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To get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something like the black curve in the graph below. -1 time (sec) 012345678 velocity (feet/sec)-4-23423131 1.0 Left endpoint approximation You decide to use a left endpoint approximation to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is

To get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something like the black curve in the graph below. -1 time (sec) 012345678 velocity (feet/sec)-4-23423131 1.0 Left endpoint approximation You decide to use a left endpoint approximation to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter10: Radical Functions And Equations
Section: Chapter Questions
Problem 15CT
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the object. -1 To get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something like the black curve in the graph below. y 1.0 Ing the time interval 0 ≤ ≤ 8, but you only have the following data about the velocity of time (sec) 012345678 velocity (feet/sec)-4-23423131 1,0 Left endpoint approximation You decide to use a left endpoint approximation to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is Show All X
Transcribed Image Text:the object. -1 To get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something like the black curve in the graph below. y 1.0 Ing the time interval 0 ≤ ≤ 8, but you only have the following data about the velocity of time (sec) 012345678 velocity (feet/sec)-4-23423131 1,0 Left endpoint approximation You decide to use a left endpoint approximation to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is Show All X
You decide to use a left endpoint approximation to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is determined by the velocity measurement at the left endpoint of each one-second interval. By using the left endpoint approximation as an approximation, you are assuming that the actual velocity is approximately constant on each one-second interval (or, equivalently, that the actual acceleration is approximately zero on each one-second interval), and that the velocity and acceleration have discontinuous jumps every second. This assumption is probably incorrect because it is likely that the velocity and acceleration change continuously over time. However, you decide to use this approximation anyway since it seems like a reasonable approximation to the actual velocity given the limited amount of data. (A) Using the left endpoint approximation, find approximately how far the object traveled. Your answers must include the correct units. Total displacement = Total distance traveled = Using the same data, you also decide to estimate how far the object traveled using a right endpoint approximation. So, you sketch the curve again with a black pen, and draw rectangles whose height is determined by the velocity measurement at the right endpoint of each one-second interval. 9 5 1,0 1,0 t 9
Transcribed Image Text:You decide to use a left endpoint approximation to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is determined by the velocity measurement at the left endpoint of each one-second interval. By using the left endpoint approximation as an approximation, you are assuming that the actual velocity is approximately constant on each one-second interval (or, equivalently, that the actual acceleration is approximately zero on each one-second interval), and that the velocity and acceleration have discontinuous jumps every second. This assumption is probably incorrect because it is likely that the velocity and acceleration change continuously over time. However, you decide to use this approximation anyway since it seems like a reasonable approximation to the actual velocity given the limited amount of data. (A) Using the left endpoint approximation, find approximately how far the object traveled. Your answers must include the correct units. Total displacement = Total distance traveled = Using the same data, you also decide to estimate how far the object traveled using a right endpoint approximation. So, you sketch the curve again with a black pen, and draw rectangles whose height is determined by the velocity measurement at the right endpoint of each one-second interval. 9 5 1,0 1,0 t 9
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