Datoteka:Lagrange polynomials for continuations of sequence 1,2,3.gif

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Sažetak

Opis
English: Lagrange polynomials and their graphs for ten possible continuations (0 to 9) of the sequence 1,2,3; each polynomial evaluates to 1,2,3, and the continuation at input 1,2,3, and 4, respectively; the "correct" continuation 4 leads to the polynomial of least degree
Datum
Izvor Vlastito djelo
Autor Jochen Burghardt
Lagrange polynomials as txt 
                               2  3     2   19  
       1, 2, 3, 0            - - x  + 4x  - -- x + 4 
                               3             3



                               1  3     2   9   
       1, 2, 3, 1            - - x  + 3x  - - x + 3 
                               2            2



                               1  3     2   8   
       1, 2, 3, 2            - - x  + 2x  - - x + 2 
                               3            3



                               1  3    2   5   
       1, 2, 3, 3            - - x  + x  - - x + 1 
                               6           6




       1, 2, 3, 4            x




                             1  3    2   17  
       1, 2, 3, 5            - x  - x  + -- x - 1 
                             6            6



                             1  3     2   14  
       1, 2, 3, 6            - x  - 2x  + -- x - 2 
                             3             3



                             1  3     2   13  
       1, 2, 3, 7            - x  - 3x  + -- x - 3 
                             2             2



                             2  3     2   25  
       1, 2, 3, 8            - x  - 4x  + -- x - 4 
                             3             3



                             5  3     2   61  
       1, 2, 3, 9            - x  - 5x  + -- x - 5 
                             6             6
Gnuplot source 
set xrange [0.9:4.1]
  plot           -2./3.*x*x*x +4.*x*x -19./3.*x +4. title "" with lines
replot           -1./2.*x*x*x +3.*x*x  -9./2.*x +3. title "" with lines
replot           -1./3.*x*x*x +2.*x*x  -8./3.*x +2. title "" with lines 
replot           -1./6.*x*x*x    +x*x  -5./6.*x +1. title "" with lines 
replot                                        x     title "" with lines
replot            1./6.*x*x*x    -x*x +17./6.*x -1. title "" with lines
replot            1./3.*x*x*x -2.*x*x +14./3.*x -2. title "" with lines
replot            1./2.*x*x*x -3.*x*x +13./2.*x -3. title "" with lines
replot            2./3.*x*x*x -4.*x*x +25./3.*x -4. title "" with lines
replot            5./6.*x*x*x -5.*x*x +61./6.*x -5. title "" with lines
pause -1

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Datum/vrijemeSmanjeni pregledDimenzijeKorisnikKomentar
trenutno22:00, 7 novembar 2013Smanjeni pregled verzije na dan 22:00, 7 novembar 20131.649 × 959 (67 KB)Jochen BurghardtUser created page with UploadWizard

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