Question

Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 28 that lies above the plane z = 3 and is oriented upward.

Name: let fx y z z tan1y2i z3 lnx2 8j zk find the flux of f across s the part of the paraboloid x2 y2 z 28 that lies above the plane z 3 and is oriented upward 79303
Uploaded: 2023-01-06T17:08:42-08:00
Duration: 3 min 36 s
Channel: Madhur L
Description: let fx y z z tan1y2i z3 lnx2 8j zk find the flux of f across s the part of the paraboloid x2 y2 z 28 that lies above the plane z 3 and is oriented upward 79303

          Let 
F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk.
 Find the flux of F across S, the part of the paraboloid 
x2 + y2 + z = 28
 that lies above the plane 
z = 3
 and is oriented upward.

Added by -Ngeles G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

01/06/2023

Step 1

To find the flux of the vector field \( F(x, y, z) = z \tan^{-1}(y^2) \mathbf{i} + z^3 \ln(x^2 + 8) \mathbf{j} + z \mathbf{k} \) across the surface \( S \), which is the part of the paraboloid \( x^2 + y^2 + z = 28 \) that lies above the plane \( z = 3 \), we will Show more…

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Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 28 that lies above the plane z = 3 and is oriented upward.