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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:
The side of a square is measured to have a length aO with an uncertay aaO. Calculate the area with its absolute uncertay.

Solution:
The area is A AF a^ A The absolute uncertay is a_A r_A A r_a^ a^ fraca_aa a^ aAF aa times a aA sisetupround-mode uncertay round-precision sisetupexponent-mode scientific sisetupuncertay-mode separate The area with absolute uncertay is thus A resultAX pm aAXsquarem
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Exercise:
The side of a square is measured to have a length aO with an uncertay aaO. Calculate the area with its absolute uncertay.

Solution:
The area is A AF a^ A The absolute uncertay is a_A r_A A r_a^ a^ fraca_aa a^ aAF aa times a aA sisetupround-mode uncertay round-precision sisetupexponent-mode scientific sisetupuncertay-mode separate The area with absolute uncertay is thus A resultAX pm aAXsquarem
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Attributes & Decorations
Tags
absolute error, area, relative error
Content image
Difficulty
(1, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration