1. Let F(x, y, z) be the vector field (x² (1 + y²z²), Q(x, y, z), ey cos(22)), where is a differentiable function of x, y, and z. Suppose div F = 2x(1 + y²z2) - 2ery sin(22) + z tan(2y + 2) + 2z2 sec²(2y + 2); and • curl F = (xey cos(22)-y tan(2y+z)-y sec² (2y+z), 2x²y²z-yery cos(22), -2x²yz²). Determine div(Q).

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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1. Let F(x, y, z) be the vector field (x²(1 + y²z²), Q(x, y, z), ey cos(22)), where is a
differentiable function of x, y, and z. Suppose
div F = 2x(1 + y2² 2²) — 2ery sin(22) + z tan(2y+z) + 2z sec² (2y + 2); and
-
• curl F = (xey cos(22)-y tan(2y+z)-y sec² (2y+z), 2x²y²z-yery cos(22), -2x²yz²).
Determine div(Q).
Transcribed Image Text:1. Let F(x, y, z) be the vector field (x²(1 + y²z²), Q(x, y, z), ey cos(22)), where is a differentiable function of x, y, and z. Suppose div F = 2x(1 + y2² 2²) — 2ery sin(22) + z tan(2y+z) + 2z sec² (2y + 2); and - • curl F = (xey cos(22)-y tan(2y+z)-y sec² (2y+z), 2x²y²z-yery cos(22), -2x²yz²). Determine div(Q).
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