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https://texercises.com/exercise/sphere-2/
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The following quantities appear in the problem:
The following formulas must be used to solve the exercise: \(\epsilon_f(a,b) \lesssim \left| \frac{\partial f}{\partial x}(a_0, b_0) \right| \Delta x + \left| \frac{\partial f}{\partial y}(a_0, b_0) \right| \Delta y \quad \)
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Exercise:
sisetupuncertay-mode separate A spherical object has a volume of VerrO. Calculate the radius and its absolute uncertay.

Solution:
The volume of a sphere is V fracpi r^ It follows for the radius r rF left frac times V pi right^/ r and for the absolute uncertay a_r r_r r fracr_V r fraca_V V left frac Vpi right^/ arF fracaVleft timessqrtpitimes V right^/ ar sisetupuncertay-mode separate round-mode uncertay round-precision exponent-mode scientific The result can be written as r resultrX pm arXcm
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Exercise:
sisetupuncertay-mode separate A spherical object has a volume of VerrO. Calculate the radius and its absolute uncertay.

Solution:
The volume of a sphere is V fracpi r^ It follows for the radius r rF left frac times V pi right^/ r and for the absolute uncertay a_r r_r r fracr_V r fraca_V V left frac Vpi right^/ arF fracaVleft timessqrtpitimes V right^/ ar sisetupuncertay-mode separate round-mode uncertay round-precision exponent-mode scientific The result can be written as r resultrX pm arXcm
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Attributes & Decorations
Tags
absolute error, error propagation, relative error
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration