# Exercici 10.10

kill(all)$

D(x,y):=sqrt(x^2 + y^2) ;

JD(x,y) = JDxy: jacobian ( [D(x,y)] , [x,y]);

'Jf(a,b) = Jfab: subst( [x=a, y=b], JDxy) ;

h = h: matrix ( [ha], [-hb]) ;

Incr_aprox = Jfab . h;

ratsimp(%);

D(a + ha, b - hb);

expand(%);

D(a,b) ;

Incr_exact= D(a + ha, b - hb) - D(a,b) ;

ratsimp(%);

a=a:15;         b=b:7;
ha=ha:0.2;     hb=hb:-0.1;

I1 : -(b*hb-a*ha)/sqrt(b^2+a^2), numer;
I2 : sqrt(hb^2-2*b*hb+ha^2+2*a*ha+b^2+a^2)-sqrt(b^2+a^2), numer;