%

#.##66&%&

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es temperaturas.lo emp/rico a los datos

lo emp/rico a los datos

f(x) = $."'+#"&'' x!N = $.$$+'+

bX AY

xlnbaln yln

ax y b

+=

+==

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F

Superior !"# Inerior !"$%# uperior !"$%#

".*$&'$$# .#"%++&' ".*$&'$".$'*+"'&% ".++$'$"$+ .$'*+"'%

a ''.%"&#%'1 &.$$&$&'+c $."+%*#"

F


"*'.*+"$'%#&" "'.++'&%&&&% "*'.*+"$'+$.##$#&+%" '."'%%#+ $.##$#&+%$."+%**'""* $.$#''"$%$+' $."+%**'""

error

2cxbxa y ++=

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A .#$*#"*+a "+.%+&+&*&1 $.$&$"%%%#

F


.*+"#" .+#%+%'& .*+$.$%"%$* $.$&+"$#+#& $.$%"%

error$.#*+%+"$ A $."$'%%%

.%+&''$*#+ L &'#."''&*.%#+$%+&%*%

.#$"+##$%%".'$'**

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errorbx AY

bxaln yln

ae y bx

+=

+=

=

( )T B A P ln

s +=

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F

Superior !"# Inerior !"$%# uperior !"$%#$.#+*%%&""' ".*%+%%%'#' $.#+*%%&

&%+.$"'#+#$# %$*&.**'%&"'% &%+.$"'

e"$."+'#%"*%'".#++#&%"%&*'.*&+$"%*#

'+.#&+%$+*&.+''##+'#'.*%#*&'*+"&$*."'%*+$"

$.$$$$$$*+#

'6.2#&$2#%'

Tc"#."" *#$*.# &".+# *%".% %"+.

&*.$%

l

f(x) = "."*%*"#!N = $.&*"'&

( )C T

B A P ln

s+

+=

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f(x) = $.$$$"+$'+x .#&"%#$%$**+"$!N = $.+&+$&*

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".#+'"

) *mm+g,

Gmm

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error

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error

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c+*

&'##$

n-)s

ln(s)

Column O

x

)s calc

s calc

4inear (s calc)s calc

Gmm

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E$$%

Column B4inear (Column B)

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tKIC $ "$ $ *$ &$$ $ $.$$ $.$$* $.$$ $

"$$ $.$** $.$&* $.$%* $.$+% $.$'#$$ $."'# $." $. $.&* $.+'*$$ $.&*" $.&+ $.&& $.%' $.%+"&$$ $.'#' $.## $.#' $."* $.%'

%$$ ".& ".* ".*&& ".*' ".&%"+$$ ".' ".#% "."* ".'% .$*''$$ .&*" .& .%+ .+* .'"#$$ *."%& *.* *.*$# *.*#+ *.&++$$ *.%' &.$&" &."' &."* &.

"$$$ &.#*& &.+ %.$"# %.""" %.$%""$$ %.'# %.#'# %.'+ +.$'% +."'%"$$ +.'#+ +.# +.% '." '.$%"*$$ '.# '.%' #.$++ #."'+ #.#+"&$$ #.%+ .$+ ."# .+ .&"

"%$$ "$.$ "$."% "$.**" "$.&&' "$.%+*"+$$ "".+* "".*# "".&' "".+"& "".'*""'$$ ".&** ".%& ".+++ ".'# ".##"#$$ "*.%" "*.'$+ "*.#

y ycalc x x x* x&$ %'."*$%#" $ $ $ $

"$$ ''.&%#++ $.$** $.$$"$# *.%*'E$$% "."#%E$$+

$$ "+".&"#*% $."'# $.$*"+#& $.$$%+*'% $.$$"$$*##*$$ #".$*"+ $.&*" $."#%'+" $.$#$$+ $.$*&%$'"%&$$ &$+.+#+"# $.'#' $.+"*+ $.'&&*& $.*#*+"'+%$$ %"'.#+%*& ".& ".%&%+& "."%#+&& .*'%$*++$$ +"".%&#& ".' *.""+& %.'%&%#%$ "$.*""+%'$$ ++.'#*$+# .&*" %.$'+" "&.*+++ *&.%'%"#$$ '##.$+'# *."%& .&''"+ *".*'%$+* #.%'$%*+$$ #".'"#%*' *.%' "%.+%'#& +".%#"$#% &%."+#*%

