Since lim bn does not equal to zero. We can use division rule.2. Assume that an-->2 and bn-->3 Evaluate lim x->inf (an-2)/bn
My favorite, the "squeeze theorem".3.We know from trignometrythat |sin(n)|<=1 for all n.This shows that 0<= |sin(n)/n|<= 1/n and hence that -1/n <=|sin(n)/n| <= 1/n. We can also evaluate the lim x->inf (sin(n)/n by using
(Other favorite is composite function rule).
We have that,(4) find lim x-->inf sin(n)/n
Both -1/n and 1/n ---> 0
Thus, limit is zero.