kill(all)$

fpprec:100;

fpprintprec:30;

van=facebook.com/LearningCalculus$

      Limit of the Sum is the Sum of the Limits

f(x):= 48*x^(1/4) + 12/sqrt(x) + 84 -
       1/x^(3/4) + 47/x^(1/4) + 96*sqrt(x);

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

newton( 1.77019*10^(-5));

newton(newton( 1.77018777444687185323237199839b-5));

newton(1.9887b0);

limit( 48*x^(1/4),x,0,plus);
limit( 12/sqrt(x),x,0, plus);
limit(1/x^(3/4),x,0,plus);
limit(47/x^(1/4),x,0,plus);
limit(96*sqrt(x),x,0,plus);

limit( 12/sqrt(x),x,0, plus);

limit(1/x^(3/4),x,0,plus);

limit(47/x^(1/4),x,0,plus);

limit(96*sqrt(x),x,0,plus);

g(x):=factor(f(x))$ g(x);

diff(num(g(x)),x)/diff(denom(g(x)),x);

foo:diff(num(%),x)/diff(denom(%),x);

limit(foo,x,0,plus);

limit(foo,x,0,minus);

fpprintprec:5;

float(1/(4+2*4^(1/3))^4);

float(0.0000177019);

find;