Limits and Continuity

Start with a map

The mind map C2: Limits & Continuity is a starting point for this page. It sets out intuitive and formal definitions of a limit at a finite point, basic examples, uniqueness and one-sided limits. The Limits official mind map offers another way in, with visual, algebraic and numerical approaches.

Start with one map and follow its branches. Then look at the other to see how it organizes the same topic. The resources were made by GoConqr users, so each offers a different presentation.

Move from limits to continuity

The note Continuity lists conditions for continuity at a point and describes a jump discontinuity. Read it alongside the flashcard deck on point continuity and kinds of discontinuity. The Limits note also discusses left-hand and right-hand limits, giving you a way to connect those ideas with the maps.

For more practice with limit notation, use the limits flashcard deck. Another deck covers asymptotes, the squeeze theorem and indeterminate forms. You can return to the maps as you work through the cards.

Combine maps and quizzes

This page includes a small set of quizzes as well as mind maps. One quiz is titled as a calculus exam, and another is titled for school-level mathematics. Use a map first to organize the ideas, then try a quiz and return to the relevant map or notes when you want to look at a topic again.

Place the topic in the unit

Limits and Continuity is one section of Limits and Introduction to Calculus in Mathematics. The resources here let you approach that section through definitions, examples, visual cases and practice materials. You can choose the format that fits where you want to begin, then move between resources for another view of the topic.

Choose a map or quiz and explore the section at your own pace.