Secant to Tangent

Shrink the interval h and watch the average rate of change converge on the instantaneous rate, with the difference quotient updating as you go.

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Used in these lessons

Build a polynomial from its zeros, change each multiplicity, and watch the curve cross, bounce or flatten while the end behaviour follows the degree.

Choose numerator and denominator factors and see which ones become vertical asymptotes, which cancel into holes, and what the degrees do to the ends.