Question

2. Let $f(x, y, z) = \ln \sqrt{x^2 + y^2 + z^2}$. Find $\int \int_S \nabla f \cdot n \, d\sigma$ if $S$ is the the portion of the solid sphere $x^2 + y^2 + z^2 = a^2$ that lies in the first octant.

Name: 2 let fx y z ln sqrtx2 y2 z2 find int ints nabla f cdot n dsigma if s is the the portion of the solid sphere x2 y2 z2 a2 that lies in the first octant 74986
Uploaded: 2023-11-21T17:35:25-08:00
Channel: Victor Salazar
Description: 2 let fx y z ln sqrtx2 y2 z2 find int ints nabla f cdot n dsigma if s is the the portion of the solid sphere x2 y2 z2 a2 that lies in the first octant 74986

          2. Let $f(x, y, z) = \ln \sqrt{x^2 + y^2 + z^2}$. Find $\int \int_S \nabla f \cdot n \, d\sigma$ if $S$ is the the portion of the solid sphere $x^2 + y^2 + z^2 = a^2$ that lies in the first octant.

2 let fx y z ln sqrtx2 y2 z2 find int ints nabla f cdot n dsigma if s is the the portion of the solid sphere x2 y2 z2 a2 that lies in the first octant 74986

Added by Enrique M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Victor Salazar

11/21/2023

Step 1

$$f(x, y, z) = \ln \sqrt{x^2 + y^2 + z^2} = \frac{1}{2} \ln (x^2 + y^2 + z^2)$$ $$\nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right)$$ $$\frac{\partial f}{\partial x} = \frac{1}{2} \cdot Show more…

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2. Let $f(x, y, z) = \ln \sqrt{x^2 + y^2 + z^2}$. Find $\int \int_S \nabla f \cdot n \, d\sigma$ if $S$ is the the portion of the solid sphere $x^2 + y^2 + z^2 = a^2$ that lies in the first octant.