/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created by wxMaxima version 0.7.5 ] */

/* [wxMaxima: section start ]
Berechnung der Ober- und Untersumme
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
f(x):=x^2;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
h:(b-a)/n;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
O(a,b,n):=ev(sum(ev(h*f(i*h)),i,1,n));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
O(a,b,n);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
O(0,2,4);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
O(0,2,8);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
U(a,b,n):=ev(sum(ev(h*f(i*h)),i,0,n-1));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
U(a,b,n);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
U(0,2,4);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
U(0,2,8);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Summenformel(n) - für die Summe der Quadratzahlen
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
load(simplify_sum)$
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
sum(i^2,i,1,n);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
simplify_sum(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
factor(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Summenformel bei der Obersumme anwenden
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
O(0,2,n);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
simplify_sum(O(0,2,n));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
obs:ratsimp(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d([%],[n,400,2000]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
limit(obs,n,inf);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Summenformel bei der Untersumme anwenden
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
simplify_sum(U(0,2,n));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ratsimp(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
limit(%,n,inf);
/* [wxMaxima: input   end   ] */

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