APFIVE Ratio Of Actual Error To Lagrange Error Bound
A 5th-degree Taylor polynomial for $$f(x) = \ln(1+x)$$ centered at $$x=0$$ is used to approximate $$\ln(1.2)$$. Given an actual error of $$0.001$$ and that $$|f^{(6)}(x)| \leq 120$$ on the interval $$[0, 0.2]$$, what is the ratio of the actual error to the maximum error determined by the Lagrange error bound?
A
13.3
B
1.2
C
93.75
D
0.375
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