real sequences analysis help
1. assume that an->2 and bn-->3 evaluate lim x->inf (2an -3bn)
a) -5 (b)0 (c) the limit doesnot exist (d) the limit cannot be determined
2. Assume that an-->2 and bn-->3 Evaluate lim x->inf (an-2)/bn
(a)0 (b) the limit doesnot exist (c) the limit canot be determined
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
(a) product rule for limit of sequences.
(b) quotient rule for limits of sequences.
(c) the squeeze theorem for sequence
(4) find lim x-->inf sin(n)/n
(a)1 (b) 0 (c) limit doesnot exist