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

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 10E

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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 9E

Chapter 4.1, Problem 11E

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A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States. They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained is summarized below. DATA: Observation 1 2 3 4 5 6 7 8 9 10 11 12 pH above 7 (X) 0.67 0.70 0.93 0.95 1.09 1.01 1.29 1.24 1.41 1.56 1.73 1.80 Units of BCI (Y) 14.4 20.9 16.2 25.0 18.9 19.8 20.7 22.1 23.9 24.9 27.6 29.7 Find the correlation coefficient between pH and BCI (round to the nearest hundredth; place your answer in the box below)

A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States. They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained is summarized below. DATA: Observation 1 2 3 4 5 6 7 8 9 10 11 12 pH above 7 (X) 0.65 0.75 0.89 0.94 1.12 1.16 1.29 1.35 1.48 1.56 1.73 1.80 Units of BCI (Y) 16.0 18.9 15.6 21.1 23.6 24.9 26.1 29.2 19.3 30.7 33.7 29.4 Find the coefficient of determination between pH and BCI (round to the nearest hundredth; place your answer in the box below)

What’s the value of t?

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 and the percentage error.

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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