A person walking along a straight path has her velocity in miles per hour at time...
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A person walking along a straight path has her velocity in miles per hour at time t given by the function v(t) 0.25t3 1.5t2 + 3t +0.25, for times in the interval 0 <t< 2. The graph of this function is also given in each of the three diagrams below. mph 3 mph 3+ mph 3- y=v(t) y=v(t) y=v(t) 2+ 2+ 2+ 1+ A4 A3 A2 B4 B3 B2 hrs B1 hrs hrs |A 1 ? 1 1 v(t) on the interval (0, 2], but the method by which the four rectangles' Note that in each diagram, we use four rectangles to estimate the area under y = respective heights are decided varies among the three individual graphs. Think about how the heights of the rectangles in the left-most diagram are being chosen. Determine the value of S = A, + A, + Az + A4 by evaluating the function y = v(t) at appropriately-chosen values and observing the width of each rectangle. Note, for example, that A3 = (1) . = 2. = 1. S = Use the rectangles in the middle diagram to find the value of T = B1 + B2 + B3 + B4. T = Use the rectangles in the right-most diagram to find the value of U = Cı + C2 + C3 + C4. U = Which estimate do you think is the best approximation of D, the total distance the person traveled on [0, 2 ? Why? 1, A person walking along a straight path has her velocity in miles per hour at time t given by the function v(t) 0.25t3 1.5t2 + 3t +0.25, for times in the interval 0 <t< 2. The graph of this function is also given in each of the three diagrams below. mph 3 mph 3+ mph 3- y=v(t) y=v(t) y=v(t) 2+ 2+ 2+ 1+ A4 A3 A2 B4 B3 B2 hrs B1 hrs hrs |A 1 ? 1 1 v(t) on the interval (0, 2], but the method by which the four rectangles' Note that in each diagram, we use four rectangles to estimate the area under y = respective heights are decided varies among the three individual graphs. Think about how the heights of the rectangles in the left-most diagram are being chosen. Determine the value of S = A, + A, + Az + A4 by evaluating the function y = v(t) at appropriately-chosen values and observing the width of each rectangle. Note, for example, that A3 = (1) . = 2. = 1. S = Use the rectangles in the middle diagram to find the value of T = B1 + B2 + B3 + B4. T = Use the rectangles in the right-most diagram to find the value of U = Cı + C2 + C3 + C4. U = Which estimate do you think is the best approximation of D, the total distance the person traveled on [0, 2 ? Why? 1,
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Related Book For
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
Posted Date:
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