Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.1 Limits, Rates of Change, and Tangent Lines - Preliminary Questions - Page 44: 4

Answer

The slope of the secant line over the interval $[x_0, x_1]$ approaches the slope of the tangent line at $x = x_0$.

Work Step by Step

The slope of the secant line over the interval $[x_0, x_1]$ approaches the slope of the tangent line at $x = x_0$. Graphically, this means that as we "zoom in" on the curve, it looks more and more like a straight line.
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