Solution Found!
Maximum surface integral Let S be the paraboloid z = a(1 ?
Chapter 13, Problem 39E(choose chapter or problem)
Maximum surface integral Let S be the paraboloid \(z=a\left(1-x^{2}-y^{2}\right)\)), for \(z \geq 0\), where a > 0 is a real number. Let \(\mathbf{F}=\langle x-y, y+z, z-x\rangle\), For what value(s) of a (if any) does\(\iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} d S\) have its maximum value?
Text Transcription:
z =a(1 - x^2 - y^2)\
Z leq 0
F = langle x - y, y + z, z - x rangle
iint_S (nabla x F) cdot n dS
Questions & Answers
QUESTION:
Maximum surface integral Let S be the paraboloid \(z=a\left(1-x^{2}-y^{2}\right)\)), for \(z \geq 0\), where a > 0 is a real number. Let \(\mathbf{F}=\langle x-y, y+z, z-x\rangle\), For what value(s) of a (if any) does\(\iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} d S\) have its maximum value?
Text Transcription:
z =a(1 - x^2 - y^2)\
Z leq 0
F = langle x - y, y + z, z - x rangle
iint_S (nabla x F) cdot n dS
ANSWER:Solution 39E
Step 1:
Given that
Let S be the paraboloid z = a(1 − x2 − y2), for z ≥ 0, where a > 0 is a real number. Let F = 〈x − y, y + z, z − x〉.