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Given information: • A different object is moving with velocity (in feet per second) described by the function v(t) = 1 – sin(t). • The object has initial position s(0) = 6. %3D %3D People often assume that the object's position function would be s(t) = t+ cos(t) +6 However, this is not right. Why not? We were given s(0) = 6, but this function has initial value s(0) = 7. %3D Actually, s(t) = t + cos(t) + 6 is correct based upon both pieces of given information. %3D We were given v(t) =1 – sin(t), but this function has derivative s'(t) = sin(t) + 6t %3D %3D

Given information: • A different object is moving with velocity (in feet per second) described by the function v(t) = 1 – sin(t). • The object has initial position s(0) = 6. %3D %3D People often assume that the object's position function would be s(t) = t+ cos(t) +6 However, this is not right. Why not? We were given s(0) = 6, but this function has initial value s(0) = 7. %3D Actually, s(t) = t + cos(t) + 6 is correct based upon both pieces of given information. %3D We were given v(t) =1 – sin(t), but this function has derivative s'(t) = sin(t) + 6t %3D %3D

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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Given information: • A different object is moving with velocity (in feet per second) described by the function v(t) =1 – sin(t). • The object has initial position s(0) = 6. People often assume that the object's position function would be s(t) = t + cos(t)+6 However, this is not right. Why not? We were given s(0) = 6, but this function has initial value s(0) = 7. Actually, s(t) =t+ cos(t) + 6 is correct based upon both pieces of given information. We were given v(t) = 1 – sin(t), but this function has derivative s'(t) = sin(t) + 6t
Transcribed Image Text:Given information: • A different object is moving with velocity (in feet per second) described by the function v(t) =1 – sin(t). • The object has initial position s(0) = 6. People often assume that the object's position function would be s(t) = t + cos(t)+6 However, this is not right. Why not? We were given s(0) = 6, but this function has initial value s(0) = 7. Actually, s(t) =t+ cos(t) + 6 is correct based upon both pieces of given information. We were given v(t) = 1 – sin(t), but this function has derivative s'(t) = sin(t) + 6t
Given information: An object is moving with velocity (in feet per second) described by the function v (t) We will reason about the object's position function, s (t).
Transcribed Image Text:Given information: An object is moving with velocity (in feet per second) described by the function v (t) We will reason about the object's position function, s (t).
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