Explanation Given: The function is f ( x ) = 2 x 2 − x , a = 5 , Δ x = − 0.4 . 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 ) = 2 x 2 − x , a = 5 , Δ x = − 0.4 . 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 ) = 4 x − 1 We apply the linear approximation to f ( x ) = 2 x 2 − x with a = 5 and Δ x = − 0.4 . Use the formula: Δ f ≈ f ′ ( a ) Δ x Δ f ≈ f ′ ( a ) Δ x = ( 4 ( 5 ) − 1 ) ( − 0.4 ) = 19 ( − 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 10E

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Chapter 4.1, Problem 9E

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Chapter 4 Solutions

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

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Chapter 4 Solutions