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- Let f(t) = t3 + sqrt(3 t). What is the general formula for the scaling factor for f(t)? What is the value of the scaling factor at C=3? If C is approximately equal to 3, and is accurate to 3 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 (3C2+3/[2 sqrt(3 C)]) / (t3+sqrt(3 C)),
so that if C=3, sf=3 (27 + 1/2)/(27+3) = 2.75.
The predicted relative error is (sf)(10 -3) = 2.75 * 10-3.
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