Maple Programme fuer Pruefung 4

lagrange:= proc(liste1, liste2) local funktion, summand, i , j: funktion := 0: summand := 0: for i from 1 to nops(liste1) do summand := op(i, liste2): for j from 1 to nops(liste1) do if (i <> j) then summand := summand * (x - op(j,liste1))/(op(i,liste1) - op(j,liste1)): end if: end do: funktion := funktion + summand: end do: end proc:

lagrange([x[0],x[1],x[2]],[f(x[0]),f(x[1]),f(x[2])]);

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simplify(evalf(lagrange([-Pi/4,0,Pi/4],[cos(-Pi/4),cos(0), cos(Pi/4)])));

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nevQ := proc(i,j) if j > 0 then return( sort( expand( ( (x-op(1+i-j,xp))*nevQ(i,j-1) - (x-op(1+i,xp))*nevQ(i-1,j-1) ) / ( op(1+i,xp)- op(1+i-j,xp) ) ))); else return( op(1+i,fp) ); end if; end proc:

f := x -> x*ln(x): xp := [8.0,8.2,8.5,8.6,8.8,9.0]: fp := map(f, xp):nevQ(5,5);

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restart:

r := proc(x,i) if i > 0 then return evalf( 1/(r(x,i-1) - a(x,i-1)) ) else return evalf(x) end if; end proc: a := (x,i) -> trunc(r(x,i)):p := proc(x,i) if i=-2 then return 0 elif i=-1 then return 1 elif i=0 then return a(x,0) else return a(x,i)*p(x,i-1)+p(x,i-2) end if; end proc:q := proc(x,i) if i=-2 then return 1 elif i=-1 then return 0 elif i=0 then return 1 else return a(x,i)*q(x,i-1)+q(x,i-2) end if; end proc:

Approximation von Pim:=[ seq(p(Pi,k)/q(Pi,k), k=0..11)];

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Fehler:abs(evalf(op(nops(m)-1,m))-evalf(Pi));

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restart:

irrZByStep := proc(x0, a, p, q, i) local xi, j, f: Digits:=20: xi := x0: f := (x) -> x**q - a**p: for j from 1 to i do xi := xi - (f(xi)/D(f)(xi)): printf("Iteration : %3d = %10.20f\tgenau = %10.20f\n", j, evalf(xi), evalf(a**(p/q))): end do: end proc:irrZByPrecision := proc(x0, a, p, q, k) local xi, j, f: Digits := abs(log[10](k))*2: xi := x0: j := 1: f := (x) -> x**q - a**p: while (abs(evalf(xi**p - a**(p/q))) > evalf(k)) do xi := xi - (f(xi)/D(f)(xi)): j := j + 1: printf("Iteration : %3d = %10.20f\t**p = %10.20f\tgenau = %10.20f\n",j, evalf(xi), evalf(xi**p), evalf(a**(p/q))): end do: printf("Genauigkeit %e erhalten nach %d Iterationsschriftten :\t10.50f", k, j, evalf(xi**p)): end proc:

sqrt(2);irrZByStep(1, 2, 1, 2, 10);

Iteration : 1 = 1.50000000000000000000 genau = 1.41421356237309504880Iteration : 2 = 1.41666666666666666670 genau = 1.41421356237309504880Iteration : 3 = 1.41421568627450980390 genau = 1.41421356237309504880Iteration : 4 = 1.41421356237468991060 genau = 1.41421356237309504880Iteration : 5 = 1.41421356237309504880 genau = 1.41421356237309504880Iteration : 6 = 1.41421356237309504880 genau = 1.41421356237309504880Iteration : 7 = 1.41421356237309504880 genau = 1.41421356237309504880Iteration : 8 = 1.41421356237309504880 genau = 1.41421356237309504880Iteration : 9 = 1.41421356237309504880 genau = 1.41421356237309504880Iteration : 10 = 1.41421356237309504880 genau = 1.41421356237309504880

irrZByPrecision(1, 2, 1, 2, 10**(-4));

Iteration : 2 = 1.50000000000000000000 **p = 1.50000000000000000000 genau = 1.41421360000000000000Iteration : 3 = 1.41666670000000000000 **p = 1.41666670000000000000 genau = 1.41421360000000000000Iteration : 4 = 1.41421570000000000000 **p = 1.41421570000000000000 genau = 1.41421360000000000000Genauigkeit 1.000000e-04 erhalten nach 4 Iterationsschriftten : 10.50f

hilb := proc ( f , gr, min , max ) local m1, i, j, a1, l1, k, m2, i2, j2, a2, l2, k2, h, g, res, loes, grad, a; with(LinearAlgebra): grad := gr+1; m2 := Matrix(grad); for i2 from 1 to grad do for j2 from 1 to grad do m2[i2,j2] := Int((x^(j2+i2-2)),x=min..max); end do; end do; a2 := Vector(grad,symbol=a); l2 := Matrix(grad,1); for k2 from 1 to grad do l2[k2,1] := Int(f(x)*x^(k2-1),x=min..max); end do; print(m2.a2=l2); m1 := Matrix(grad); for i from 1 to grad do for j from 1 to grad do m1[i,j] := int((x^(j+i-2)),x=min..max); end do; end do; a1 := Vector(grad,symbol=a); l1 := Vector(grad); for k from 1 to grad do l1[k] := int(f(x)*x^(k-1),x=min..max); end do; print(m1.a1=l1); for i from 1 to grad do h := 0; for j from 1 to grad do h := h + a[j]*m1[i,j]; end do; g[i] := h = l1[i]; print(g[i]); end do; res:=solve({seq(g[i],i=1..grad)},{seq(a[i],i=1..grad)}); loes := 0; for i from 1 to grad do loes := loes + a[i]*x^(i-1); end do; printf("\t\t\tDie Loesung lautet\n:"); print(eval(evalf(loes),evalf(res))); return (eval(loes,res)); end proc:

g := unapply(hilb(x->x*ln(x), 3, 1, 4),x);

