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The formula for the uncertainty in ² is A(x²) = 2xAx. a) James tries to derive this formula starting from the expression A(zy)= = xy√(Ax/x)² + (Ay/y)2 and setting y = x. He ends up with A(2²) = √2xAx. What was his mistake? b) What happens when a is very small? How about when a is very large?

The formula for the uncertainty in ² is A(x²) = 2xAx. a) James tries to derive this formula starting from the expression A(zy)= = xy√(Ax/x)² + (Ay/y)2 and setting y = x. He ends up with A(2²) = √2xAx. What was his mistake? b) What happens when a is very small? How about when a is very large?

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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7. The formula for the uncertainty in a² is A (x²) = 2xAx. a) James tries to derive this formula starting from the expression A(ry) = xy√(Ax/x)² + (Ay/y)² and setting y = x. He ends up with A(22) = √2xAx. What was his mistake? b) What happens when a is very small? How about when x is very large?
Transcribed Image Text:7. The formula for the uncertainty in a² is A (x²) = 2xAx. a) James tries to derive this formula starting from the expression A(ry) = xy√(Ax/x)² + (Ay/y)² and setting y = x. He ends up with A(22) = √2xAx. What was his mistake? b) What happens when a is very small? How about when x is very large?
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