Limits and Continuity

The Limits and Continuity chapter in Math Calculus on STEM Calculators focuses on the core ideas that launch differential calculus, with interactive tools for evaluating limits, one-sided limits, limits at infinity, and understanding asymptotes and infinite behavior. It supports common techniques such as limit laws, direct substitution, algebraic simplification (factoring, rationalizing), and recognizing when a limit does not exist.

On this page you can practice typical calculus limit problems, explore indeterminate forms like 0/0, verify results numerically with tables or graph-based intuition, and classify continuity using precise definitions. Many tools also help you identify removable, jump, and infinite discontinuities, check continuity at a point or on an interval, and apply continuity ideas used in the Intermediate Value Theorem and modeling.

The difficulty level ranges from beginner-friendly AP Calculus introductions to more advanced university-style continuity and limit reasoning, making it useful for students, teachers, and self-learners alike. Teachers can demonstrate limit behavior clearly, students can check homework and build speed with step-by-step guidance, and advanced users can quickly validate tricky limits and continuity conditions before moving into derivatives and deeper calculus topics.