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restart;

tschebyschew := proc ( i , min , max ) return seq(1/2*((max-min)*cos((2*k-1)/(2*i)*Pi)+min+max),k=1..i); end proc:lagrange := proc( liste1 , liste2) local res, zaehler, nenner, laenge, i, n; Digits:=20; res := 0; if nops(liste1) = nops(liste2) then laenge := nops(liste1); for n from 1 to laenge do zaehler := 1; nenner := 1; for i from 1 to laenge do if i <> n then zaehler := zaehler * (x - op(i,liste1)); nenner := nenner * (op(n,liste1)-op(i,liste1)); end if; end do; res := res + ((zaehler/nenner)*op(n,liste2)); end do; else printf("Die Listen sind nicht gleich lang"); end if; res := sort(expand(res)); return res; end proc:

Funktion N\344hern:l1 := [1.0,2.0,3.0,4.0];

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l2 := map(x->x*ln(x),l1);

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fa:=lagrange(l1,l2);

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N\344herung mit Tscherbyschlampel1 := [tschebyschew(4,1,4)];

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l2 := map(x->x*ln(x),l1);

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fb:=sort(evalf(lagrange(l1,l2)));

NiM+SSNmYkc2Ii1JKWxhZ3JhbmdlR0YlNiRJI2wxR0YlSSNsMkdGJQ==

restart;lagrange:= proc(liste1, liste2) local funktion, summand, i , j: funktion := 0: summand := 0: for i from 1 to nops(liste1) do summand := op(i, liste2): for j from 1 to nops(liste1) do if (i <> j) then summand := summand * (x - op(j,liste1))/(op(i,liste1) - op(j,liste1)): end if: end do: funktion := funktion + summand: end do: end proc:li1:=[-2,-1,0,1,2];

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li2:=map(x->exp(abs(x)),li1);

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g:=lagrange(li1,li2);

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sort(simplify(expand(g)));

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restart;tschebyschew := proc ( x , i ) if i = 0 then return 1; elif i = 1 then return x; else return 2*x*tschebyschew(x,i-1)-tschebyschew(x,i-2); end if; end proc:tschebyschewNull := proc ( i , min , max ) return seq(1/2*((max-min)*cos((2*k-1)/(2*i)*Pi)+min+max),k=1..i); end proc:

g:=expand(tschebyschew(x,7));

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nulls:=evalf(tschebyschewNull(7,-1,1));

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g:=expand(tschebyschew(x,4));

NiM+SSJnRzYiLCgqJEkieEdGJSIiJSIiKSokRigiIiMhIikiIiJGLg==

plot(g,x=-1..1);

