Is the precise definition of a limit worth covering in Calc 1?

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I'm teaching calc 1 this semester and am trying to decide if I should cover the precise definition of a limit.

My first impression was that I should. It helped me to gain a deeper understanding of calculus.

But I think most students won't gain that understanding and the ones who do are mostly math majors who will have plenty of other opportunities to learn it down the road. So I could use the time to focus more on other concepts.

Any input on this matter would be appreciated.