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4. (a) Show that the divergence theorem holds for the vector field F = 2xî + yz} – 3z²k where o is the surface æ2 = 9 (b) Compute the gradient field of the surface ø(x, y, z) = 3x²y + 5y ln(2z) – 4ze² and hence graph the gradient field. (2]

4. (a) Show that the divergence theorem holds for the vector field F = 2xî + yz} – 3z²k where o is the surface æ2 = 9 (b) Compute the gradient field of the surface ø(x, y, z) = 3x²y + 5y ln(2z) – 4ze² and hence graph the gradient field. (2]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. (a) Show that the divergence theorem holds for the vector field F = 2xi + yzj – 3z2 k where o is the surface x? = 9 – y? – z2. (b) Compute the gradient field of the surface o(x, y, z) = 3x²y+ 5y ln(2z) – 4ze" and hence graph the gradient field. [2]
Transcribed Image Text:4. (a) Show that the divergence theorem holds for the vector field F = 2xi + yzj – 3z2 k where o is the surface x? = 9 – y? – z2. (b) Compute the gradient field of the surface o(x, y, z) = 3x²y+ 5y ln(2z) – 4ze" and hence graph the gradient field. [2]
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