LSUlUExPVEc2Ji0lJ0NVUlZFU0c2JDdncDckJCEiIiIiISQiIiJGLDckJCEzJ3BtbSJIVSwiKikqISM9JCIzRDxBSlRoSy4kKUYyNyQkITMhUkxMJGUlRz95KkYyJCIzRVd1Knp5MCMqcCdGMjckJCEzdSoqKipcKG9VSW4qRjIkIjNqQTxNITQlPiY9JkYyNyQkITNwbW1tO3AwayYqRjIkIjNORihbb0d0KWVQRjI3JCQhMyRITDMtKSpHI3AlKkYyJCIzbCIpPiRmQ0B0ZSNGMjckJCEzRisrdlY1U3UkKkYyJCIzW01VYCJbKXl5OUYyNyQkITNebTtIMkpkeiMqRjIkIjM2KWY7SENDdEolISM+NyQkITN2S0wkMzxYWj0qRjIkITN2VndIJ3BSUGImRlM3JCQhMydmbVQmUTc1eSEqRjIkITNlRFVyWiVRZGYiRjI3JCQhMzoqKipcaUlkOSgqKUYyJCEzRVFLLjgsS2tERjI3JCQhM1lMJGVSUDhbJykpRjIkITNONENDWjBBak1GMjckJCEzbm1tbVQlcCJlKClGMiQhM0lkZC8pXDtYSCVGMjckJCEzJmVtbW13bk1hKUYyJCEzUCNcMFZtcDh4JkYyNyQkITM6bW1tIjRtKEckKUYyJCEza1Uuazt5JCopKnBGMjckJCEzKSoqKipcaSZbMzoiKUYyJCEzNlZbXjFGMCopekYyNyQkITMiUUxMM2kuOSF6RjIkITM5Sm0jb09GTncpRjI3JCQhMyczKytEdyRILnhGMiQhM3cyImUlKVEwP0kqRjI3JCQhMyJvbW1UIVI9MHZGMiQhMyI+N3M9MHQneicqRjI3JCQhM0srK11pIz1FUyhGMiQhM1V0dUVSYXg6KSpGMjckJCEzdEtMJDNpXytJKEYyJCEzKlFqMVB2bUwiKipGMjckJCEzQ21tO3pwWyg+KEYyJCEzdjtMWCwqcFIoKipGMjckJCEzdyoqKipcUDgjXDQoRjIkITNhcUNBVGwzKioqKkYyNyQkITMlb21tVCF5JSkpKXBGMiQhM1JhbDwlPjQkKikqKkYyNyQkITMkUkxMM0Z1RilvRjIkITM2JltwSVF0WiUqKkYyNyQkITMsLCtdUDJxd25GMiQhM0U7TTBlJW9xJykqRjI3JCQhMypwbW1UP0YxbidGMiQhMzEmKj1SaSVmeHYqRjI3JCQhM3RMTCRlXGciZmtGMiQhM3BWMWNFRmpeJSpGMjckJCEzXCsrXSh5JHBaaUYyJCEzYCUqbzQmPj16LipGMjckJCEzM0xMTCR5YUUiZUYyJCEzXzpfNVF2NCgqeUYyNyQkITNobW1tIj5zJUhhRjIkITNZUUI9Q1A7Sm1GMjckJCEzUysrK10kKjQpKlxGMiQhMydmSDVoJmZSIypcRjI3JCQhMzgrKytdXyZcYyVGMiQhMzEoKltaJSlIKyg+JEYyNyQkITMwKysrXTFhWlRGMiQhM1dcdi4vJ3lWUiJGMjckJCEzdm1tOy8jKVtvUEYyJCIzPzglbzQtKmVBREZTNyQkITNoTExMJD1leEokRjIkIjNNIWVuKHAkM0w7I0YyNyQkITMqUkxMTHRJZiRIRjIkIjMvJ0d1I0c0aylwJEYyNyQkITNdKytdUFl4IlwjRjIkIjNmI1xzZipbRFRgRjI3JCQhM0dNTExMN2kpNCNGMiQiM1RKKXBydDI9aidGMjckJCEzZCoqKipcUCdwc20iRjIkIjNzcyhlc0woKXokeUYyNyQkITMoKSoqKipcNzRfYzdGMiQiM00vKHBXO21vdilGMjckJCEzKTNMTEwzeCV6IylGUyQiM09dMFFGOE9iJSpGMjckJCEzZktMJGU5ZDtKJ0ZTJCIzMmF6JkdZdERvKkYyNyQkITNKTUxMM3MkUU0lRlMkIjNXaFlVYk1MXCkqRjI3JCQhM1QsK11pdkZAQUZTJCIzIylRPCpSKW9hZyoqRjI3JCQhM1xeb21tO3pyKSohI0AkIjMleVNmI1E/IyoqKioqRjI3JCQiMyZ5SyQzX05sLjVGUyQiM3c+WjhbQSU+KioqRjI3JCQiM0BDTCQzLURnNSNGUyQiM0h4YnAxSWBrKipGMjckJCIzZT9MZSpbJ1IzS0ZTJCIzbjhAcjBWdDwqKkYyNyQkIjMlcEpMJGV6dzVWRlMkIjNSWUgoM1w5OyYpKkYyNyQkIjNMYG1tbUorSWlGUyQiM2ksP3dSO3EhcCpGMjckJCIzciopKioqXFBRI1wiKUZTJCIzTHlzKTNiWkFaKkYyNyQkIjNHS0xMZSIqW0g3RjIkIjM8WSMqUWVjJyozKSlGMjckJCIzSSoqKioqKipwdnhsIkYyJCIzLVN2MitiJT0neUYyNyQkIjMkeioqKipcX3FuMiNGMiQiM0d6aThLTVYpcCdGMjckJCIzVikqKipcaSZwQFsjRjIkIjNSYyM0ajZaWlAmRjI3JCQiM0IpKioqKlwyJ0hLSEYyJCIzPDdWcHhodzdQRjI3JCQiM0VsbW1tWnZPTEYyJCIzeGA5UC0ocFgzI0YyNyQkIjNoKioqKioqXDJnb1BGMiQiM0tbQXIuL3Q8REZTNyQkIjNVS0wkZVI8KmZURjIkITN2KSopcEQ6XSNbOUYyNyQkIjNtKioqKioqXClIeGUlRjIkITN5YiNlKnBKIlJIJEYyNyQkIjNja207SCFvLSpcRjIkITNHRihvJnpWLmhcRjI3JCQiM3kpKioqXDdrLjZhRjIkITNIaWoyQ2RBbGxGMjckJCIzI2VtbW1UOUMjZUYyJCEzJz1nTDVHXmsjekYyNyQkIjMyKioqKlxpISozYGlGMiQhMyZ6XFUuImVyXCEqRjI3JCQiM1htbSJ6XCVbZ2tGMiQhMyszYjFNaipRWCpGMjckJCIzJVFMTEwkKnp5bSdGMiQhM3hzSU8tQ19hKCpGMjckJCIzZExMM0ZlI1J4J0YyJCEzJnlmZUZyL1knKSpGMjckJCIzSUxMJDNzcip6b0YyJCEzZHFOMjsrOVYqKkYyNyQkIjMuTExlOXcsJylwRjIkITMvUXZuSV5jKSkqKkYyNyQkIjN3S0xMM04xIzQoRjIkITNLN2hQJGYjSCoqKipGMjckJCIzZ2w7YSlHSnM+KEYyJCEzJz49KjM+ZzJ1KipGMjckJCIzYyoqKlwobyEqUi10RjIkITNdIyl6NipHYDoiKipGMjckJCIzXkwkZSpbb2MydUYyJCEzPDk2cyRIMCwiKSpGMjckJCIzTW1tO0hZdDd2RjIkITNAWEsiZlYqM28nKkYyNyQkIjMiSEwkZWs2LDF4RjIkITM5IyllakVMdCZIKkYyNyQkIjNZKioqKioqKnAoRyoqeUYyJCEzRWluInl1byx4KUYyNyQkIjMpSExMM1UvMzcpRjIkITNRdWI2QnFVbHpGMjckJCIzXW1tbVQ2S1UkKUYyJCEzTEEjZUtOKyZHcEYyNyQkIjNhKioqKlxQJFsvYSlGMiQhMyUzMmcxaEIueiZGMjckJCIzZktMTExiZFEoKUYyJCEzK0pdcChSaitXJUYyNyQkIjNgbW0ielc/KVwqKUYyJCEzWSdmblUkUUVfRkYyNyQkIjNbKytdaWAxaCIqRjIkITNyMkBPb2ohcCN6RlM3JCQiM1orK0RKJmZARSpGMiQiMzgpRyJ5PS89Z0NGUzckJCIzWCsrKytQRGokKkYyJCIzIzNyJFxFWGFfOEYyNyQkIjNYKyt2b3lNayUqRjIkIjMjPTFLUD5PKEdERjI3JCQiM1crK11QP1dsJipGMiQiMyMpeipHWFpna3gkRjI3JCQiM0wrXTdHOjN1JypGMiQiM01TQzRAeD8qPiZGMjckJCIzQisrdj01cyN5KkYyJCIzXSl6NmBFNyI0bkYyNyQkIjM3K11QNDBPIiopKkYyJCIzOSo0NiI0InAmMyQpRjI3JEYtRi0tJSZDT0xPUkc2JiUkUkdCRyQiIzVGKyRGLEYrRmBobC0lK0FYRVNMQUJFTFNHNiRRIng2IlEhRmVobC0lJVZJRVdHNiQ7JCEjNUYrRl5obDskITJPT0NYJXkjKlI1ISM7JCIyQXYnPSZlKSoqUjVGYGlsLSUlRk9OVEc2JCUqSEVMVkVUSUNBR0ZfaGw=

restart;liste := [seq(i+(i-1),i=1..100)];

