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AP® Calculus AB-BC

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Taylor Series Error (Lagrange Error Bound)

APCALC-ZJEMBU

If $| f^{ n }( x ) | <1$, where $f^{n} (x)$ is the nth derivative of $f(x)$, what is the minimum number of terms of the Taylor series for $f(x)$ centered at $x=2$ needed to approximate $f(2.1)$ with an error less than $0.001$?​

A

$1$

B

$2$

C

$3$

D

$4$

E

$5$