(*$B- Aufgabe 7.14B *)
PROGRAM newton;
VAR xn,x,eps,fa,fb,fm,is:real;

FUNCTION g(x:real):real;
FUNCTION f(t:real):real;
BEGIN  f:= exp(x*sqr(t)) END;
(*$I A7.4 FUNCTION adapt *)
BEGIN
  fa:=f(0); fb:=f(1); fm:=f(0.5);
  g := adapt(0,1,fa,fm,fb,is) - 2;
END;

FUNCTION gs(x:real):real;
FUNCTION f(t:real):real;
BEGIN  f:= sqr(t)*exp(x*sqr(t)) END;
(*$I A7.4 FUNCTION adapt *)
BEGIN
  fa:=f(0); fb:=f(1); fm:=f(0.5);
  gs := adapt(0,1,fa,fm,fb,is);
END;

BEGIN
   writeln('Startwert eingeben'); read(xn);
   writeln('eps = ?'); read(eps); is := eps/1e-11;
   REPEAT
      x := xn;  xn := x -g(x)/gs(x); writeln(xn);
   UNTIL abs(xn-x)<eps*abs(x);
   writeln('x =', xn,'  f(x) =',g(xn))
END.