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

nops(liste);

NiMiJCsi

restart;liste1:=[seq(sqrt(i),i=1..10)];

NiM+SSdsaXN0ZTFHNiI3LCIiIiokIiIjI0YnRikqJCIiJEYqRikqJCIiJkYqKiQiIidGKiokIiIoRiosJEYoRilGLCokIiM1Rio=

liste2:=map(x->1-abs(cos(x)),liste1);

NiM+SSdsaXN0ZTJHNiI3LCwmIiIiRigtSSRjb3NHNiRJKnByb3RlY3RlZEdGLEkoX3N5c2xpYkdGJTYjRighIiIsJkYoRigtRio2IyokIiIjI0YoRjRGLywmRihGKC1GKjYjKiQiIiRGNUYoLCZGKEYoLUYqNiNGNEYoLCZGKEYoLUYqNiMqJCIiJkY1RigsJkYoRigtRio2IyokIiInRjVGKCwmRihGKC1GKjYjKiQiIihGNUYoLCZGKEYoLUYqNiMsJEYzRjRGKCwmRihGKC1GKjYjRjpGKCwmRihGKC1GKjYjKiQiIzVGNUYo

restart;Sum(i^(3/2),i=10..50);

NiMtSSRTdW1HNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiRJImlHRigjIiIkIiIjL0YrOyIjNSIjXQ==

sum(i^(3/2),i=10..50);

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

restart;g:=x*sqrt(x+1)+ln(sqrt(x+1));

NiM+SSJnRzYiLCYqJkkieEdGJSIiIiwmRihGKUYpRikjRikiIiNGKS1JI2xuRzYkSSpwcm90ZWN0ZWRHRjBJKF9zeXNsaWJHRiU2IyokRipGK0Yp

f:=unapply(g,x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJjkkIiIiLCZGLkYvRi9GLyNGLyIiI0YvLUkjbG5HNiRJKnByb3RlY3RlZEdGNkkoX3N5c2xpYkdGJTYjKiRGMEYxRi9GJUYlRiU=

siehe aufgabe 2 definition von tschebyschew

gemeinsamkeit kann fuer verschiedene x-werte verwendet werdenunterschied einfache funktionen (ohne if, for, while) mit f:=x-> komplizierte mit f := proc(x) ...

restart;with(stats);

NiM3KkkmYW5vdmFHNiJJKWRlc2NyaWJlR0YlSSRmaXRHRiVJK2ltcG9ydGRhdGFHRiVJJ3JhbmRvbUdGJUkqc3RhdGV2YWxmR0YlSSpzdGF0cGxvdHNHRiVJKnRyYW5zZm9ybUdGJQ==

xp := [1940,1950,1960,1970,1980,1990,2000];

NiM+SSN4cEc2IjcpIiVTPiIlXT4iJWc+IiVxPiIlISk+IiUhKj4iJSs/

fp := [132165,151326,179323,203302,226542,249633,274882];

NiM+SSNmcEc2IjcpIidsQDgiJ0U4OiInQiR6IiInLUw/IidVbEEiJ0wnXCMiJyMpW0Y=

ff := fit[leastsquare[[x,y], y=a*x+b, {a,b}]]([xp,fp]);

NiM+SSNmZkc2Ii9JInlHRiUsJkkieEdGJSMiJikqUikiI04jISlSIXk7JCIiKCIiIg==

f :=unapply(evalf(rhs(ff)), x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCY5JCQiK2RHJSoqUiMhIickIStWVFZEWCEiJCIiIkYlRiVGJQ==

plot(f(x),x=1930..2010);

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

f1:=abs(132165-f(1940));

NiM+SSNmMUc2IiQiKCsrciIhIiQ=

f2:=abs(151326-f(1950));

NiM+SSNmMkc2IiQiKEclR0ohIiQ=

f3:=abs(179323-f(1960));

NiM+SSNmM0c2IiQiJ1YicCkhIiQ=

f4:=abs(203302-f(1970));

NiM+SSNmNEc2IiQiJzooWykhIiQ=

f5:=abs(226542-f(1980));

NiM+SSNmNUc2IiQiJidHKikhIiQ=

f6:=abs(249633-f(1990));

NiM+SSNmNkc2IiQiJ1UiPikhIiQ=

f7:=abs(274882-f(2000));

NiM+SSNmN0c2IiQiJ0gvViEiJA==

Fehler:=(f1+f2+f3+f4+f5+f6+f7)/7;

NiM+SSdGZWhsZXJHNiIkIitydih5NyIhIic=

f(2005);

NiMkIiomR15rRyEiJA==

restart;tschebyschew := proc ( i , min , max ) return seq(1/2*((max-min)*cos((2*k-1)/(2*i)*Pi)+min+max),k=1..i); end proc:Length := proc(ll) return nops(ll); end proc: Last := proc(ll) return op(-1, ll); end proc: Append := proc(ll, x) return [op(ll), x]; end proc: Member := proc(ll, p) return op(p, ll); end proc: Take := proc(ll, n) if n > 0 then return [ op(1..n, ll) ] elif n < 0 then return [ op(n..-1, ll) ] end if; end proc: with(plots, listplot):lagrange := proc(xl, fl) local i, j, l, ll, pol; ll := []: pol := 0: i := 1: while i <= Length(xl) do l := 1; j := 1; while j <= Length(xl) do if j <> i then l := l*(x-Member(xl, j))/(Member(xl, i) - Member(xl, j)); end if; j := j+1; end do; ll := Append(ll, l); pol := pol + l*Member(fl, i); i := i+1; end do: return( sort( expand( pol ) ) ); end proc:f:=(x)->1/2*cos(x)+1/3*sin(2*x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSRjb3NHRiU2IzkkIyIiIiIiIy1JJHNpbkdGJTYjLCRGMEYzI0YyIiIkRiVGJUYl

mini:=0;

