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Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² = 25, 0≤z≤4; ƒ(x, y, z) = e¯² Consider the shown work. To = аф де d ¡ (5 cos 0, 5 sin 0, z) = (–5 sin 0, 5 cos 0, 0) де d T₂ = (5 cos 0, 5 sin 0, z) = (0,0,1) dz i N(0, z) = T₁ × T₂ = -5 sin 0 0 ||N(0, z)|| = (5 cos 0)² + (5 sin 0)² + 0 = √/25 (cos² 0 + sin² (0) 2π 2) ds = √²+ √ * • j 5 cos 0 0 = : (5 cos 0)i + (5 sin ¤)j = (5 cos 0, 5 sin 0, 0) 0 [[ f(x, y, z) dS = e² do dz = √25=5

Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² = 25, 0≤z≤4; ƒ(x, y, z) = e¯² Consider the shown work. To = аф де d ¡ (5 cos 0, 5 sin 0, z) = (–5 sin 0, 5 cos 0, 0) де d T₂ = (5 cos 0, 5 sin 0, z) = (0,0,1) dz i N(0, z) = T₁ × T₂ = -5 sin 0 0 ||N(0, z)|| = (5 cos 0)² + (5 sin 0)² + 0 = √/25 (cos² 0 + sin² (0) 2π 2) ds = √²+ √ * • j 5 cos 0 0 = : (5 cos 0)i + (5 sin ¤)j = (5 cos 0, 5 sin 0, 0) 0 [[ f(x, y, z) dS = e² do dz = √25=5

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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Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² = 25, 0≤ z ≤ 4; f(x, y, z) = e¯² Consider the shown work. To = T, = аф де = д (5 cos 0, 5 sin 0, z) = (-5 sin 0, 5 cos 0, 0) do d -(5 cos 0, 5 sin 0, z) = (0,0,1) дz i N(0, z) = T₁ × T₂ = -5 sin 0 0 ||N(0, z)|| = 5 cos 0 0 2π 4 [[ f(x, y, 2) ds = [²* ["^ e S (5 cos 0)² + (5 sin 0)² + 0 = e² do dz k 0 = (5 cos 0)i + (5 sin 0)j = 1 Identify the first error in the work shown. /25 (cos² 0 + sin²0) The surface integral is written incorrectly. No errors exist in the work shown. The parametrization of the cylinder is incorrect. The normal vector N(0, z) is incorrect. (5 cos 0, 5 sin 0, 0) √25 = 5
Transcribed Image Text:Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² = 25, 0≤ z ≤ 4; f(x, y, z) = e¯² Consider the shown work. To = T, = аф де = д (5 cos 0, 5 sin 0, z) = (-5 sin 0, 5 cos 0, 0) do d -(5 cos 0, 5 sin 0, z) = (0,0,1) дz i N(0, z) = T₁ × T₂ = -5 sin 0 0 ||N(0, z)|| = 5 cos 0 0 2π 4 [[ f(x, y, 2) ds = [²* ["^ e S (5 cos 0)² + (5 sin 0)² + 0 = e² do dz k 0 = (5 cos 0)i + (5 sin 0)j = 1 Identify the first error in the work shown. /25 (cos² 0 + sin²0) The surface integral is written incorrectly. No errors exist in the work shown. The parametrization of the cylinder is incorrect. The normal vector N(0, z) is incorrect. (5 cos 0, 5 sin 0, 0) √25 = 5
Identify the first error in the work shown. The surface integral is written incorrectly. No errors exist in the work shown. The parametrization of the cylinder is incorrect. The normal vector N(0, z) is incorrect. The tangent vectors To and T₂ are incorrect. Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² =25, 0≤ z ≤ 4; f(x, y, z) = e¯² (Express numbers in exact form. Use symbolic notation and fractions where needed.) s f(x, y, z) ds
Transcribed Image Text:Identify the first error in the work shown. The surface integral is written incorrectly. No errors exist in the work shown. The parametrization of the cylinder is incorrect. The normal vector N(0, z) is incorrect. The tangent vectors To and T₂ are incorrect. Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² =25, 0≤ z ≤ 4; f(x, y, z) = e¯² (Express numbers in exact form. Use symbolic notation and fractions where needed.) s f(x, y, z) ds
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