"$$$ "$$.'*' &.#*& *.*+'%%+ "".%#'++ %&+.$&+'*""$$ ""$.''+&% %.'# **.&$#& "*."$$%% """+.""""$$ "$%.*+'# +.'#+ &+.$&'+ *".&*"+ "$.%#*'""*$$ "&.'"*&+ '.# +".%""$& *.*++#& *'*.&+&$"&$$ "*".%#"" #.%+ #$.$*+ '"#.*+$"#' +&**.+**#*"%$$ "%$".#%* "$.$ "$".##$" "$.% "$&$"."%"+$$ "+$.%"%'" "".+* "+.#%%"+ "&#.'+'' "+$.**"'$$ "+.'"'+ ".&** "%&.%' "".##+' *#&.#"#&"#$$ "#$".+"'& "*.%" "#&.'"%#" %"$.&+%*# *&"".'*%

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/calc

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%$ +$ '$ #$ $ "$$$.$$ $.$$+ $.$"" $.$"' $.$% $.$**$.$ $."$' $."* $."&" $."% $."'#$." $.*"' $.*&& $.*' $.&$" $.&*"$.%+ $.+* $.++ $.'$' $.'&+ $.'#'".$$ ".$ ".$% "."&* "." ".&

".%$% ".%+" ".+"' ".+'% ".'** ".'."$" ."+% .* .+ .*+* .&*".'# .#%& .# *.$$ *.$'# *."%&*.%&+ *.++ *.'$# *.' *.#'* *.%'&.*#' &.&'% &.%+& &.+%* &.'&* &.#*&%. %.*& %. %.%#% %.+# %.'#+.'+ +.*'' +.&'# +.%# +.+#* +.'#+'.*"" '.&"' '.%& '.+* '.'& '.##.*' #.%$# #.+ #.'*" #.#&& #.%+.%& .+* .'%* .#+# .#& "$.$

"$.+' "$.'+ "$."* "".$ ""."&+ "".+*"".# "".+% ".$# "." ".*"+ ".&**"*.$"& "*."* "*.&+ "*.*+" "*.&'+ "*.%"

x% x+ x' residual !esumen$ $ $ %'."*$%#"

*."*%E$$# "."%E$$ &.+"#E$"" .$%&'"*& stadísticas de la regresión

$.$$$"'#+ *."#$'E$$% %.++"+E$$+ *#.%#$"+&Coeciente d $.&"%$.$"'%# $.$$+&"$$# $.$$'+'% "#.'+'#&Coeciente d $.##%%*$.*$"$'** $.*'+$"$' $."#+$& +.+#+"'+% !- austad $.#$'#"&.%%*&*% *.+'$%*+'& &.%%##$++* "'.#+%*&* Error t/pico &.+++$&%"#.&'&" **.""%&% %.*&%' "".%&#& 01servacion "#&.$**&*' $+.&$$$ %$".'%#&+ *."+*"+"*".""$%&' #&.*++++ *"$&.'#'$# "".*"$""A23455 6E 7A!5A28A'$."*$'$' *#*#.#$'" "%"$."+$" #.#"&+*$# Grados de libert +*.%'$# "'%.+#' +"+#$.*$+& .'*+' !egresi9n '+&%"."#$ *'#'.#* "%%*.+"# .''+&%"# !esiduos """&*$.#"" '+%.&&'* ++++.%$# %.*+'#$# Total "#''"."$+ **+&*.+&" "#**+*%.* %.#+%*''"%'+".+&+ %"+$&".*%# &+"+++.& #.&'"##%'" Coefcientes"$%$.#% "$+$##.' "$'"*%." ".#%*"+* 5ntercepci9n %'."*$%#""#"&+.#* $&"*#*.$% $'.* .%"%'$+& 7aria1le " +*#.%%$"'

'$#&.'' *+*+.# &%*"*%.# '.#*'%*%7aria1le *"%.+#'&+*'".*" +*$&*+.&& #%+%+&"*.' ".+"'&&+* 7aria1le * .'%"&%#

7aria1le & "'.&%$$&7aria1le % ".+&&$%$%%

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die

$

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7aria1le + $.$#$*+%7aria1le ' $.$$"%'#'

!esultados de datos de pr

Percentil Y

.+*"%'#% $'.#&'*+#& "$$"*."%'#&' $$"#.&"$%+ *$$*.+#&"$% &$$#.&'*+#& %$$*&."$%+* +$$*.&'*+#& '$$

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ycalc

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a de cuadra io de los cua F lor crítico de F

%+**$%.% #"**.*+ "**+.&"'+ *."&E$"%++&.** +$#.%#*#%

%'$$$$$

Error típico Estadístico t Probabilidad Inerior !"# Superior !"#nerior !"$%#

"+.$$*+* *.%*"%"+ $.$$&'$"+' ".%%+*$" .#+#"% ".%%+*$"+'.*+%"%& .&'#++ ".%#+E$$+ &$.#'+*' '#+.#*$*' &$.#'+*''$.%$"+ &.&&++"$#" $.$$$#&" &'".&+$+ "%.&#*' &'".&+$+*$.&'#&% *.'+$# $.$$'"$#$ **."'+" "++.**"' **."'+"