NiM+SSVtaW5pRzYiIiIh

maxi:=3;

NiM+SSVtYXhpRzYiIiIk

plot(f(x),x=mini..maxi);

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

li01:=[0,1,2,3];

NiM+SSVsaTAxRzYiNyYiIiEiIiIiIiMiIiQ=

li02:=evalf(map(f,li01));

NiM+SSVsaTAyRzYiNyYkIisrKysrXSEjNSQiK19IXUtkRikkISttIjRNZyVGKSQhK3h1TSIpZUYp

P04:=unapply(simplify(lagrange(li01,li02)),x);

NiM+SSRQMDRHNiJmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsKiokOSQiIiQkIitZIilSYUwhIzUqJEYuIiIjJCErKD5TKGY6ISIqRi4kIit5MWIoSCJGNyQiKysrKytdRjIiIiJGJUYlRiU=

plot({f(x)-P04(x)},x=0..3);

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

fehler:=abs(evalf(f(x))-P04(x));

NiM+SSdmZWhsZXJHNiItSSRhYnNHSSpwcm90ZWN0ZWRHRig2IywuLUkkY29zRzYkRihJKF9zeXNsaWJHRiU2I0kieEdGJSQiKysrKytdISM1LUkkc2luR0YtNiMsJEYwJCIiIyIiISQiK0xMTExMRjMqJEYwIiIkJCErWSIpUmFMRjMqJEYwRjkkIisoPlMoZjohIipGMCQhK3kxYihIIkZEJCErKysrK11GMyIiIg==

plot(fehler,x=0..3);

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

li11:=[evalf(tschebyschew(4,mini,maxi))];

NiM+SSVsaTExRzYiNyYkIisqSD5lKUchIiokIitcXi11P0YpJCIrNyZbKGYjKiEjNSQiKiwyPTkiRik=

li12:=map(f,li11);

NiM+SSVsaTEyRzYiNyYkISsvWzRwayEjNSQhK1x6dkZfRikkIit2QnQyaUYpJCIrOiNbP3MmRik=

P4:=unapply(simplify(lagrange(li11,li12)),x);

NiM+SSNQNEc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwqKiQ5JCIiJCQiK2UqKTQnXCQhIzUqJEYuIiIjJCErayY+dmkiISIqRi4kIitFWFQ2OUY3JCIrSVdZPFZGMiIiIkYlRiVGJQ==

plot({f(x),P4(x)},x=mini..maxi);

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

feh4:=unapply(abs(evalf(f(x))-P4(x)),x);

NiM+SSVmZWg0RzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkYWJzR0kqcHJvdGVjdGVkR0YuNiMsLi1JJGNvc0c2JEYuSShfc3lzbGliR0YlNiM5JCQhKysrKytdISM1LUkkc2luR0YzNiMsJEY2JCIiIyIiISQhK0xMTExMRjkqJEY2IiIkJCIrZSopNCdcJEY5KiRGNkY/JCErayY+dmkiISIqRjYkIitFWFQ2OUZKJCIrSVdZPFZGOSIiIkYlRiVGJQ==

plot(feh4(x),x=mini..maxi);

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

feh4(0);

NiMkIipxYmAjbyEjNQ==

li21:=[tschebyschew(8,mini,maxi)];

NiM+SSVsaTIxRzYiNyosJi1JJGNvc0c2JEkqcHJvdGVjdGVkR0YrSShfc3lzbGliR0YlNiMsJEkjUGlHRisjIiIiIiM7IyIiJCIiI0YzRjEsJi1GKTYjLCRGLyNGNEYyRjNGM0YxLCYtRik2IywkRi8jIiImRjJGM0YzRjEsJi1GKTYjLCRGLyMiIihGMkYzRjNGMSwmRkIjISIkRjVGM0YxLCZGPEZIRjNGMSwmRjdGSEYzRjEsJkYoRkhGM0Yx

li22:=evalf(map(f,li21));

NiM+SSVsaTIyRzYiNyokIStfQyE9LychIzUkISstNDgiKXBGKSQhK0JucyR5J0YpJCErKj0tNWAjRikkIitCc14jKlJGKSQiK1tHRXByRikkIitaMl1ia0YpJCIrbFQnKio9JkYp

P8:=unapply(sort(simplify(lagrange(li21,li22))),x);

NiM+SSNQOEc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwyKiQ5JCIiKCQiKyZvIikqKWYnISM3KiRGLiIiJyQhKyVlalVCKCEjNiokRi4iIiYkIitSSnknXCMhIzUqJEYuIiIlJCErJkd4RnoiRjwqJEYuIiIkJCErJVszQjEkRjwqJEYuIiIjJCErcEQ9IylIRjxGLiQiKykzcUZ0J0Y8JCIrO1RZKSpcRjwiIiJGJUYlRiU=

feh8:=unapply(abs(evalf(f(x))-P8(x)),x);

NiM+SSVmZWg4RzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkYWJzR0kqcHJvdGVjdGVkR0YuNiMsNi1JJGNvc0c2JEYuSShfc3lzbGliR0YlNiM5JCQhKysrKytdISM1LUkkc2luR0YzNiMsJEY2JCIiIyIiISQhK0xMTExMRjkqJEY2IiIoJCIrJm8iKSopZichIzcqJEY2IiInJCErJWVqVUIoISM2KiRGNiIiJiQiK1JKeSdcI0Y5KiRGNiIiJSQhKyZHeEZ6IkY5KiRGNiIiJCQhKyVbM0IxJEY5KiRGNkY/JCErcEQ9IylIRjlGNiQiKykzcUZ0J0Y5JCIrO1RZKSpcRjkiIiJGJUYlRiU=

plot(feh8(x),x=mini..maxi);

