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1 sec. and Find the average rate of change of d(t) between the values (a) t = t = 3 sec., between (b) t = 2 sec. and t = 3 sec., between (c) t = 2.5 sec. and t = 3 sec., and between (d) t = 2.9 sec. and t = 3 sec.

1 sec. and Find the average rate of change of d(t) between the values (a) t = t = 3 sec., between (b) t = 2 sec. and t = 3 sec., between (c) t = 2.5 sec. and t = 3 sec., and between (d) t = 2.9 sec. and t = 3 sec.

Calculus: Early Transcendentals
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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d (t) = 6(1.490-¹). Notice that this equation suggests that at t = 0, the rim was 6 inches above the ground. Our goal is to estimate the rate of change of d(t) at precisely the time t = 3 seconds. This will be accomplished by making use of the average rate of change and differ- ence quotient concepts that were previously defined. Part I Find the average rate of change of d(t) between the values (a) t = 1 sec. and t = 3 sec., between (b) t = 2 sec. and t = 3 sec., between (c) t = 2.5 sec. and t = 3 sec., and between (d) t = 2.9 sec. and t = 3 sec. Part 2 What do the average rates of change found in Exercise 3 represent with respect to the rim of the tire and its proximity to the street? Part 3 We want to find out how fast the rim of the tire is approaching the street at the instant t = 3 sec. Discuss how using the average rate of change is an approxima- tion but not exact at the instant t = 3 sec.
Transcribed Image Text:d (t) = 6(1.490-¹). Notice that this equation suggests that at t = 0, the rim was 6 inches above the ground. Our goal is to estimate the rate of change of d(t) at precisely the time t = 3 seconds. This will be accomplished by making use of the average rate of change and differ- ence quotient concepts that were previously defined. Part I Find the average rate of change of d(t) between the values (a) t = 1 sec. and t = 3 sec., between (b) t = 2 sec. and t = 3 sec., between (c) t = 2.5 sec. and t = 3 sec., and between (d) t = 2.9 sec. and t = 3 sec. Part 2 What do the average rates of change found in Exercise 3 represent with respect to the rim of the tire and its proximity to the street? Part 3 We want to find out how fast the rim of the tire is approaching the street at the instant t = 3 sec. Discuss how using the average rate of change is an approxima- tion but not exact at the instant t = 3 sec.
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