L'Hospital-type rules for monotonicity and limits: Discrete case

Details L'Hospital-type rules for monotonicity and limits: Discrete case L'Hospital-type rules for monotonicity and limits: Discrete case

2006-11-21

arxiv.org/abs/math/0611665v1

Mathematics

Classical Analysis and ODEs

6 pages

Scientific paper

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.

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