If one molecule of the product c is formed from one molecule of the reactant a and one molecule of the reactant b, and the initial concentrations of a and b have a common value [a]=[b]= a moles/l, then [c]= a2kt/(akt+1), where k is a constant.

(a) find the rate of reaction at time t.
(b) if x=[c], what is dx/dt in terms of a, k, and x?
(c) what happens to the concentration as t→[infinity]?
(d) what happens to the rate of reaction as t→[infinity]? (what do the results mean in (c) and (d) in practical terms? )