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Ratio Of Actual Error To Lagrange Error Bound

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A 5th-degree Taylor polynomial for f(x)=ln⁡(1+x)f(x) = \ln(1+x) centered at x=0x=0 is used to approximate ln⁡(1.2)\ln(1.2). Given an actual error of 0.0010.001 and that ∣f(6)(x)∣≤120|f^{(6)}(x)| \leq 120 on the interval [0,0.2][0, 0.2], what is the ratio of the actual error to the maximum error determined by the Lagrange error bound?

A

1.2

B

93.75

C

0.375

D

13.3

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