-%%PLOTG6&-%'CURVESG6$7[x7$$""!F+$"3!R:+++%)e`"!#@7$$"3"***\7.K[V?!#?$"3:@^e<X!GS"F.7$$"3#)***\iSmp3%F2$"3U'y8ix"ot7F.7$$"3t**\P4'\/8'F2$"3*)[F0fiW[6F.7$$"3l****\7G$R<)F2$"3vxz0t#Hq-"F.7$$"3'**\i:gT<-"!#>$"3cH+3A%HO4*!#A7$$"3&***\(=#**3E7FG$"34y4Z2?!Q&zFJ7$$"3%**\(=U#Q/V"FG$"3(G,iZ'y9]oFJ7$$"3$*****\ilyM;FG$"3@aN%4M7?y&FJ7$$"34+D"G)[8R=FG$"3r6Nd&o[([ZFJ7$$F1FG$"3*4K_Z)zr\PFJ7$$"3t*\PM_JyC#FG$"3[Z3o&4*G%y#FJ7$$"3!****\P%)z@X#FG$"3PTQA"eQ=&=FJ7$$"31+D1k"Gll#FG$"3B(Rh?X1v^*!#B7$$"3()**\P%[w3'GFG$"3+/-a(y1<M)!#C7$$"3q*\(o/[AlIFG$"3gs/_$eGw`(F\p7$$"3')*****\7t&pKFG$"3529b#R#Qg:FJ7$$"3.+DJX9#RZ$FG$"3<hj")3u-PBFJ7$$"3>+]il(p#yOFG$"3ql)p"fkF%3$FJ7$$"3N+v$f3=E)QFG$"3-1$pl$3q-QFJ7$$"3$)***\iSmp3%FG$"39Re%ojkG\%FJ7$$"3W**\(o/jc\%FG$"37?]2x7j!z&FJ7$$"3z****\(ofV!\FG$"3Nc#*Qcv%>)pFJ7$$"37+]7Gj08`FG$"3(GhO?Vt52)FJ7$$"3v***\(oHv@dFG$"3c-<5v&f@1*FJ7$$"3Q**\P4'\/8'FG$"3I()pd"G\#f**FJ7$$"3s******\i9RlFG$"33#4*4O!Gm2"F.7$$"3:+vVtdN]sFG$"3#[%o/I)Gn>"F.7$$"3e+](oHl:'zFG$"3OW&*4[4m#H"F.7$$"3.,DJ?[xs')FG$"3t*>>PZ"Gm8F.7$$"32++vVV)RQ*FG$"3%ooFj))f$>9F.7$$"3"*\(=nQ>&45!#=$"3*fS$QR3e`9F.7$$"3&**\i!R.k!3"Ffu$"3jN1A!)oaq9F.7$$"3)\PM_"3?;6Ffu$"3%R'3/5$QIZ"F.7$$"3+]iS"Hh<:"Ffu$"3-GFI76yr9F.7$$"3,D"yvw@t="Ffu$"3DBOG*o`pY"F.7$$"3/++vVA)GA"Ffu$"3g$p%f+)H(e9F.7$$"3(**\(=U"[GQ"Ffu$"3u1/i?#fTQ"F.7$$"3;+]iSS"Ga"Ffu$"3:'pqmy[%e7F.7$$"3)*\P%)*)pzA;Ffu$"3#phmE:?/="F.7$$"33+D1R*zFq"Ffu$"31#*3&zb5U4"F.7$$"3=]7G))Gw#y"Ffu$"3nuy$3[_6+"F.7$$"3+++]Peui=Ffu$"3UU/7DB)[-*FJ7$$"3*)**\il*eK%>Ffu$"351%eR(yx')zFJ7$$"31++v$4sP-#Ffu$"3.BV.D6_9pFJ7$$"3A+](=A&G/@Ffu$"3VLD"[DU#=eFJ7$$"37+++]$)z%=#Ffu$"3%H>/F$RH2ZFJ7$$"3++]7y9JlAFfu$"3a`&R^+'G!f$FJ7$$"3<++D1Y#eM#Ffu$"3Ky<i-#>^Z#FJ7$$"3L+]PMxLECFfu$"3T0Dx%)y,p8FJ7$$"3A++]i3&o]#Ffu$"3q^><(R=cy#F\p7$$"3<]7yD8)pe#Ffu$"36#yWd=EE&yF\p7$$"37+D1*y6rm#Ffu$"3Ci?SZHPA=FJ7$$"33]PM_ACZFFfu$"3+B`sXi+GGFJ7$$"3.+]i:FPFGFfu$"3wh1a`k"zz$FJ7$$"3**\i!*yJ]2HFfu$"3_PN?#oZ$GZFJ7$$"3$**\(=UOj()HFfu$"3OxB`t$3gh&FJ7$$"3*)\(oa5kx1$Ffu$"3iJ#QSFY!ekFJ7$$"3%)***\(oX*y9$Ffu$"31pe#)3U-_sFJ7$$"37++]ipZ'H$Ffu$"3S&*ooXtR!f)FJ7$$"3")***\iNf]W$Ffu$"3OW<k>L)pu*FJ7$$"3_******\<k$f$Ffu$"3)4`"=<0fr5F.7$$"3z***\P9CAu$Ffu$"3;^"zfSt%\6F.7$$"3_***\igsg*QFfu$"3=WPAr<:57F.7$$"3!)***\(o5#*\SFfu$"3.rRak6)3D"F.7$$"3%********HXo7%Ffu$"3()HAiW;&RE"F.7$$"33++DJ&pP?%Ffu$"3])*)H$ezGs7F.7$$"3n****\iPp!G%Ffu$"3+E%eUo-gF"F.7$$"3!)