Explanation Given information: To approximate 97 by regarding 97 as being near 81 (instead of 100) Let the function f ( x ) = x . Let the function is passes through the point ( x 0 , f ( x 0 ) ) and the slope of line is f ' ( x 0 ) . So, the equation of tangent line is f ( x ) − f ( x 0 ) = f ' ( x 0 ) ( x − x 0 ) f ( x ) ≈ f ( x 0 ) + f ' ( x 0 ) ( x − x 0 ) The above tangent line formula is valid for Δ x = ( x − x 0 ) sufficiently small. Let x = 97 and x 0 = 81 , because 97 is being near 81 instead of 100. So, Δ x = ( x − x 0 ) Δ x = ( 97 − 81 ) Δ x = 16 Substitute these values into tangent line formula

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.8, Problem 57PS

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To approximate 97 by regarding 97 as being near 81 (instead of 100).

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Chapter 3.8, Problem 56PS

Chapter 3.8, Problem 58PS

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Chapter 3 Solutions

Calculus

Ch. 3.1 - Prob. 1PS Ch. 3.1 - Prob. 2PS Ch. 3.1 - Prob. 3PS Ch. 3.1 - Prob. 4PS Ch. 3.1 - Prob. 5PS Ch. 3.1 - Prob. 6PS Ch. 3.1 - Prob. 7PS Ch. 3.1 - Prob. 8PS Ch. 3.1 - Prob. 9PS Ch. 3.1 - Prob. 10PS

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To approximate 97 by regarding 97 as being near 81 (instead of 100).

Solution Summary: The author explains how to approximate sqrt97 by regarding 97 as being near 81 (instead of 100).

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To approximate 97 by regarding 97 as being near 81 (instead of 100).

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Chapter 3 Solutions