11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Textbook Question

Chapter 14.5, Problem 3E

Finding Surface AreaIn Exercises 3–16, find the area of the surface given by z = f ( x , y ) that lies above the region R .

f ( x , y ) = 2 x + 2 y

R: triangle with vertices ( 0 , 0 ) , ( 4 , 0 ) , ( 0 , 4 )

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Chapter 14.5, Problem 2E

Chapter 14.5, Problem 4E

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Tutorial Exercise Find the area of the part of the plane 3x + 2y + z = 6 that lies in the first octant. Part 1 of 5 2 The surface S is the graph of a function z = f(x, y) over a region D in the xy-plane. The surface area of S can be calculated by A(S) = az 1 + dz dA. ду f(x, y) = 6 – 3x az 2y. We, therefore, have ax əz -3 and -2 The plane 3x + 2y + z = 6 is the graph of the function z = 3.x ду Part 2 of 5 Therefore, =7 V1+(-3)² + (-2)² dA = V14 dA. Since we want the area of the section of the plane that lies above the first octant, then the region D will be the triangular region bounded by the x-axis, the y-axis, and the line formed by the intersection of the plane with the plane z = 0. Substituting z = 0 into 3x + 2y + z = 6 and solving for y, we find that this line of intersection has the equation y = x + Submit Skip (you cannot come back)

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Chapter 14 Solutions

Calculus (MindTap Course List)

Ch. 14.1 - CONCEPT CHECK Iterated Integral Explain what is...Ch. 14.1 - Prob. 2E Ch. 14.1 - Question: Evaluate the integral: 0x(2xy)dy Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...

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Finding Surface AreaIn Exercises 3–16, find the area of the surface given by z = f ( x , y ) that lies above the region R . f ( x , y ) = 2 x + 2 y R : triangle with vertices ( 0 , 0 ) , ( 4 , 0 ) , ( 0 , 4 )

Solution Summary: The author calculates the area of the surface by z=2x+2y above the region R, which is triangles with vertices.

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Chapter 14 Solutions