+.*"++' .'*++"%'# $.$"*"% *".$**' *.*#%$$'"* *".$**'$.+#+'"%+ .**"#%'+ $.$*%+%# $."*$*+*% *."%+$+&'% $."*$*+*%

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$.$*''"* ."%+%*"% $.$%*##% $."+&+&* $.$$"+&""* $."+&+&*$.$$$'+'& ".#%"& $.$'$*# $.$$$"'*'& $.$$**** $.$$$"'*'&

1a1ilidad

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uperior !"$%#

.#+#"%'#+.#*$*'

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*.*#%$$'"**."%+$+&'%

Gráfco de probabilidad nor

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residual

residual

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$.$$"+&""*$.$$****

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al

alalalalal

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n="

TimeKh G(C

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&'"x .%**"#"$++ Column 6

4inear (Column 6)

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Ccalc

Column L

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D x" x x"x" xx x"x+ " $ " $ $

'#.' $.% $.#++ $.% $.'&%+ $.&**'+.' $.% $.#++ $.% $.'&%+ $.&**

%&.+ " $ " $ $+&.# $.% $.#++ $.% $.'&%+ $.&**'#. $.% $.#++ $.% $.'&%+ $.&**'.& $ $ $ $ $$.% $ $ $ $ $

* $ $ $ $ $#+.* $ $ $ $ $

!esumen

stadísticas de la regresiónCoeciente d $.&&*''Coeciente d $.$"&*&+!- austad $.''#*$&Error t/pico +.%&+&$'01servacione "$

A23455 6E 7A!5A28AGrados de libert a de cuadra io de los cua F lor crítico de

!egresi9n % "%+'.'$'** *"*.%&"&+' '.*"++& $.$*#*&*

!esiduos & "'".&"++' &.#%%&"+' Total "'*."


5ntercepci9n $1. *.'*$&* #.$&%#" .+"+"E$$+ #.'""**"7aria1le " 16.'&&&& *.''%+#+" &.*+""+'" $.$"$%"" %.#%+#%+7aria1le &.&%%($2 *.''+' $.#*+$+ $.&$*$+ '.""+&'&&%7aria1le * "16.( %.++*% ."$*#%$% $.$&*++"* *.&$+&'7aria1le & "1%.2#1##$ %.+++#%%& *.$**#%%& $.$*#+*&"+ *.&%'#7aria1le % "6.$61'&2 '.%%*%#' $.&"'"*# $.&$''$"#& '.'&##&

D x" x x"x" xx x"x+ '% %+% & "%$

'#.' +$ .#++ *+$$ #."*%+ "'".+'+.' *$ .#++ $$ #."*%+ #%.#%&.+ "% % & *$+&.# *$ "."*& $$ ".#%%+ *&.$'#. +$ "."*& *+$$ ".#%%+ +#.$&

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'.& &% $% & $$.% &% $% & $

* &% $% & $#+.* &% $% & $

!esumen

stadísticas de la regresión ++.%+'++&Coeciente d $.&&*''Coeciente d $.$"&*&+!- austad $.''#*$&Error t/pico +.%&+&$'01servacione "$


!egresi9n % "%+'.'$'** *"*.%&"&+' '.*"++& $.$*#*&*!esiduos & "'".&"++' &.#%%&"+'

Total "'*."


5ntercepci9n ++.%+'++& *&.%'%++ ".$&%$** $."%+&"& "+*.+"$'7aria1le " .++%"#'* $.'+#*&* *.&++$'+%& $.$%+'%"# $.%*$#"'7aria1le #.++$#&& %.+*%+ *.&&%+% $.$*"&&* "".&%7aria1le * $.$"#***** $.$$+# ."$*#%$% $.$&*++"* $.$*%#&7aria1le & "'.$"$$" %.+++#%%& *.$**#%%& $.$*#+*&"+ *.&%'#

7aria1le % $.*#'"&& $.%"'#+* $.&"'"*# $.&$''$"#& $.*&'+#

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?? a$=".#Q a"="+.******Qa=*.*''%#"%Qa""="+.%Qa="'.$"$$"?? xp=":.":"Qyp=":.":"Q?? Gx yH=meshgrid(xp,yp)Q?? =a$Ma"RxMaRyMa""Rx.-MaRy.-Ma"Rx.RyQSSS ndened function or varia1le Ua"U. ?? a$=".#Q a"="+.******Qa=*.*''%#"%Qa""="+.%Qa="'.$"$$"?? xp=":.":"Qyp=":.":"Q?? =a$Ma"RxMaRyMa""Rx.-MaRy.-Ma"Rx.RyQ?? mesh(x,y,)

