  Assuming that a "derivative" ratio rho:=f'/g' of the ratio r:=f/g of
differentiable functions f and g is monotonic (that is, rho is increasing or
decreasing), it was shown in previous papers that then r can switch at most
once, from decrease to increase or vice versa. In the present paper, "discrete"
versions of such l'Hospital-type rules for monotonicity (as well as "discrete"
versions of l'Hospital's rules for limits) are obtained, for functions f and g
defined on an interval of integers.
