das Limit
limit
A fixed boundary that must not be exceeded, for example a speed limit or a maximum amount.
Das Tempolimit auf dieser Landstraße liegt bei 80 km/h.
The speed limit on this country road is 80 km/h.

limit
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limit
A fixed boundary that must not be exceeded, for example a speed limit or a maximum amount.
Das Tempolimit auf dieser Landstraße liegt bei 80 km/h.
The speed limit on this country road is 80 km/h.

'Limit' is a loanword from English that has been fully integrated into the German language. Note the neuter article 'das Limit'.
Gibt es für dieses Projekt ein finanzielles Limit?
Is there a financial limit for this project?
There are several fixed expressions with 'Limit'. When someone reaches the limit of their performance, they are 'am Limit' (at their limit) or 'geht an sein Limit' (pushes themselves to their limit). Something that exceeds a boundary 'geht über das Limit hinaus' (goes beyond the limit).
Nach dem Marathon war ich körperlich total am Limit.
After the marathon, I was physically completely at my limit.
'Limit' is often used as the base word in compounds to define a specific type of boundary. Common examples are 'das Tempolimit' (the speed limit), 'das Zeitlimit' (the time limit), or 'das Alterslimit' (the age limit).
Bitte halten Sie sich an das Zeitlimit von 20 Minuten für Ihren Vortrag.
Please keep to the 20-minute time limit for your presentation.
In the meaning 'Grenze der Belastbarkeit' (limit of endurance), 'Limit' is often used personally. Typical expressions are 'sein persönliches Limit erreichen' (to reach one’s personal limit) or 'das Limit der Kreditkarte ausschöpfen' (to use up the credit card limit).
Ich habe mein monatliches Datenlimit schon wieder erreicht.
I’ve already reached my monthly data limit again.
border / limit
'die Grenze' and 'das Limit' can both refer to a point that one should not or cannot go beyond. In this meaning, they are often very similar. 'Grenze' is more general and can also be used figuratively for personal strength, patience, or possibilities. 'Limit' often sounds more specific: it is often about a fixed number, quantity, speed, or amount of money. The words can be confused because both mark an end. For rules with numbers, 'Limit' is very natural; for personal or general limits, 'Grenze' often fits better.

Vor dem Wochenende gilt auf dieser Straße ein Limit von 30 Kilometern pro Stunde.
Before the weekend, a limit of 30 kilometers per hour applies on this road.
Nach drei Stunden ohne Pause kam ich an meine Grenze.
After three hours without a break, I reached my limit.