In other words, there is no connection limit, but the more connections you have, the higher your CPU might get and depending on what DO configuration you have for your droplet, if it gets to 100%, you just scale up get more cpu/memory. But don't worry about it until you actually see 100% cpu, so start with lower plan and upgrade as needed. At some point if, you may also want scaling out, in other words, get multiple droplets, not just 1 and to split your traffic between multiple machines.
so I would say, no, you'll never need dedicated machine if you can properly scale out your traffic and distribute your load. So DO, like other cloud VM providers can handle any size app.
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