Calculus › Section B · Limits › Topic B.4

Continuity and one-sided limits

Some functions you can draw without lifting your pen; others break. Continuity makes that idea exact, and one-sided limits are the precise way to talk about what happens at each side of a break.

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In this topic

Approaching from one side only
The existence test
Worked example: both sides of a seam
Continuity at a point
Three kinds of discontinuity
Worked example: classifying breaks
Which functions are continuous?
Continuity on an interval
The Intermediate Value Theorem
Worked example: trapping a root
Common mistakes to avoid
Key takeaways

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