Explanation Given: The function is W ( x ) = w R 2 x 2 ( for x ≥ R ) . Here, R = 3960 miles is the radius of the earth. The figure is: 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 W ( x ) = w R 2 x 2 . Part a: We have to find the weight lost at altitude h miles above the earth’s surface. We have to apply the linear approximation with a = R and Δ x = h . Use the formula: Δ f ≈ f ′ ( a ) Δ x We can rewrite the formula as: Δ W ≈ W ′ ( R ) Δ x Differentiate the function with respect to x . W ′ ( x ) = − 2 w R 2 x 3 Now, find the linear approximation when R = 3960 miles

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.1, Problem 41E

To determine

a. Show that the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h.

b. Estimate the weight lost by a 200-lb football player flying in a jet at an altitude of 7 miles.

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Chapter 4.1, Problem 40E

Chapter 4.1, Problem 42E

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Chapter 4 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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a. Show that the weight lost at altitude h miles above the earth’s surface is approximately Δ W ≈ − ( 0.0005 w ) h . b. Estimate the weight lost by a 200-lb football player flying in a jet at an altitude of 7 miles.

Solution Summary: The author explains how to determine the weight lost at altitude h miles above the earth's surface.

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a. Show that the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h.

b. Estimate the weight lost by a 200-lb football player flying in a jet at an altitude of 7 miles.

Want to see the full answer?

Chapter 4 Solutions

a. Show that the weight lost at altitude h miles above the earth’s surface is approximately Δ W ≈ − ( 0.0005 w ) h . b. Estimate the weight lost by a 200-lb football player flying in a jet at an altitude of 7 miles.

Solution Summary: The author explains how to determine the weight lost at altitude h miles above the earth's surface.

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a. Show that the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h. b. Estimate the weight lost by a 200-lb football player flying in a jet at an altitude of 7 miles.

Want to see the full answer?

Chapter 4 Solutions

a. Show that the weight lost at altitude h miles above the earth’s surface is approximately ΔW≈−(0.0005w)h.

b. Estimate the weight lost by a 200-lb football player flying in a jet at an altitude of 7 miles.