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General Engineering Introduction/Error Analysis/Calculus of Error/multiply proof
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Multiplying by a Constant Proof
if then
Algebra Proof
start with the formula: dependent equals constant times independent
substitute the measured value of x (and x's error) and set equal to y plus the unknown error in y that we are interested in:
subtract the top equation from the bottom:
and are left with the equation: error in y equals constant times error in x
Calculus Proof
start with the formula: dependent equals constant times independent
then