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- Let f(t) = t2 + cos(1000 t). What is the general formula for the scaling factor for f(t)? What is the value of the scaling factor at C=0? If C is approximately equal to 0, and is accurate to 4 decimal digits, what is the predicted relative accuracy of f(C)?
The scaling factor is given by the formula
sf = C f’(C) / f(C) = C (2C-1000sin(1000C))/(C2+cos(1000C)),
so that if C=0, sf=0. The predicted relative error is
(sf)(10 -4) = 0.
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