>

> foersteafledte:=diff(sin(x^2),x);

> andenafledte:=diff(sin(x^2),x,x);

> tredieafledte:=diff(sin(x^2),x,x,x);

>

> y1:=evalf(2*cos(2^2)*2);

> y2:=evalf(-4*sin(2^2)*2^2+2*cos(2^2));

> y3:=evalf(-8*cos(2^2)*2^3-12*sin(2^2)*2);

> y0:=evalf(sin(2^2));

>

> approx1:=y0+y1*(x-2);

> approx2:=y0+y1*(x-2)+(1/2)*y2*(x-2)^2;

> approx3:=y0+y1*(x-2)+(1/2)*y2*(x-2)^2+(1/6)*y3*(x-2)^3;

>

> plot([sin(x^2),approx1,approx2,approx3],x=0..4,y=-10..10, color=[black,blue,red,green]);

>