Скачать или смотреть Calculus 1 — 8.1: Derivative via Limit Definition

How do you find the slope at a single point when slope requires two points? This video reveals the elegant solution: start with two points, then use limits to bring them infinitely close together. You'll see exactly how the difference quotient transforms into the derivative formula.

📚 Key concepts covered:
• The difference quotient [f(x₀ + h) - f(x₀)] / h as the slope of a secant line
• Why we can't just plug in h = 0 (the 0/0 problem)
• How limits let us approach zero without reaching it
• The geometric meaning: secant lines rotating into tangent lines
• Complete worked example with y = x² at x = 3

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SOURCE MATERIALS
The source materials for this video are from    • Calculus 1 Lecture 1.5:  Slope of a Curve,...