?? contour(x,y,)?? meshc(x,y,)?? surf(x,y,)?? surfc(x,y,)?? ++.%+'+ .++%"#'* #.++$#&& $.$"#***** "'.$"$$" $.*#'"&&SSS ++.%+'+ .++%"#'* #.++$#&& $.$"#***** "'.$"$$" $.*#'"&& VError: nexpected WAT4AL expression. ?? a$=++.% .++%"#'* #.++$#&& $.$"#***** "'.$"$$" $.*#'"&&SSS a$=++.% .++%"#'* #.++$#&& $.$"#***** "'.$"$$" $.*#'"&& VError: nexpected WAT4AL expression. ?? a$=++.%+'++*'Qa"=.++%"#'*&Qa=#.++$#&&&Qa""=$.$"#******Qa

a" =

$.*

?? xp="$:":#$Qyp=":.$%:Q

?? Gx yH=meshgrid(xp,yp)Q?? =a$Ma"RxMaRyMa""Rx.-MaRy.-Ma"Rx.RyQ?? surfc(x,y,)??

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".'##.'.

%#.#+$.%##*."".#".#".#".#

a$ a" a a""".# "+.***** *.*''%#"% "+.%

F

Superior !"#nerior !"$%#uperior !"$%#

"$$.##'#+' #.'""**" "$$.##'#+'+.''$#" %.#%+#%+ +.''$#""*.#'"+'$# '.""+&'&&% "*.#'"+'$#

$.'%*%#& *.&$+&' $.'%*%#&".&%&*#&+ *.&%'# ".&%&*#&+

"&.$$$$ '.'&##& "&.$$$$

%&.&%+%."%"&%.#*+&%.$#

"&%".++%##".#*

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**+.'%"'**+.'%"'**+.'%"'**+.'%"'

.++%"#'* #.++$#&& $.$"#***** "'.$"$$" $.*#'"&&

F


*$.&'+'&'+ "+*.+"$' *$.&'+'&'+&.#$$$% $.%*$#"' &.#$$$%"%*.#*+'&' "".&% "%*.#*+'&'

$.$$$#&*'* $.$*%#& $.$$$#&*'*".&%&*#&+ *.&%'# ".&%&*#&+

$.&++'**& $.*&'+# $.&++'**&

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Qa"=+.#+"&*"#'Q

Qa"=+.#+"&*"#'Q

="'.$"$$"*Qa"=$.*#'"&&

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a a""'.$"$$" +.#+"&*"

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Experiencia x" x x* x"x" xx" " " $ " " " " $ " "* " " $ " "& " " $ " "

% " $ " " $+ " $ " " $' " $ " " $# " $ " " $ $ " " $ "

"$ $ " " $ """ $ " " $ "" $ " " $ ""* $ $ $ $ $"& $ $ $ $ $"% $ $ $ $ $

!esumen


Coeciente d $.#"$&+Coeciente d $.+&%#*+!- austad $.##*&Error t/pico +.+#&"'&01servacione "%


!egresi9n "*$.'$#* "$"&%.%*" "&.&# #.##'626!esiduos % *%+".+% '".*%

Total "& '".****

Coefcientes Error típico stadístico Probabilidad Inerior !"#

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5ntercepci9n +& "%.&$"&* &$.&%&&$" ".'*"+E$$' %#&.*#%*a" .*'% .&*+"*&$" $.*%" #.&66#%&2 "&.##"*%&'a + "".'#**'* $.%*"**" #.61%(1#% ."##"a* &*.% "".'#**'* *.#*&'#%"" $.$""##"' '.&"##"a"" .% "%.$"*+" +.$+#%**% $.$$"'%&%% "*".*+*+*a *+.'% "%.$"*+" .&"'%&%&" #.#6#2$$ .*+*+*&

a** "#.% "%.$"*+" "."+%+% #.2%%$#$' %'.%'+*+*a" ".% "*.*&&'$#' ".&+"%*** #.2#&% %*.#$*++%#a"* "$.% "*.*&&'$#' #."#+'+%&% $.$$$&& '&.&+**&a* +* "#."#%''% *.&+&&+%' $.$"'+$$# "$.'$"+

!esultados de datos de pro1a1ilidad +&

Percentil Y

*.******** *%$"$ &%#"+.++++++' %**.******* %*%

*$ %+**+.++++++' %#$&*.******* %%

%$ %+%+.++++++' %+*.******* +$$

'$ +$'+.++++++' +&%#*.******* +

$ +%*+.++++++' +%+

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(a) Bit the secondorder model.(1) erform the canonical analysis. Xhat type of surfacehas 1een foundS(c) Xhat operating conditions on x", x, and x* lead to thestationary pointS

