GSP4 qTQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$ LGraph Tools` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H GenevaOArial'''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':')P~@Pu@4( 4`.Q@: &  nQ\aAx6( 6\.B@: &  nQ\aAy='   9b ~<0>gP B0@@MDw+Xw~Sw  f~H:   """")"""")@N L <0> p0@$dLdL 6F p  p   N L  <0>gP p0@$dLdL 6F p  p   N L  <0> p0@$dLdL 6F p  p   G 9  n <0>gP N0 2$2$eMDw$wwp p nQ\aAq-#TQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. 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The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$&LRoot f(x0) = 0: Select f(x) - SeedPtArialnQ\aAAP~@Pu@ 9^  <0>:/ >0`w@ww 8UnQ\aAf 'nQ\aAS[1]-r\V@Pu@A3    <0>0 ! b  ;<0>:/ B0%%eMDw$wwp` N L  W<0>:/ p0@$dLdL 6F p  p   G 9 n  q<0>:/ N0 #!#!eMDw$wwp p nQ\aAf0 ! b  <0>:/ B0##eMDw$wwp` 0 ! b  <0>:/ B0!&!&eMDw$wwp` E8 nQ\aAPL@    jK nQ\aA[1]MA  nQ\aA[1]X RootA3     <0> nQ\aAx[rod]B3     <0> nQ\aAy[rod]N/#Vlg frst funktionen f(x) og dernst et punkt P i nrheden af den sgte rodV{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$4LIntersection f(x)=g(x): Select f(x) - g(x) - SeedPtArialnQ\aAA 9^  <0>>< >0`w@ww 8UnQ\aAg  9^  <0>>< >0`w@ww 8UnQ\aAf 'nQ\aAS[1]tA3    9<0>N L  l<0>:/ p0@$dLdL 6F p  p   nQ\aAf']N L  <0>:/ p0`5`@F`l`F p  p   nQ\aAg']G 9  <0>:/ f0('('eMDw$ww p p  p p nQ\aANewtonf0 ! b  <0>:/ B0  eMDw$wwp` 0 !  b  <0>:/ B0%%eMDw$wwp` 0 !  b  <0>:/ B0  eMDw$wwp` E8 nQ\aAPL@    |*b nQ\aA[1]MA  nQ\aA[1]X& Intersection A3    <0>0 ! b  +<0>:/ B0eMDw$wwp` 0 ! b  G<0>:/ B0  eMDw$wwp` `/#Vlg frst funktionerne f(x) og g(x) og dernst et punkt i nrheden af det sgte skringspunktV{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$(LMax/Min f'(x0)=0: Select f(x) - SeedPt ArialnQ\aAAP~@h4Fr@ 9^  <0>:/ >0`w@ww 8UnQ\aAf 'nQ\aAS[1] b@ s@N L  <0>:/ p0@$dLdL 6F p  p   nQ\aAf']N L  9<0>:/ p0@$dLdL 6F p  p   nQ\aAf''G 9 n  S<0>:/ N0 0(0(eMDw$wwp p nQ\aANewton A3    <0>nQ\aAm[1]n0 ! b  <0>:/ B0 % %eMDw$wwp` 0 ! b  <0>:/ B0**eMDw$wwp` E8 nQ\aAAL@   K?J nQ\aA[1]MA  nQ\aA[1]X "ExtremumeA3     <0>B3     <0>H/#Vlg frst funktinen f(x) og dernst et punkt i nrheden af toppunktet {A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LTangent: Select f(x) - PtArial GenevaO&nQ\aA Rringspunkte v@ 9^  <0>:/ >0`w@ww 8UnQ\aAf 'nQ\aAS[1]gA3   <0>$nQ\aA x[Contact]t0 ! b X<0>:/ B0$$eMDw$wwp` N L y<0>:/ p0@$dLdL 6F p  p   0 ! b  <0>:/ B0##eMDw$wwp` 0 !b <0>:/ B0%%eMDw$ww`0 ! b <0>:/ B0%%eMDw$ww``E8TanE8 gentt?   2$  >>>>>>>>>>>>>nQ\aAt[1]t?{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$6LTangent of inflection f''(x0)=0: Select f(x) - SeedPtArial GenevaOnQ\aAAP@3@ 9^  <0>:/ >0`w@ww 8UnQ\aAf 'nQ\aAS[1]=: :uUمu@N L  <0>:/ p0@$dLdL 6F p  p   N L  9<0>:/ p0@$dLdL 6F p  p   nQ\aAf''N L  S<0>:/ p0@$dLdL 6F p  p   nQ\aAf'''=A3    m<0>G 9 n  <0>:/ N0 2$2$eMDw$wwp p nQ\aANewton:0 ! b  <0>:/ B0""eMDw$wwp` 0 !  b  <0>:/ B0 % %eMDw$wwp` E8 nQ\aAPL@   = nQ\aA[1]MA  nQ\aA[1]X $ inflectionlA3   <0>B3    <0>0 !j  <0>:/ J0 ( (eMDw$wwp` p` 0 !b  +<0>:/ B0""eMDw$ww`E8" tangentn?  2$  c>>>>>>>>>>>>>manQ\aAt[1]e\/#Vlg frst funnktionen f(x) og dernst et punkt i nrheden af vendetangentens rringspunktn{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LNormal: Select f(x) - PtArial GenevaOnQ\aAP`k@ 9^  <0>:/ >0`w@ww 8UnQ\aAf 'nQ\aAS[1]A3    <0>0 ! b  ;<0>:/ B0(  eMDw$ww p` E8NorN L  W<0>:/ p0@$dLdL 6F p  p   0 !b  q<0>:/ B0(""eMDw$ww `0 !j  <0>:/ J0(%%eMDw$ww `p` E8 mal?   2$   >>>>>>>>>>>>>1nQ\aAt[1]?