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YouTubeDerek Banas
Calculus 7 Limit Definition of a Derivative
Episode 1 showed a secant line collapsing into a tangent. This is the algebra for that picture. The slope of a secant is rise over run: the rise is f(x+h) − f(x), the run is h. That fraction is the difference quotient. The derivative is what it approaches as h goes to zero. Worked on f(x) = x², step by step: expand (x+h)², the x² terms ...
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