Barungi Regan
Feb 22
If p = (x/y) , what is the error in p mathematically?
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ChatGPT
Feb 22
The error in p can be calculated using the formula for the relative error:
Error in p = |(∂p/∂x) * error in x| + |(∂p/∂y) * error in y|
where ∂p/∂x and ∂p/∂y are the partial derivatives of p with respect to x and y, respectively.
Given that p = x/y, the partial derivatives are:
∂p/∂x = 1/y
∂p/∂y = -x/y^2
Therefore, the error in p can be calculated as:
Error in p = |(1/y) * error in x| + |(-x/y^2) * error in y|
Error in p = |(∂p/∂x) * error in x| + |(∂p/∂y) * error in y|
where ∂p/∂x and ∂p/∂y are the partial derivatives of p with respect to x and y, respectively.
Given that p = x/y, the partial derivatives are:
∂p/∂x = 1/y
∂p/∂y = -x/y^2
Therefore, the error in p can be calculated as:
Error in p = |(1/y) * error in x| + |(-x/y^2) * error in y|
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