kill(all)$ fpprec:60;

     Van | facebook.com/LearningCalculus

f(x):=x*sinh(x)/(1+cosh(x))^2;

fp(x):=''(ratsimp(diff(f(x),x)));

limit(f(x),x,inf);

newton(t):=bfloat(subst(t,x,x-fp(x)/diff(fp(x),x)));

for i: 1 thru 10 do
(a:newton(2.01911309981960620039446037536992523477761009462472649505947b0),
 a:newton(a),("answer  ", [a,newton(a)]))$

a;

f(a);

fp(a);