Explanation Given information: A bicyclist pedals along a straight road with velocity, v and she stars 5 miles from the lake. Positive velocities take her away from lake and negative velocities take her toward lake. Formula used: For a continuous function f ( t ) , a ≤ t ≤ b , the left-hand and right-hand sums are given by L = L eft-hand sum = f ( t 0 ) Δ t + f ( t 1 ) Δ t + ... + f ( t n − 1 ) Δ t U = Right-hand sum = f ( t 1 ) Δ t + f ( t 2 ) Δ t + ... + f ( t n ) Δ t Where Δ t = b − a n ∫ a b v ( t ) d t = U + L 2 Calculation: Positive velocities take her away from lake and negative velocities take her toward lake. From the graph, we can observe that it is having negative velocity and then positive so till last time. That is 1 hour. We know that Δ t = b − a n Here, [ a , b ] = [ 0 , 1 ] and n = 6 as total number of grids horizontally. Δ t = 1 − 0 6 = 1 6

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 5.4, Problem 25P

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The time when she farthest from lake, and the farthest distance.

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Chapter 5.4, Problem 24P

Chapter 5.4, Problem 26P

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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The time when she farthest from lake, and the farthest distance.

Solution Summary: The author calculates the distance between a bicyclist and lake. Positive velocities take her away from the lake and negative.

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To find: The time when she farthest from lake, and the farthest distance.

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Chapter 5 Solutions

To find:

The time when she farthest from lake, and the farthest distance.