Explanation Given: The function is f ( x ) = 1 + x , a = 3 , Δ x = 0.2 . 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 Percentage error = | Error Actual value | × 100 % Calculation: The function is f ( x ) = 1 + x , a = 3 , Δ x = 0.2 . 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 ) = 1 2 1 + x We apply the linear approximation to f ( x ) = 1 + x with a = 3 and Δ x = 0.2 . Use the formula: Δ f ≈ f ′ ( a ) Δ x Δ f ≈ f ′ ( a ) Δ x = 1 2 1 + 3 ( 0

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 4.1, Problem 9E

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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 8E

Chapter 4.1, Problem 10E

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Chapter 4 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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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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