Limits? Any type of exponential function? You don't go from 9.999 to 10, you go from 9.999 to 9.999 and then to 9.999 such that your speed reaches infinity when your warp factor reaches 10. For a super simple formula, think about V = 9c/(10-W). At W=1 your velocity is equal to c, the speed of light. As W increases your velocity increases. At W = 10 you would have a divide by 0 and infinite speed, but as W gets closer and closer to 10 your speed increases dramatically without W ever reaching 10. As others have explained, once starships started to routinely go at Warp 9.999 it began to become cumbersome to talk about speeds like that, so the formula was changed to something like 14c/(15-W). Warp 1 still equals the speed of light, but now you have 15 numbers until you reach infinite, and Warp 13 is really something like Warp 8.71 on the old scale. Of course the actual formula is probably slightly more complex and would provide more granular differences at slower speeds, but it gives you a rough idea of how it could work.
So there you go, as warp drive got better and better and speeds like "Warp 9.999999999999999999999999" started sounding really silly someone decided sod it and to just change things about. After all, it's a bit of a leap from even the Enterprise's top speed and being infinitely fast so having a bit more of a sliding scale rather than a massive jump between warps 9 and 10 makes sense.
In short, the description in the tech manual was a reference to the Infinite Improbability Drive in "The Hitchhiker's Guide To the Galaxy". Apparently, Braga didn't get the joke, and we got "Threshold" as a result.
Sometime between TOS and TNG the warp scale was somewhat re-drawn. It could be argued that the "transwarp" drive being tested with the Excelsior is the warp drive we now have in TNG, causing a recalibration of the warp scale. The "old" Warp 13 and such we see them talk about in TOS is now a common place warp 9 in TNG, for example. However you want to assume that warp drive works (whether the ship is expanding space behind it whole contracting the space in front of it, or slipping into a lower dimension where the distance between two points is smaller as being on the smaller outside arc of a "circular" universe) Warp 10, "infinite speed" is the point at which that is done at the very most limit. Space has been so bundled up infront of you there's nothing to expand behind, you've moved into such a lower dimension of "sub space" that you're at the point in the middle of the circle. You're "everywhere at once." When you consider the rather fantastical concept this implies, and the fact that it'd take infinite energy to go infinite speed you realize more and more how utterly stupid Threshold was. (Even moreso that the Starfleet Corps of Engineers have studied this and working on this for decades and have came to these conclusions or up with nothing, and "somehow" a rag-tag bunch of people on a meaningless scout ship stuck light years away from "civilization" were able to pull it off. But I digress.) Obviously in AGT's future timeline (if it was a "then" "real one" and not a Q "dicking with Picard" nonsense) the warp scale had, yet again, be re calibrated allowing for more whole-number points betwen "Warp 9" and "Warp Infinity." "Warp Infinity" now became another number and more stable higher Warp Speeds got whole numbers as opposed to "Warp 9.76323021439641698471181901238189." Now, in "Where No One Has Gone Before..." we've a unusual situation with The Traveler and what he is capable of. Geordi remarks that his readout shows the ship moving past Warp 10 (they're traveling faster than infinity and in theory can be anywhere they want to be in the entire of all of existence instantly) while Data says his read out shows the ship having never passed Warp 1.5. They end up in Triangulum after a few minutes of travel so they're obviously not moving "faster than infinity" further shown by the fact they didn't use more than infinite fuel to get where they are going. (All of the nonsense with the Traveler aside.) It's possible Geordi's display was just trying to "make sense" of what was going on and may have been taking the warp chart and basically showing the speed they're going on that same calculation ignoring the Warp 10=infinity aspect. So in WNOHGB "we're now moving past Warp 10" would be like someone in, say, the distant Trek future moving at Warp 52 (Infinity being Warp 100, or something.) In essence Geordi's display was recalibrating the Warp Scale on the fly so that it'd make sense before it's fragile isolinear mind imploded. Data's science-based operations console was a bit more logic minded and was able to compute what was happening factoring all of the other dynamics of the ship, the universe and everything. Near as it could tell all of the systems were showing the ship moving at Warp 1.5 (Geordi's was basing speed based on comparing the outside movements. I.E. Data's computer was looking at speedometer, Geordi's was looking outside, pacing the side markers on the highway and doing the math and getting a speed that way. ) The ship's own ability to move at Warp 1.5 with ease coupled with The Traveler's ability to manipulate mind and machine caused the ship to get propelled into Triangulum and eventually to "the edge of the universe."
You know, I'm not a Braga hater (though I've managed to avoid most of what seems to be considered his worst offenders, including Threshold, I think he was a good writer of slightly bonkers quirky scripts but not a very able showrunner) but I really hope that's true.
They didn't show it in the episode, but a few hours later everyone turned into lizards. Fortunately, thanks to Voyagers experiences they have perfected the treatment to turn them back, so it's all good.
Yet another Star Trek inconsistency. Either they rejigged the scale where warp ten was the maximum but designated as warp twenty, for instance. The point being the speeds attained approached infinity as x, the warp speed, approached ten, so new speed limits and warp levels were required to accommodate for these speeds. Or the VOY writers got lazy and forgot that warp ten wasn't the limit. I don't know...
Supposedly, Braga put it in there to cheese off those of us who care about such things, not taking into account how easy a retcon it is to just say that they redid the scale again.
Which is why the Voyager episode was so stupid, they should never be able to reach infinite velocity, whatever warp value you assign to it in the 23rd, 24th, or 25th century.
A few writers can't help themselves. They always want the ship to go faster, even if warp 10 is infinite velocitiy. Warp infinity-point-nine-five?