{A tool in this document was created with a newer version of Sketchpad and cannot be read. 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The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$4LIntegral with one fct: Select f(x) - N - ptA - ptBArial GenevaO !^  <0> >0`w@ww 8UnQ\aAn nQ\aABnQ\aAA 9^  <0>H >0`w@ww 8UnQ\aAf 'nQ\aAS[1] 0X0W0 !b  9<0>:/ B0@ % %eMDw$ww`A3    m<0>A3    <0>0 !n  S<0>:/ N0 @ ' 'eMDw$ww` `` nQ\aAhB3    <0>nQ\aAm[2] 0 !  b  <0>:/ B0@##eMDw$ww``0 !   <0>A n  0:@))eMDw$ww`` p``   p`` p``   E8 nQ\aAAY@$   W0 nQ\aA[1]MA  nQ\aA[1]XnQ\aABB3    <0>nQ\aAm[1]0 !  b  <0>:/ B0@ " "eMDw$ww``"nQ\aAIntegral  nQ\aAC0 !b  -<0>:/ B0  % %eMDw$ww``A3    I<0>E8nQ\aAD0 ! b  e<0>:/ B0 !!eMDw$wwp` E8nQ\aAE nQ\aAj0 !b  <0>:/ B0( ( (eMDw$ww ` Ko K@#+,   ?  nQ\aAL[1]/#Vlg frst funktionen der skal integreres f(x). Vlg dernst antallet af deleintervaller N. Vlg endeligt startpunktet A og slutpunktet B.0{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$@LIntegral between two fcts: Select f(x) - g(x) - N - ptA - pt BtArial GenevaOnQ\aABnQ\aAA !^  <0> >0cw@ps|wTTnQ\aAN  9^  <0>H >0cw@ps|wTTnQ\aAg  9^  <0> >0cw@ps|wTTnQ\aAf 'nQ\aAS[1]lA3    9<0>A3    U<0>0 !n  <0>:/ N0 (''eMDw$ww ` `` nQ\aAhB3    <0>0 !  b  <0>:/ B0())eMDw$ww ``G 9 j  <0>:/ J0(1%1%eMDw$ww p p d0 !b o<0>:/ B0(%%eMDw$ww `0 !   d<0> 0:(&&eMDw$ww `` p``   p`` p``   E8 nQ\aAAY@$   Uzz nQ\aA[1]MA nQ\aA[1]XnQ\aABB3   <0>0 !  b <0>:/ B0( ' 'eMDw$ww ``$nQ\aA Integralet  nQ\aACA3   <0>0 ! b <0>:/ B0(%%eMDw$ww p` 0 ! b <0>:/ B0($$eMDw$ww p` E8nQ\aADE8nQ\aAE nQ\aAj0 ! f  <0>:/ F0(&&eMDw$ww `` K K@#+0   ?  nQ\aAL[1]0{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$(LArc length: Select f(x) - N - ptA - ptBArial GenevaO !^  <0>:/ >0`w@ww 8UnQ\aAN nQ\aABnQ\aAA 9^  <0>:/ >0`w@ww 8UnQ\aAf 'nQ\aAS[1] A3    <0>A3    ;<0>N L  W<0>:/ p0@$dLdL 6F p  p   G 9n  q<0>:/ N0 (/'/'eMDw$ww  p  nQ\aAf0 !b <0>:/ B0( ) )eMDw$ww `0 !n  <0>:/ N0 ($$eMDw$ww ` `` nQ\aAh0 !  b  <0>:/ B0(%%eMDw$ww ``B3    <0>nQ\aAm[2] 0 !   \<0>H<O4 0:( & &eMDw$ww `` p``   p`` p``   E8 nQ\aAAY@$   ^4nQ\aA[1]MA nQ\aA[1]XnQ\aABB3   <0>nQ\aAm[1]0 !  b !<0>:/ B0(%%eMDw$ww ``$nQ\aA arc length  nQ\aACA3   !<0>0 ! b !<0>:/ B0(  eMDw$ww p` E8nQ\aAD#*  ? nQ\aAL[1]ev/#Vlg frst funktionen f(x). Vlg dernst antallet af deleintervaller N. Vlg endelig startpunktet A og slutpunktet B.{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$.LAntiderivative: Select f(x) - N - x0 - endPtlArial GenevaO !^  <0> >0`w@ww 8UnQ\aAN nQ\aABPu@nQ\aAA@u@ 9^  <0>H >0`w@ww 8UnQ\aAf 'nQ\aAS[1] A3    U<0>B3    q<0>  nQ\aAAA3    <0>B3    <0>nQ\aAm[2] A3     <0>0 !b  <0>:/ B0@ % %eMDw$ww`0 ! n  <0>:/ N0 @ ' 'eMDw$ww` `` nQ\aAh0 !  b  <0>:/ B0@##eMDw$ww``0 !    <0>H<O4 0:@))eMDw$ww`` p``   p`` p``   E8nQ\aABY@$   W0 nQ\aA[1]MA nQ\aA[1]XnQ\aACB3    <0>nQ\aAm[1]0 !  b  <0>:/ B0@ " "eMDw$ww``"nQ\aAIntegral0 ! b  1<0>:/ B0''eMDw$ww``E8 nQ\aAD#*@   ? nQ\aAL[1]0 !b  M<0>:/ B0eMDw$ww``E8 nQ\aAEA3    i<0>E8nQ\aAF /#Vlg frst funktionen f(x). Vlg dernst antallet af intervalinddelinger N. Vlg herefter startpunktet A for stamfunktionens graf. Vlg endelig et slutpunkt B for stamfunktionens definitionsmngde.