(d) Xhat operating conditions would you recommend if itis important to o1tain a viscosity that is as close to +$$as possi1leS

x*x* x"x x"x* xx* y$ " $ $ %*%$ " $ $ %#$$ " $ $ %+$ " $ $ %+*

" $ " $ +&%" $ " $ &%#" $ " $ *%$" $ " $ +$$" $ $ " %%" $ $ " +" $ $ " %*" $ $ " +%+$ $ $ $ +%*$ $ $ $ %$ $ $ $ +$

F

#.#(


Gráfco de pr

ycalc

y

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++*.+"$&+" %#&.*#%* ++*.+"$&+"**.+*"*%&' "&.##"*%&' **.+*"*%&'*&."##" ."##" *&."##"

"&.%#""$ '.&"##" "&.%#""$%*."'*+*+# "*".*+*+* %*."'*+*+#'%.#+*+* .*+*+*& '%.#+*+*

$.%'+*+* %'.%'+*+* $.%'+*+*"&.#$*++%# %*.#$*++%# "&.#$*++%#"&*.%%*+++ '&.&+**& "&*.%%*+++

"+.%"#*% "$.'$"+ "+.%"#*%

.*'% + &*.% .% *+.'% "#.%

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ycalc%**.+%%".*'%%#&.+%%+&.*'%

+%+.*'%&%+.+%*%".*'%%##.+%

+"+.%+"+.%

%&+%++&+&+&

babilidad normal

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".% "$.% +*

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siguientes est;n disponi1les donde " = partes 20 por "$ millones de partes de aire6eterminar el factor irritante como una funci9n de " y

" D"$ ".% +%

" "% '"% "# #"+ " %" + ""$" *$ "% *% "%# &$ "*$

Wodelo " (0o parecen ser cuadraticas)y=a$Ma"x"Max

Exp " D Dcalc error" "$ ".% +% '$.++#" %.++#" " "% ' '+."&'"*+ &."&'"*%* "% "# # #$.'$##"$$' ".""#*"& "+ " % $.+&&"+&'+ &.*%%#*%&% " + ""$ "$*.+*%%#*% +.*+&&"+&'++ " *$ " ""%.$#'$* +.$"$'' % *% "% "%.&"&'%' $.&"&'%'%# # &$ "*$ "*#.&$+"'#% #.&$+"'#&

!esumen

Estadísticas de la regresión

Coeciente de $.'*+%*&Coeciente de $.$"*$&!- austado $.'"'%Error t/pico +.#"%$$'+&01servacione #

A23455 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F alor crítico de

!egresi9n &*&.+%&+ ""'.*+* &%.%##*$"&" #.###6162'!esiduos % *.%& &+.&&&%$#$"

Total ' &&++.#'%


5ntercepci9n &%."''*&%%& "%.$&*" .++%&*&% $.$*"#*" +.$##$$+7aria1le " .+'%+" %."&$&&+& $.%"*"%#"&' $.+'$"## "+.$'#'%+''7aria1le &.$*++"*' *.*"%&$ ".+'### $.+$+'$+' &.*"$%'%

ro1lema ".%+ El factor irritante D de aire contaminado puede determinarse en funci9n de las c

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!esultados de datos de pro1a1ilidad

Percentil Y

+.% +%"#.'% '*".% #&*.'% %%+.% ""$+#.'% "#".% "%*.'% "*$

Wodelo y=a$Ma"x"MaxMa"x"x

E " x"x D Dcalc" "$ ".% "% +% +&.$*#**# " "% "#$ ' '*.+"##""%** "% "# '$ # #".&%+#*%& "+ " **+ % %.$"$'%% " + && ""$ ""$.$%'%%+ " *$ +*$ " "".+*#*&+' % *% #'% "% "%."$"%$$%# # &$ ""$ "*$ "*$.$+$&&+

!esumen


Coeciente de $.%#%Coeciente de $.$#"'*!- austado $.#&"#$*Error t/pico ".$$*%*'"&*01servacione #

A23455 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F alor crítico de!egresi9n * &&+.#&++%* "'.+"%%%" "&''."&'*$+ 1.(2'(!"##6!esiduos & &.$#*&'" ".$$'$#+'#

Total ' &&++.#'%


5ntercepci9n ".*$'"%#%# *.#"+&&%%+ $.*&%"#"& $.'&$$$'# "".$**+'7aria1le " ".&'''#"++ $.''"'+&*& ".&$'"%# $."&'&%'& *.+&$%*&

