Explanation Given: The atmospheric pressure at altitude h ( kilometers ) for 11 ≤ h ≤ 25 . The function is P ( h ) = 128 e − 0.157 h kilopascals . 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 Δ f = f ( a + Δ x ) − f ( a ) . Calculation: The function is P ( h ) = 128 e − 0.157 h kilopascals . Part a: Differentiate the function with respect to h . P ′ ( h ) = 128 ( − 0.157 ) e − 0.157 h = − 20.096 e − 0.157 h Now, apply the linear approximation with a = 20 and Δ h = 0.5 . Use the formula: f ′ ( a ) ( Δ x ) = f ( a + Δ x ) − f ( a ) P ′ ( a ) ( Δ h ) = P ( a + Δ h ) − P ( a ) − 20.096 e − 0.157 ( 20 ) ( 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.1, Problem 39E

To determine

a. Estimate ΔP at h=20 when Δh=0.5.

b. Find the actual change and compute the percentage error in the linear approximation.

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Chapter 4.1, Problem 38E

Chapter 4.1, Problem 40E

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Chapter 4 Solutions

CALCULUS (CLOTH)

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a. Estimate Δ P at h = 20 when Δ h = 0.5 . b. Find the actual change and compute the percentage error in the linear approximation.

Solution Summary: The author explains the linear approximation of Delta f.

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a. Estimate ΔP at h=20 when Δh=0.5.

b. Find the actual change and compute the percentage error in the linear approximation.

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Chapter 4 Solutions

a. Estimate Δ P at h = 20 when Δ h = 0.5 . b. Find the actual change and compute the percentage error in the linear approximation.

Solution Summary: The author explains the linear approximation of Delta f.

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a. Estimate ΔP at h=20 when Δh=0.5. b. Find the actual change and compute the percentage error in the linear approximation.

Want to see the full answer?

Chapter 4 Solutions

a. Estimate ΔP at h=20 when Δh=0.5.

b. Find the actual change and compute the percentage error in the linear approximation.