Continuity Explained: The 3 Conditions Every Function Must Pass

Описание: What does it really mean for a function to be continuous? Beyond the "pencil test," mathematicians use exactly three conditions to determine if a function is smooth at any point. Master this checklist and you'll never second-guess continuity again.

📚 Key concepts covered:
• The intuitive "pencil test" for continuity and its limitations
• The three formal conditions: f(c) defined, limit exists, limit equals f(c)
• Three types of discontinuity: holes, jumps, and removable discontinuities
• How to systematically verify continuity at any point
• Why all three conditions must hold simultaneously

⏱️ Timestamps:
0:00 - The pencil test challenge
0:30 - Building intuition with visual examples
3:00 - The three formal conditions explained
4:00 - Matching discontinuity types to failed conditions
5:00 - Step-by-step continuity verification

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📖 ORIGINAL SOURCE
This video distills concepts from educational content on continuity.
Original Video:    • Calculus 1 Lecture 1.4:  Continuity of Fun...  
All credit for the original instruction belongs to the source creator.

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📢 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. Each video targets one core idea and explains it clearly.

🔗 GitHub: https://github.com/Augustinus12835/au...

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