Explanation Given: The function is f ( x ) = 1 1 + x 2 , a = 3 , Δ x = 0.5 . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where f ( a + Δ x ) = f ( a ) + f ′ ( a ) Δ x Formulas: Percentage error = | Error Actual value | × 100 % Calculation: The function is f ( x ) = 1 1 + x 2 , a = 3 , Δ x = 0.5 . We need to calculate Δ f ≈ f ′ ( a ) Δ x by using linear approximation of Δ f . Differentiate the function with respect to x f ′ ( x ) = − 2 x ( 1 + x 2 ) 2 We apply the linear approximation to f ( x ) = 1 1 + x 2 with a = 3 and Δ x = 0.5 . Use the formula: Δ f ≈ f ′ ( a ) Δ x Δ f ≈ f ′ ( a ) Δ x = − 2 ( 3 ) ( 1 + ( 3 ) 2 ) 2 ( 0

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 11E

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Find the value of Δf. Also, compute both the errors and the percentage error.

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Chapter 4.1, Problem 10E

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Chapter 4 Solutions

Calculus: Early Transcendentals

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Find the value of Δ f . Also, compute both the errors and the percentage error.

Solution Summary: The author calculates the value of Delta f by using a linear approximation.

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Find the value of Δf. Also, compute both the errors and the percentage error.

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Chapter 4 Solutions