Скачать или смотреть Calculus 1 — 8.2: Tangent Lines Using Derivatives

Learn the step-by-step process for finding tangent lines using the derivative formula. This video walks through two complete examples—a polynomial (y = x²) and a rational function (y = 3/x)—showing you exactly how to handle the algebra that trips up most students.

You'll master the key techniques: proper substitution of (x₀ + h) as a single input, resolving the 0/0 indeterminate form through factoring, and simplifying complex fractions with common denominators.

📚 KEY CONCEPTS COVERED:
• The derivative formula m = lim(h→0) [f(x₀+h) - f(x₀)]/h for finding exact tangent slopes
• Why (x₀ + h) must be substituted as ONE unified input—not separated
• How the 0/0 indeterminate form signals you need to factor and cancel h
• Polynomial technique: expansion and factoring (demonstrated with y = x²)
• Rational function technique: common denominators and complex fraction simplification (demonstrated with y = 3/x)
• Writing tangent line equations using point-slope form

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