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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 = 5arrow_forwardHow do I evaluate this surface integral?arrow_forwardConsider the surface xyz 24. A. Find the unit normal vector to the surface at the point (2, 3, 4) with positive first coordinate. B. Find the equation of the tangent plane to the surface at the given point. Express your answer in the form ax + by + cz + d = 0, normalized so that a = 12. = 0. %Darrow_forward
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