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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 15.7, Problem 16E

Textbook Problem

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Using the Divergence Theorem In Exercises 9-18, use the Divergence Theorem to evaluate

**and find the outward flux of F through the surface of the solid S bounded by the graphs of the equations. Use a computer algebra system to verify your results.**

To determine

**To calculate:** The value of

**Given:**

The vector field, *S*:

**Formula used:**

The divergence theorem,

**Calculation:**

The divergence of vector field **F** is calculated as below:

For the surface bounded by *S*:

Converting it into polar coordinates, As

Multivariable Calculus

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Finding Work in a Conservative Force Field In...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Evaluating a Line Integral Using Green's Theorem...Ch. 15 - Work In Exercises 59 and 60, use Greens Theorem to...Ch. 15 - Work In Exercises 59 and 60, use Greens Theorem to...Ch. 15 - Area In Exercises 61 and 61, use a line integral...Ch. 15 - Area In Exercises 61 and 62, use a line integral...Ch. 15 - Sketching a Parametric Surface In Exercise 63 and...Ch. 15 - Sketching a Parametric Surface In Exercise 63 and...Ch. 15 - Graphing a Parametric SurfaceIn Exercise 65 and...Ch. 15 - Graphing a Parametric SurfaceIn Exercise 65 and...Ch. 15 - Representing a Surface Parametrically In Exercises...Ch. 15 - Representing a Surface Parametrically In Exercises...Ch. 15 - 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Heat Flux Consider a single heat source located at...Ch. 15 - Heat Flux Consider a single heat source located at...Ch. 15 - Moments of Inertia Consider a wire of density...Ch. 15 - Moments of Inertia Using the formulas from...Ch. 15 - Laplace's Equation Let F(x,y,z)=xi+yj+zk, and let...Ch. 15 - Greens Theorem Consider the line integral...Ch. 15 - Area Use a line integral to find the area bounded...Ch. 15 - Area Use a line integral to find the area bounded...Ch. 15 - Work The force field F(x,y)=(x+y)i+(x2+1)j acts on...Ch. 15 - Work The force field F(x,y)=3x2y2i+2x3yj is shown...Ch. 15 - Area and Work How does the area of the ellipse...Ch. 15 - Verifying Identities (a) Let f and g be scalar...

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