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7aria1le '.%##''' $.%*'%"' "&.""#"" $.$$$"&+"$ +.$+*'#$*7aria1le * $.""+$"&& $.$$''%&%% "%.$%#%*'' $.$$$""*%$ $."*''*&&%


Percentil Y

+.% +%"#.'% '*".% #&*.'% %%+.% ""$+#.'% "#".% "%*.'% "*$

Wodelo * y=a$Ma""x"x"MaxxMa"x"x

E " x"x" xx x"x" "$ ".% "$$ "%+.% "% " "% "&& % "#$* "% "# % *& '$& "+ " %+ &&" **+% " + *+" +'+ &&+ " *$ &&" $$ +*$

' % *% +% "% #'%# # &$ '#& "+$$ ""$

!esumen


Coeciente de $.&'"**Coeciente de $.###'"'%*!- austado $.#$%%%+'Error t/pico ""."&'%##

01servacione #


!egresi9n * *+.#$$$&% "**.+++# "$.+&''" #.#22&&6!esiduos & &'.$'&%%" "&.+#'*##

Total ' &&++.#'%


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5ntercepci9n ++.%'&'$' "*.'"%*#%% &.#'"#* $.$$#&'#+ #.##"$#7aria1le " &."*%#%&&% &.%**%'#& $."'%"" $.&"**&$#% "+.'*$%7aria1le .*"#$*&* .%''$$% $.$$+#"' $.&"#%&'''* .&'+'#"%%7aria1le * +.'%++$#%& +.#&*%&& $."'$"+' $.&""$'"' ".'%"'**


Percentil Y

+.% +%"#.'% '*".% #&*.'% %%+.% ""$+#.'% "

#".% "%*.'% "*$

Wodelo & cuadratica completa

E " x"x" xx x"x" "$ ".% "$$ "%+.% "% " "% "&& % "#$* "% "# % *& '$& "+ " %+ &&" **+

% " + *+" +'+ &&+ " *$ &&" $$ +*$' % *% +% "% #'%# # &$ '#& "+$$ ""$

!esumen


Coeciente de $.#++##Coeciente de $.'*%*!- austado $.$+&$''Error t/pico $.''#"$%&'01servacione #


!egresi9n % &&+%.+#$%# #*."*+"$%% "&%.&#%+ $.$$$++#*#*!esiduos "."&&'#% $.%'*+"&

Total ' &&++.#'%

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a# *$."#$*'%& "+.$%'*+"" ".%&'&*## $."&$*&"'% *#."'"""$*a1 &.$&&$'+ "$.#+"#* .""**+# $."%'&+$* '$.#"$&&+&+a2 ".%#%'$&% +.'$"%+'%& *."$#&"' $.$#&''"%' '.*#'"*%%a11 *."+'"%*+" ".$'*%#' ."'$'%$* $."+"'#* *."%%*+#%

a22 "."&*%#+*% $.%+&&&+% ."'#**' $."+"&+"" ".""%"%'&a12 *.+'$'#+" ".'+'#&+#$% .&*##&'' $."%**+ "".%'*&%#'&


Percentil Y

+.% +%"#.'% '

*".% #&*.'% %%+.% ""$+#.'% "#".% "%*.'% "*$

Eemplo ".& 7amos a desarrollar una ecuaci9n para los datos so1re la capacidad de calor de v

T GJH Cp GcalKmolJH

*$$ ".+%&$$ +.'& Cp=1$M1"TM1%$$ *.# Cp=1$M1"TM1+$$ *'.'& Cp=1$M1"T'$$ &".'% Cp=1"T#$$ &%.$+$$ &'.#*

"$$$ %$."+

Cp=1"T T GJH Cp GcalKmolJH Cpcalc residual*$$ ".+% "+.$*#"%'# .'&+"#&"$%&$$ +.'& .%*#&"$%* &.$"%'#&'&%$$ *.# #."'*$+*"+ &.++'*+#&+$$ *'.'& **.#$'+*"%' *.**+#&""'$$ &".'% *.&&*+#& .*$''+*"%'#$$ &%.$+ &%.$'+#&"$% $.$"+#&"$%*$$ &'.#* %$.'""&&'*+# .##"&&'*+#&

"$$$ %$."+ %+.*&+$%+* +."#+$%+*"+!esumen

110 xaa y ++=

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Coeciente de $.%*"$"*Coeciente de $.$+&%#!- austado $.#&''#%""%Error t/pico &.$*&$%%'"

01servacione #

A23455 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F

!egresi9n " "$+&.%*%$+ "$+&.%*%$+ '&".$&*'***!esiduos ' ""*.+*&$# "+.#$&+'

