Continuity on Intervals: How to Check Endpoints with One-Sided Limits скачать в хорошем качестве

Continuity on Intervals: How to Check Endpoints with One-Sided Limits

How do you prove a function is continuous on an entire interval—especially at the endpoints where it just stops? This video breaks down the difference between open and closed intervals, explains why one-sided limits are essential at boundaries, and walks through a complete proof using f(x) = √(16 - x²). Key concepts covered: • Continuity on open intervals requires checking every interior point with two-sided limits • Closed intervals demand one-sided limit verification at endpoints (right-hand at left endpoint, left-hand at right endpoint) • The direction of approach is determined by where the interval exists—you can only approach from inside • Complete three-step process for proving continuity on [a, b] • How to handle half-open intervals like [a, b) and (a, b] ━━━━━━━━━━━━━━━━━━━━━━━━ ORIGINAL SOURCE ━━━━━━━━━━━━━━━━━━━━━━━━ This video distills concepts from:    • Calculus 1 Lecture 1.4:  Continuity of Fun...   Full credit to the original creator. Please visit and support the original lecture! ━━━━━━━━━━━━━━━━━━━━━━━━ About Lecture Distilled ━━━━━━━━━━━━━━━━━━━━━━━━ Long lectures. Short videos. Core insights. We transform lengthy academic lectures into focused concept videos that respect your time while preserving the essential mathematics. 🔗 GitHub: https://github.com/Augustinus12835/au... #Calculus #Continuity #OneSidedLimits #IntervalContinuity #MathProof #Limits #CalculusTutorial #Mathematics