What is it
A limit describes the value a function approaches as its input gets arbitrarily close to a particular point, without necessarily ever reaching it — the formal foundation on which all of calculus, including derivatives and integrals, is built.
Why it matters
Limits are what make calculus mathematically rigorous rather than just intuitive — before limits were formalised, mathematicians struggled for over a century to justify why calculus actually worked, and the epsilon-delta definition finally resolved that.
Exam tip
When a limit produces an indeterminate form like 0/0, don't assume the limit doesn't exist — techniques like factorising, rationalising, or L'Hôpital's rule almost always reveal a genuine finite value hiding behind the indeterminate form.
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