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The phrase "approaches the maximum" is correct and usable in written English.
It can be used in contexts where something is nearing its highest limit or capacity.
Example: "As the temperature rises throughout the day, it approaches the maximum recorded level for this time of year."
Alternatives: "nears the peak" or "gets close to the maximum".
Exact(23)
Scientists using a novel printing method have managed to make a color image whose resolution approaches the maximum theoretical limit.
The effect was sharper 75 or 100 years ago, historical data shows, but as national literacy approaches the maximum of 100percentt, differences flatten out.
In the latter case, as x approaches the maximum value, the curve defined by f rises more and more slowly, levels out, and then starts to fall.
On a calm-weather day, a nonstop flight from New York to Los Angeles already approaches the maximum range of a Boeing 737 or Airbus A320, common aircraft on that route and others like it.
Perhaps the best examples, in which the sequential experience of indoor and outdoor space approaches the maximum, are the religious, educational, and civic complexes of Europe, developed before the idea of gridiron subdivision fragmented environmental design.
Tesla should have made it very clear that the 200-mile stretch between the two supercharger stations approaches the maximum distance and that all range maximization strategies should be employed".
Similar(37)
Shorter routes therefore corresponded to higher efficiency values (approaching the maximum of 1).
Should Starmer be influenced by the substantial prison sentence passed on people like Woods -- approaching the maximum, given the one-third discount for an immediate plea of guilty?
"(6) enhance the quality of renewable resources and approach the maximum attainable recycling of depletable resources". 83 Stat.
Several key parameters are optimized to approach the maximum liquefaction rate and exergy utilization rate.
In negative incremental forming, a characteristic thinning band occurs on the parts when wall angles approach the maximum obtainable [D.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com