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Consider a closed rectangular box with a square base, as shown in the figure. Assume x is measured with an error of at most 0.8% and y is |dx[ measured with an error of at most 0.30%, so we have <0.008 and |dyl <0.003. y a. Use a differential to estimate the relative error in computing the box's volume V. V |ds| b. Use a differential to estimate the relative error in computing the box's surface area S. S

Consider a closed rectangular box with a square base, as shown in the figure. Assume x is measured with an error of at most 0.8% and y is |dx[ measured with an error of at most 0.30%, so we have <0.008 and |dyl <0.003. y a. Use a differential to estimate the relative error in computing the box's volume V. V |ds| b. Use a differential to estimate the relative error in computing the box's surface area S. S

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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Consider a closed rectangular box with a square base, as shown in the figure. Assume x is measured with an error of at most 0.8% and y is y |dx| <0.008 and measured with an error of at most 0.30%, so we have |dy| <0.003. y X. |dv] in computing the box's volume V. V a. Use a differential to estimate the relative error |ds| in computing the box's surface area S. S b. Use a differential to estimate the relative error |dv] % а. V (Type an integer or a decimal. Round to two decimal places as needed.) |ds| b. % (Type an integer or a decimal. Round to two decimal places as needed.)
Transcribed Image Text:Consider a closed rectangular box with a square base, as shown in the figure. Assume x is measured with an error of at most 0.8% and y is y |dx| <0.008 and measured with an error of at most 0.30%, so we have |dy| <0.003. y X. |dv] in computing the box's volume V. V a. Use a differential to estimate the relative error |ds| in computing the box's surface area S. S b. Use a differential to estimate the relative error |dv] % а. V (Type an integer or a decimal. Round to two decimal places as needed.) |ds| b. % (Type an integer or a decimal. Round to two decimal places as needed.)
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