taylor(log(1+x),x,0,20);
f(x):=''%;
float(f(.1));
float(log(1.1));

taylor(log(1+x),x,0,20);
f(x):=''%;
float(f(.5));
float(log(1.5));

taylor(log(1+x),x,0,20);
f(x):=''%;
float(f(1.));
float(log(2.));

taylor(log(1+x),x,0,200)$
f(x):=''%$
float(f(1.));
float(log(2.));

taylor(log(1+x),x,0,300)$
f(x):=''%$
float(f(1.));
float(log(2.));

taylor(log(1+x),x,0,500)$
f(x):=''%$
float(f(1.));
float(log(2.));

taylor(log(1+x),x,0,20);
f(x):=''%;
float(f(1.5));
float(log(2.5));

taylor(log(1+x),x,0,200);
f(x):=''%;
float(f(1.5));
float(log(2.5));

taylor(log(1+x),x,0,20);
f(x):=''%;
float(f(2.));
float(log(3.));

taylor(log(1+x),x,0,200);
f(x):=''%;
float(f(2.));
float(log(3.));