(a) State the three possible relationships between the degrees of two non-zero polynomials P(x) and Q(x) that determine the behaviour of the quotient Q(x)P(x) as x→∞.
(b) Give an algebraic justification for the case in which degP<degQ. Take degP=m and degQ=n with m<n and show, by suitable manipulation of the quotient, that the limit is zero.
(c) Construct one explicit example for each of the three cases mentioned in part (a) and write the corresponding limit in each case.