kill(all)$

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);

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);