otodik

>	f:=x->sqrt(x);

>	ap:=x->x/4+1;

>	plot([f(x),ap(x)],x=1..6,color=[red,blue]);

>	[evalf(4+i/10),evalf(f(4+i/10)),evalf(ap(4+i/10)),evalf(f(4+i/10)-ap(4+i/10))] $i=-5..5;

>

>	linearis:=proc(f,a,x) return (f(a)+D(f)(a)*(x-a)); end proc;

>

>

>

>	f:=x->sqrt(x);

>	linearis(f,4,2);

>	kvadratikus:=proc(f,a,x) return (f(a)+D(f)(a)*(x-a)+1/2*(D@@2)(f)(a)*(x-a)^2); end proc;

>	kvadratikus(f,4,2);

>

>	taylor1:=proc(f,n,a,x) local i, t; t:=0; for i from 0 to n do t:=t+(D@@i)(f)(a)/i!*(x-a)^i; end do; return t; end proc;

>	taylor1(f,5,0,x);

>	f:=x->sin(x);

>

>	ts:=taylor(exp(x),x=3,5);

>	pts:=convert(ts,'polynom');

>	fts:=x->exp(3)+exp(3)*(x-3)+1/2*exp(3)*(x-3)^2+1/6*exp(3)*(x-3)^3+1/24*exp(3)*(x-3)^4;

>	evalf(fts(3.5));

>	g:=x->1/sqrt(1-4*x);

>	a:=taylor(g(x),x=0,5);

>	fts:=unapply(a,x);

>

>	with(combinat);

Warning, the protected name Chi has been redefined and unprotected

>	binomial(2*40,40);

>	coeftayl(g(x),x=0,40);

>

>	z:=x->1/(1-x)^(n+1);

>	b:=coeftayl(z(x),x=0,3);

>	subs(n=5,b);

>	binomial(8,3);

>	explim:=Limit(Sum(x^i,i=0..n),n=infinity);

>	explim1:=limit(sum(x^i,i=0..n),n=infinity);

>	subs(x=0.3,explim1);

>

>	evalf(%,20);

>	1/(1-0.3);

>