Mr. Integral

THE BIG IDEA

Limits & Continuity

What happens as we get close to a point?

A limit describes nearby behavior, even when the function at the point is missing or different. Compare both sides, connect agreement to continuity, then use algebra to reveal difficult limits.

Begin the first lesson →See the lesson route ↓

5 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Nearby behavior
  2. matching the actual value defines02Continuity
  3. continuity on an interval ensures03Guaranteed crossings
  4. rewriting expressions reveals04Limit methods

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit5 lessons
  1. 01Limits and One-Sided BehaviorDistinguish a nearby trend from the value at a point and decide when a two-sided limit exists.
  2. 02Continuity and Piecewise FunctionsCheck the three continuity conditions and choose parameters that join pieces correctly.
  3. 03Intermediate Values and Root BracketingUse continuity to establish existence without claiming uniqueness or an exact solution.
  4. 04Infinite Limits and AsymptotesAnalyze unbounded behavior and end behavior without treating infinity as an ordinary number.
  5. 05Factoring, Rationalizing and Squeezing LimitsChoose a valid simplification or bound when direct substitution is inconclusive.