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: 9

Answer

(a) $$v_{ave1}=48.$$ (b) $$v_{ave2}=64.$$ (c) $$v_{ave3}=80;$$ (d) $$v_{ave}=96-16h;$$

Work Step by Step

By definition, the average velocity is the change in position over the time interval, divided by the length of that interval: (a) $$v_{ave1}=\frac{s(4)-s(1)}{4-1}=\frac{-16\cdot4^2+128\cdot4-(-16\cdot1^2+128\cdot1)}{3}=\frac{144}{3}=48.$$ (b) $$v_{ave2}=\frac{s(3)-s(1)}{3-1}=\frac{-16\cdot4^2+128\cdot4-(-16\cdot1^2+128\cdot1)}{2}=\frac{128}{2}=64.$$ (c) $$v_{ave3}=\frac{s(2)-s(1)}{2-1}=\frac{-16\cdot2^2+128\cdot2-(-16\cdot1^2+128\cdot1)}{1}=80;$$ (d) $$v_{ave}=\frac{s(1+h)-s(1)}{1+h-1}=\frac{-16\cdot(1+h)^2+128\cdot(1+h)-(-16\cdot1^2+128\cdot1)}{2}=\frac{-16-2\cdot16h-16h^2+128+128h+16-128}{h}=\frac{96h-16h^2}{h}=96-16h;$$
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