Скачать или смотреть Calculus 1 — 5.4: Limits and the Tangent Line to y = x²

How do you find the slope of a curve at a single point when slope requires two points? This video walks through the tangent line problem on y = x², using secant lines, numerical tables, and algebraic factoring to evaluate limits — arriving at the foundational idea behind the derivative.

Key concepts covered:
• The tangent line problem: why slope at a single point requires a new approach
• Secant lines rotating toward the tangent line as point Q approaches point P
• The indeterminate form 0/0 as a signal to investigate further, not a final answer
• Estimating limits with numerical tables (one-sided and two-sided)
• Evaluating limits algebraically using difference-of-squares factoring and cancellation
• Why a limit describes approaching behavior, not arriving behavior
• How f(a) and the limit as x approaches a can differ (functions with holes)
• Worked example: limit as x approaches 1 of (x-1)/(x²-1) = 1/2
• Deriving the tangent line equation y = 2x - 1 at the point (1, 1) using point-slope form
• How the limit of secant slopes is precisely the definition of the derivative

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SOURCE MATERIALS
The source materials for this video are from    • Calculus 1 Lecture 1.1:  An Introduction t...