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Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 15.7 - Problem 5
Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 15.7 - Problem 5

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# ?In Exercises 1 - 6, verify the Divergence Theorem by evaluating $$\int_{S} \int \mathrm{F} \cdot \mathrm{N} d S$$ as a surface inte

ISBN: 9781285774770 141

## Solution for problem 5 Chapter 15.7

Calculus: Early Transcendental Functions | 6th Edition

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Problem 5

In Exercises 1 - 6, verify the Divergence Theorem by evaluating

$$\int_{S} \int \mathrm{F} \cdot \mathrm{N} d S$$

as a surface integral and as a triple integral.

$$\mathbf{F}(x, y, z)=x z \mathbf{i}+z y \mathbf{j}+2 z^{2} \mathbf{k}$$

S: surface bounded by $$z=1-x^{2}-y^{2}$$ and z = 0

Text Transcription:

int_S int F cdot N dS

F(x, y, z) = xzi + zyj + 2z^{2}k

z = 1 - x^2 - y^2

Step-by-Step Solution:

Step 1 of 5) Figure 12.21 The osculating circle for the parabola y = x2 at the origin (Example 4).

Step 2 of 2

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?In Exercises 1 - 6, verify the Divergence Theorem by evaluating $$\int_{S} \int \mathrm{F} \cdot \mathrm{N} d S$$ as a surface inte