Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.1 The Idea of Limits - 2.1 Exercises: 5

Answer

These procedures are equivalent if we look at the graph of the function $s(t)$ that says what is the position at the given time $t$.

Work Step by Step

These procedures are equivalent: 1) The average velocity on the time interval $[t,t+h]$ is equal to the slope of the secant line through the points $(t,s(t))$ and $(t+h,s(t+h))$ on the graph of the position versus time $s(t)$ 2) As we make $h$ smaller and smaller the average velocity will become closer and closer to the instantaneous velocity, while the slope of the secant line through the mentioned points will become closer and closer to the slope of the tangent at $(t,s(t))$ 3) The instantaneous velocity is actually equal to the slope of the tangent at $(t,s(t))$, where $s(t)$ is the position at time $t$.
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