10th Edition

ISBN: 9780100453777

Author: Larson

Publisher: YUZU

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Textbook Question

Chapter 8.6, Problem 72E

Building Design The cross section of a precast concrete beam for a building is bounded by the graphs of the equations

x = 2 1 + y 2 , x = − 2 1 + y 2 , y = 0 , and y = 3

where x and y are measured in feet. The length of the beam is 20 feet (see figure).

Chapter 8.6, Problem 72E, Building Design The cross section of a precast concrete beam for a building is bounded by the graphs

(a) Find the volume V and the weight W of the beam. Assume the concrete weighs 148 pounds per cubic foot.

(b) Find the centroid of a cross section of the beam.

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Chapter 8.6, Problem 71E

Chapter 8.6, Problem 74E

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Taylor Series Approximation Example- H.W More terms used implies better approximation f(x) 4 f(x) Zero order f(x + 1) = f(x;) First order f(x; + 1) = f(x;) + f'(x;)h 1.0 Second order 0.5 True f(x + 1) = f(x) + f'(x)h + ƒ"(x;) h2 2! f(x+1) 0 x; = 0 x+1 = 1 x h f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2 51 Taylor Series Approximation H.w: Smaller step size implies smaller error Errors f(x) + f(x,) Zero order f(x,+ 1) = f(x) First order 1.0 0.5 Reduced step size Second order True f(x + 1) = f(x) + f'(x)h f(x; + 1) = f(x) + f'(x)h + "(xi) h2 f(x,+1) O x₁ = 0 x+1=1 Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5 iterations (or & s= 5%) for f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2 52

Chapter 8 Solutions

EBK CALCULUS

Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 6E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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Solution Summary: The author calculates the volume V and the weight W of a concrete beam. The cross section of the beam is bounded by graphs.

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Chapter 8 Solutions