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Let F\vec { F } Be a Smooth Vector Field F\vec { F}

question 56

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Let F\vec { F } be a smooth vector field.The flux of F\vec { F} out of a small sphere of radius r centered at the point (1, π\pi , 2 π\pi ) is 12 π\pi r3. Find divF\operatorname { div } \vec { F } at (1, π\pi , 2 π\pi ) and use the result to estimate the flux of F\vec {F } out of the small cube of side 0.025 centered around the point (1, π\pi , 2 π\pi ) .

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