When driving, we try to approach and stay near the speed limit. Well, some of us do, anyway.
Limits in calculus have a similar idea; we’re trying to approach some number. We actually pick numbers that are close to some number. Infinitesimally close. Maybe too close, like a close talker. Limits are useful because they get us close to an instant, which is an abstract idea. An instant is difficult to wrap your head around. A limit is much more concrete and mathematical. It brings a sense of peace and justice to a chaotic world. Or is that just us?