kill(all)$

van=facebook.com/LearningCalculus$

     Nawar Alasadi's problem says find limit of f(y)/g(y):

f(y):=sqrt(y^2 + y + 1) - 1;
g(y):=sin(4*y);
h(y):= f(y)/g(y)$ h(x);

     Use L'Hopitals Rule Once

hp(y):=''(diff(f(y),y)/diff(g(y),y));

limit(hp(y),y,0);

limit(h(y),y,0);