Let S be the plane z = -3 with 0≤x≤ 1 and 0 ≤ y ≤ 1 oriented downward. SS₂² F.d5>0. (a) Find a vector field so that (b) Find a scalar function f(x, y, z) so that [[ f(x, y, z)dS < 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Can you answer question 1 please

1. Let S be the plane z = -3 with 0≤x≤ 1 and 0 ≤ y ≤1 oriented downward.
TIE
F.ds>0.
S
(a) Find a vector field F so that
(b) Find a scalar function f(x, y, z) so that f(x, y, z)dS < 0.
S
2. Let F = xi+yj + zk and let f(x, y, z) = x²e-².
(a) Describe a surface S together with orientation so that
(b) Explain why you cannot find a surface S so that
[[F.
S
F · dŠ < 0.
[[ f(x, y, z)dS < 0.
S
Transcribed Image Text:1. Let S be the plane z = -3 with 0≤x≤ 1 and 0 ≤ y ≤1 oriented downward. TIE F.ds>0. S (a) Find a vector field F so that (b) Find a scalar function f(x, y, z) so that f(x, y, z)dS < 0. S 2. Let F = xi+yj + zk and let f(x, y, z) = x²e-². (a) Describe a surface S together with orientation so that (b) Explain why you cannot find a surface S so that [[F. S F · dŠ < 0. [[ f(x, y, z)dS < 0. S
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