***\P*zhdVFfu$"3Who*p"*>_F"F.7$$"3A++v$fQen%Ffu$"394CKEHFF7F.7$$"33++v$>fS*\Ffu$"3d3nf/#Qe6"F.7$$"3G+++D#fE:&Ffu$"3iLt@&Hz//"F.7$$"3]++Dc#f7J&Ffu$"3m9]*o$3AT&*FJ7$$"3s++](Gf)paFfu$"3W&***>%*>M%e)FJ7$$"3$)***\(=$f%GcFfu$"359s:De!3b(FJ7$$"3U*\7`%*)f"z&Ffu$"3c=*)*[g3]U'FJ7$$"36+](=dQZ&fFfu$"3=?2xr(HHD&FJ7$$"3!3]P%)>yy6'Ffu$"34A7mGnS^SFJ7$$"3Q+++Dy,"G'Ffu$"3eq3N\9_OGFJ7$$"3(3+voH6ZU'Ffu$"3$*f0-Lm\n<FJ7$$"3C++voZSolFfu$"3kZ!R&>Ou'4(F\p7$$"32](=n8GVg'Ffu$"3/fw"G$)H0[%F\p7$$"3#**\(o/:DSmFfu$"3hOb#\X9%y=F\p7$$"3Rv=n)=8#emFfu$"3F'RN!yxhIeFbp7$$"3w\ils[<wmFfu$"3&\='Qg"zE3(Fbp7$$"37C1kcl8%p'Ffu$"3%G*)HT+7a*>F\p7$$"3g**\iS#)47nFfu$"3e3\')f&4#yKF\p7$$"3G*\il(\%Ry'Ffu$"3;u^jCdxi$)F\p7$$"33++]7<zboFfu$"3*)ozRGp`O8FJ7$$"3k**\7Glb<qFfu$"3V;N(3+R!GCFJ7$$"3J++vV8KzrFfu$"3rVZF,^HjMFJ7$$"3)4+v$fh3TtFfu$"30w]wWj^LWFJ7$$"3`+++v4&G](Ffu$"3mzwrlE5J`FJ7$$"3z****\7+GlwFfu$"38g66`6$G:'FJ7$$"3<+++]!4x#yFfu$"3](Rs")of&*)oFJ7$$"3_++](3Q,*zFfu$"3">(G$Q0cr`(FJ7$$"3!)*****\7nD:)Ffu$"3[_z]pai#4)FJ7$$"39+++v!GcY)Ffu$"370#**[m:s*))FJ7$$"3Z+++D!*oy()Ffu$"3>YT'**Hd0N*FJ7$$"3o]Pfe8w\))Ffu$"3JkC$f=i`S*FJ7$$"3y*\(=#pL3#*)Ffu$"3^aXS)HVFW*FJ7$$"3)*\7yDg!>**)Ffu$"3"f,48oLHY*FJ7$$"3=+]Pf$yH1*Ffu$"3Pr'\27%>m%*FJ7$$"3R](oHp]S8*Ffu$"3^'=9"4?"GX*FJ7$$"3f+DcEI70#*Ffu$"3v#[;Z>+JU*FJ7$$"3o\i:g`>w#*Ffu$"33tR&)>eRx$*FJ7$$"3))***\PpnsM*Ffu$"34&*\*)["fgJ*FJ7$$"3e+]P4_J&o*Ffu$"3jI/qQ5oA))FJ7$$"3,++]siL-5!#<$"3p2%ow21?.)FJ7$$"3,++DJL(4."Fh]m$"3(*ew!)H=)*prFJ7$$"3,+++!R5'f5Fh]m$"3)[?`yAg(phFJ7$$"3++v=(4AH4"Fh]m$"3%)enr$\,?)[FJ7$$"3)***\P/QBE6Fh]m$"3ng.MU@)o^$FJ7$$"3&**\(o4.sb6Fh]m$"3UMUuJ8***G#FJ7$$"3"******\"o?&="Fh]m$"3R1Xc!\SZ3"FJ7$$"3!*\P%)*\#Q,7Fh]m$"3Gy#)o8)[BX%F\p7$$"3))*\(o%=ev@"Fh]m$"3z:dYM:aA<F\p7$$"34]7`pQtL7Fh]m$"3!*of'ze)fHwF\p7$$"32+]Pa&4*\7Fh]m$"3>/Ksq3`A8FJ7$$"32++v3dr!G"Fh]m$"3rq-_s<R)G#FJ7$$"33+]7j=_68Fh]m$"3lc()pBU40JFJ7$$"3>+vV`[mV8Fh]m$"3ACT0\/'3y$FJ7$$"34++vVy!eP"Fh]m$"3G'4o3)*)zlUFJ7$$"3/]7G$\m0R"Fh]m$"3=J'fnE/LU%FJ7$$"3)**\7G9D`S"Fh]m$"3!fN,1h4*RXFJ7$$"32D"yvY/FT"Fh]m$"3o)RK/j6Ie%FJ7$$"3:]PM#z$3?9Fh]m$"3%)oZNE+4;YFJ7$$"3,v$4r6juU"Fh]m$"3X+4/F*\#RYFJ7$$"34+](=WU[V"Fh]m$"3*p*3$y%Rh_YFJ7$$"36voaS?!GW"Fh]m$"3_nOdX#3il%FJ7$$"3!*\(=#R;w]9Fh]m$"3tfW')e\w[YFJ7$$"3"\i!*yB@(e9Fh]m$"39/S6WC]IYFJ7$$"3$**\il$3om9Fh]m$"3"p7,1()f;g%FJ7$$"3&*\i!R.+E["Fh]m$"3H;Dh1.H8XFJ7$$"3)****\7B>&)\"Fh]m$"3owm9dP&fQ%FJ7$$"3(**\7`P!fJ:Fh]m$"3a(y'3XAL3SFJ7$$"3)***\P>:mk:Fh]m$"3?Z5F'G$>+NFJ7$$"3'***\iv&QAi"Fh]m$"3wI?g(egKR#FJ7$$"31++vtLU%o"Fh]m$"3*[wJK+.z/"FJ7$$"3(**\i!>T[+<Fh]m$"3/A"R(36w**pF\p7$$"3()**\Pk[a;<Fh]m$"3LC7DHu*\e$F\p7$$"3$*\7.P_dC<Fh]m$"3gD17CHg6>F\p7$$"3++vo4cgK<Fh]m$"3LbFW1GReEFbp7$$"31]PM#)fjS<Fh]m$"3oK'=aTP([8F\p7$$"3!******\Nm'[<Fh]m$"3p"QcVy>(GHF\p7$$"3-+](o'44!y"Fh]m$"3Z0"*4E(z'>()F\p7$$"3"****\(yb^6=Fh]m$"3q4`M)3$\w8FJ7$$"3&**\il]?