Total # ""'#.&#*

Coefcientes Error típico Estadístico t Probabilidad

5ntercepci9n $ Err:%" Err:%" Err:%"

7aria1le " $.$%+*&+$%* $.$$$+#+* '.""#&+ .*"%*%E$$#

Cp=1$M1"TM1T

T GJH T- Cp GcalKmolJH Cpcalc residual*$$ $$$$ ".+% ".#%#*** $.&%#****&$$ "+$$$$ +.'& +.+$&"$'"& $."*%##%'%$$ %$$$$ *.# *.%$"+$'"& $.#*#%'+$$ *+$$$$ *'.'& *'.%$#*** $."&'"+++'

'$$ &$$$$ &".'% &".#'%%*%'" $."%%*%'"$$ +&$$$$ &%.$+ &%.*%"+& $."+&#+$$ #"$$$$ &'.#* .$"*+$% $.""*+$

"$$$ "$$$$$$ %$."+ &.##*'% $.'+%

!esumen


Coeciente de $.'&%&Coeciente de $.&"&

!- austado $.##'#Error t/pico $.#$%%01servacione #

A23455 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F

!egresi9n ''.+#%'+ *#.#&#+* &"#.+!esiduos % $.&$%+"#" $.$#""'+

Total ' '#.*'&"#'%

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Coefcientes Error típico Estadístico t Probabilidad

1$ %.$%+"*$% $.#+'+&"%'+%.#'&&" $.$$"$#*'1" $.$%"$'" $.$$#$#* *.+&+" &.#&'*E$$'1 &.$*%"E$$% ."'&&E$$+ "#.*+#$+& #.#$#+$E$$+

257E4 Temperatura 7elocidad de aresi9n x" x

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01servacione "%


!egresi9n #+%.%#*** +".*#" .%&*#%&%"* $.$""&%*!esiduos % %"#.'% "$&*.'%

Total "& '".*****


5ntercepci9n +& "#.+%%&& **.&%*"+#&.++*E$$' %'+.$%"%+7aria1le " .*'% "".&"# $.#$'+** $.&&"''# ".#+*%#*7aria1le '.+% "".&"# .&"#%"+*+ $.$+$'%%% ".'*+*%#+7aria1le * + "".&"# .'+%$'% $.$'"#'&*'% %%.*+"*%#*7aria1le & '% "+.#"*"%# &.&+$'"##" $.$$++*%%& ""#."%*7aria1le % ".% "+.#"*"%# "."%#$%## $.#&+*" *.'"%*7aria1le + *%.'% "+.#"*"%# ."+*"$'' $.$#+#$#'+& '#.+%*

7aria1le ' ".% "+."%*%%# ".$'"+&&* $.#"*%%+%+ +".$&$&'#+7aria1le # "$.% "+."%*%%# +.'+*"%$% $.$$"$'*%# +'.'%%"&7aria1le "'.'% "+."%*%%# ".$### $.*""%"%& *.''&$&'#+

-2

-1

-2-1.5

-1-0.5

00.5

1-400

-200

0

200

400

600

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y = partes de 0 por "$$ millones de partes de aire.

or los residuales, se puede decir Fue es cuadratica


#&.*+*$' +.$##$$+ #&.*+*$'"$.''&#" "+.$'#'%+'' "$.''&#"".'+*#$"# &.*"$%'% ".'+*#$"#

ncentraciones de 0 y 20 en la atm9sfera. 4os datos

X1

D

X1

Ex

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residual$.+"+$+""&

".+"##""%'$.%'&*"'+&

$.$"$'%$.$%'%%$'

$.*+$"+%*+$."$"%$$%*#$.$+$&&+$"

Parece e'ponencial


.##*%'+ "".$**+' .##*%'+$.+&&#*"%# *.+&$%*& $.+&&#*"%#

Column O

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.$#""+'&+* +.$+*'#$* .$#""+'&+*$.$&$#& $."*''*&&% $.$&$#&

D Dcalc esidual+% '&.++&"&'$ .++&"&'$&' '#.*++' +.*+++'# '#."'$$"& *.##%$+% .%$$#'"+ .&$"#&*

""$ "$&."++*%&* %.#**+&%'$" "$+.'$*%$+% "%.+&*&

"% "#.+%+"+*" *.+%+"+*$#+"*$ "*'."%"*&* '."%"*&#+


Column 5

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"$&.#+%'$% #.##"$# "$&.#+%'$%#.&%"*'*+" "+.'*$% #.&%"*'*+"&.#**""% .&'+'#"%% &.#**""%%.'+%"$& ".'%"'** %.'+%"$&

