Limits and Continuity

Calculus makes one core claim: that change can be measured at a single instant, rather than only across an interval. Limits are the mechanism that makes this possible, letting you pin down what a function approaches even when direct substitution fails. Continuity is the condition under which limits behave predictably, and understanding where continuity breaks tells you exactly where calculus gets complicated. Every derivative, every integral, every convergence argument you write in this course depends on limit reasoning you build here. Get comfortable with the language now, because it never goes away.

10–12% of exam