>%=Fh]m$"3o\KJN%o=y"FJ7$$"3)***\PMaKs=Fh]m$"3wb1*GrJ()4#FJ7$$"33+D"G#\31>Fh]m$"3ZtZ+=0)RM#FJ7$$"3&****\7TW)R>Fh]m$"3UM"[zz;.[#FJ7$$"33+v=7;,b>Fh]m$"38s!HO#G^3DFJ7$$"3****\78)y,(>Fh]m$"3=b'H*["pz^#FJ7$$"3*)*\iS,Y`)>Fh]m$"3g5t$y4b-^#FJ7$$"3z*****\@80+#Fh]m$"3&eIhH'*or[#FJ7$$"3q***\Pm,H.#Fh]m$"3COY)y5IfR#FJ7$$"30++]7,Hl?Fh]m$"3*oN4_"4HmAFJ7$$"3')**\P4w)R7#Fh]m$"3!f"z_S9/;?FJ7$$"3;]iSw0.S@Fh]m$"3knJJy-;h>FJ7$$"3-+vVVN2c@Fh]m$"3MFWRf!H#=>FJ7$$"3()\(o/^;@<#Fh]m$"3_&H(4%[k.*=FJ7$$"3<++]x%f")=#Fh]m$"3B%)f%z[B0)=FJ7$$"33](=#fYD.AFh]m$"3W^3PWY=!*=FJ7$$"3)**\P4%)\$=AFh]m$"3[0'4<j=.#>FJ7$$"3*)\ilA]WLAFh]m$"3*RJT^inF(>FJ7$$"3!)**\P/-a[AFh]m$"3&zB="4%*4\?FJ7$$"3q**\7Ly4!G#Fh]m$"3%[AOnHl4H#FJ7$$"3/+](=Yb;J#Fh]m$"32=o\09t[EFJ7$$"3()****\i@OtBFh]m$"3p5)H\<10n$FJ7$$"3')**\PfL'zV#Fh]m$"3=^,c_"z@3&FJ7$$"3>+++!*>=+DFh]m$"3(GOLo')>?^'FJ7$$"3L+]7ed*>`#Fh]m$"3%4?tHh&H]rFJ7$$"3.++DE&4Qc#Fh]m$"3zWR9:GJ]wFJ7$$"3%)\7G$p%ezDFh]m$"3<7/4_isGyFJ7$$"35+DJg)f`f#Fh]m$"3;*>P>(*3<&zFJ7$$"3,D"GQWZKg#Fh]m$"3+wt!p$eO!*zFJ7$$"3O]PMF]86EFh]m$"3laA&RoxF,)FJ7$$"3Fv$f3hA!>EFh]m$"3s(Q&=RLB=!)FJ7$$"3=+]P%>5pi#Fh]m$"3h?jzPV21!)FJ7$$"3R]7`MfSTEFh]m$"3t#3$oOv%e$zFJ7$$"3;+vou;!fl#Fh]m$"3;U&eC^o5!yFJ7$$"3#*\P%[T(RqEFh]m$"3sMCWrzg*f(FJ7$$"39+++bJ*[o#Fh]m$"3%\I6F/%[ItFJ7$$"36+]7j17=FFh]m$"3"e&4qmP4jkFJ7$$"34++Dr"[8v#Fh]m$"3h;FW=JD%G&FJ7$$"30+]i]s1"y#Fh]m$"3q@*e4.Ye/%FJ7$$"3++++Ijy5GFh]m$"3pOZ:%HP:w#FJ7$$"3.+v=nIZUGFh]m$"37'fU&R9;b:FJ7$$"32+]P/)fT(GFh]m$"3'>%[Wo)y,R)F\p7$$"3B]7.n=u")GFh]m$"3Q7TJ88[tyF\p7$$"3'**\(oHRK*)GFh]m$"3us;0:s)G'zF\p7$$"3o\PM#*f!p*GFh]m$"3.@()GGp?P()F\p7$$"3&)*****\0)[/HFh]m$"3O\^K5'f!G5FJ7$$"3=+DJ!=_'>HFh]m$"3wAPUZA$Rg"FJ7$$"31+]i0j"[$HFh]m$"3_CM!RY9Gg#FJ7$$"3yu=UnU'H%HFh]m$"3;E1Ws/!\M$FJ7$$"3%*\(=#HA6^HFh]m$"3d/wg5-r\UFJ7$$"35Dc,">g#fHFh]m$"3fjMR*yzKL&FJ7$$"3E+D"G:3u'HFh]m$"3B2=!\nMEh'FJ7$$"3%y$4rL@[rHFh]m$"3\UkSkELJtFJ7$$"3Uv$4Y6cb(HFh]m$"3sp;r12$e5)FJ7$$"3b7y]&4I'zHFh]m$"3n%H1=p`&Q*)FJ7$$"38]iSwSq$)HFh]m$"3BNB\Oi*>$)*FJ7$$"3r(o/t0yx)HFh]m$"3T/;C1C()y5F.7$$"3%[7.#Q?&=*HFh]m$"3wK<(*Rv8"="F.7$$"3Wi:5>g#f*HFh]m$"3ezdlRiE!H"F.7$$""$F+$"3`"*\]bs`19F.-%&COLORG6&%$RGBG$"#5!""$F+F[]oF\]o-%+AXESLABELSG6$Q"x6"Q!Fa]o-%%VIEWG6$;F\]o$"#IF[]o;$!/JuL>h+GFG$"2'GS97&[lc"F2-%%FONTG6$%*HELVETICAGFj\o

feh8(0.1);

NiMkIihPK1giISM1

fehler:=proc(f,mini,maxi,step) local i,res; res := 0; for i from mini by step to maxi do if f(i) > res then res := f(i); end if; end do; return res; end proc:fehler(feh8,mini,maxi,0.01);

NiMkIiglKWVgIiEjNQ==

fehler(feh8,mini,maxi,0.001);

NiMkIiglKWVgIiEjNQ==

fehler(feh8,mini,maxi,0.0001);

NiMkIiglKWVgIiEjNQ==