  We prove that a function definable with parameters in an o-minimal structure
is bounded away from infinity as its argument goes to infinity by a function
definable without parameters, and that this new function can be chosen
independently of the parameters in the original function. This generalizes a
result in a paper of Friedman and Miller. Moreover, this remains true if the
argument is taken to approach any element of the structure (or plus/minus
infinity), and the function has limit any element of the structure (or
plus/minus infinity).
