In Chapter 1, we saw that an object with position function s(t) has an average velocity on the interval [a, b] s(b)-s(a) of AV[a,b] . More recently, we found that for b-a an object with velocity function v(t), the average value of its velocity function on [a, b] is = VAVG[a,b] Så v(t)dt. Are the average velocity on b-a a the interval [a, b] and the average value of the velocity function on [a, b] the same thing? Why or why not? Explain. -
In Chapter 1, we saw that an object with position function s(t) has an average velocity on the interval [a, b] s(b)-s(a) of AV[a,b] . More recently, we found that for b-a an object with velocity function v(t), the average value of its velocity function on [a, b] is = VAVG[a,b] Så v(t)dt. Are the average velocity on b-a a the interval [a, b] and the average value of the velocity function on [a, b] the same thing? Why or why not? Explain. -
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![In Chapter 1, we saw that an object with position function \( s(t) \) has an average velocity on the interval \([a, b]\) of
\[
AV_{[a,b]} = \frac{s(b) - s(a)}{b-a}.
\]
More recently, we found that for an object with velocity function \( v(t) \), the average value of its velocity function on \([a, b]\) is
\[
v_{AVG_{[a,b]}} = \frac{1}{b-a} \int_a^b v(t) \, dt.
\]
Are the average velocity on the interval \([a, b]\) and the average value of the velocity function on \([a, b]\) the same thing? Why or why not? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5963b474-a441-468b-8c4e-b34b2e3806b1%2F76afed71-94eb-4255-aedd-c4c32883f438%2F5fvl9h8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Chapter 1, we saw that an object with position function \( s(t) \) has an average velocity on the interval \([a, b]\) of
\[
AV_{[a,b]} = \frac{s(b) - s(a)}{b-a}.
\]
More recently, we found that for an object with velocity function \( v(t) \), the average value of its velocity function on \([a, b]\) is
\[
v_{AVG_{[a,b]}} = \frac{1}{b-a} \int_a^b v(t) \, dt.
\]
Are the average velocity on the interval \([a, b]\) and the average value of the velocity function on \([a, b]\) the same thing? Why or why not? Explain.
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