D Dcalc residual+% +&.''+$ $.*$'#$' '.+*%*+% $.+*%*+%# #".#&"" $.$"%$#'% &.*"&%" $.+$#$%$

""$ "$.#%#*# $."$&"+"'" "."*%*## $."*%*##*"% "%.%$'$+ $.%$'$+$#"*$ ".+#&*%' $.*"%+&""'

Column 5

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"$$.$$'#+" *#."'"""$* "$$.$$'#+".'&+& '$.#"$&&+&+ .'&+&%$.%$$"$% '.*#'"*%% %$.%$$"$%.%###*$&$' *."%%*+#% .%###*$&$'

*.&$#+%&&% ".""%"%'& *.&$#+%&&%*.+*&$*$ "".%'*&%#'& *.+*&$*$

por de 1enceno como funci9n de la temperatura. 4os valores experimentales se muestran en l

T

"KT

Column E

2112

2

222

2

11122 x xa xa xa x +++

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'.+%+

opt


+'".&'#&$& %'+.$%"%+ +'".&'#&$&*#.'*+*%#* ".#+*%#* *#.'*+*%#*%+.#+*%#* ".'*+*%#+ %+.#+*%#**.*+"*%#+ %%.*+"*%#* *.*+"*%#+*".'#$&$$' ""#."%* *".'#$&$$'+.'"%* *.'"%* +.'"%*

'.&+% '#.+%* '.&+%

.$&$&'#+ +".$&$&'#+ .$&$&'#+"%$.''&$&' +'.'%%"& "%$.''&$&'%.'&$&'#+ *.''&$&'#+ %.'&$&'#+

-1

01

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X2

D

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Gráfco de probabilidad normal

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ta1la

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Column B

2

210 T bT bb ++

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residual

*"$.%

"$.%*

%.#'%

"#.+%"#.+%%.#'%

#.#'%&.*'%

&.*'%#.#'%

%

&aleatorio

a1& a2&1#$.2( 1%.%(

"%$ ".% "$.%

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".% * "'.'%"$.% "'.'% '".%

."#&%+$$.#'"*'$#%

.'%#+$"&%"

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Column W

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x-MxM"=$

x f(x) fU(x) conv x +

$.% .% * $.'% "$.% $.%+% ".% ".% "

$.+% $."&$+% $.'% ".% "$.#"% $.$*%"%+% $.*'% $.* "

$.$+% $.$$#'#$+ $."#'% $.""%*#&+ "$.%*"% $.$$"'' $.$*'% $.$%"'&"& "

$.'+%+% $.$$$%&* $.$&+#'% $.$&%$"+$.###"% $.$$$"*'** $.$*&*'% $.$"$.&"&$+* *.&**E$$% $.$""'"#'% $.$$%##%$.'$'$*" #.%#*"E$$+ $.$$%#%*# $.$$&+%$.#%*%"+ ."&%#E$$+ $.$$+ $.$$"&+"%$.+'%# %.*+&&E$$' $.$$"&+& $.$$$'**%

$.+**' ".*&""E$$' $.$$$'*& $.$$$*++$.#"+# *.*%#E$$# $.$$$*++" $.$$$"#*"'$.$#&% #.*#"E$$ $.$$$"#*"" ."%'E$$%$.%& .$%%E$$ ."%%*E$$% &.%'#E$$%$.''"" %.*#'E$"$ &.%''+E$$% .#E$$%$.##%+ ".*$'E$"$ .###E$$% "."&&E$$%$.&# *.'&E$"" "."&&&E$$% %.'E$$+$.'"& #."#%%E$" %.'$E$$+ .#+"E$$+$.#%' .$&+&E$" .#+"$E$$+ ".&*"E$$+$.# %.""%E$"* ".&*$%E$$+ '."%*E$$'$.+& ".'$E$"* '."%+E$$' *.%'+E$$'$.# *."'&E$"& *.%'+*E$$' ".'##E$$'$." '.*+E$"% ".'##"E$$' #.&"E$$#

" $ #.&$'E$$# &.&'$E$$#" $ #.&$'E$$# $" $ #.&$'E$$# $" $ #.&$'E$$# $" $ #.&$'E$$# $" $ #.&$'E$$# $" $ #.&$'E$$# $" $ #.&$'E$$# $

" $ #.&$'E$$# $" $ #.&$'E$$# $

( ) ( )1 4

x x f −=−−

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x f fU fUU conv

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The function to 1e minimied is f(x) = x- x and is illustrated in Bigure E%. la.points 1racPeting the minimum ( ".', $.", ".%) are used to start the search forminimum oY (x)Q we use eFually spaced points here 1ut that is not a reFuirementhe method.

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