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Let $f( x ) =\cfrac{1}{ x+1 } $.

If the $2^{nd}$ degree Taylor polynomial for $f(x)$ about $x = 0$ is used to approximate $f(1)$ on the interval $[0, 1]$, what is the Lagrange error bound to find the maximum error?

A

$\cfrac{2}{3}$

B

$\cfrac{1}{3}$

C

$\cfrac{1}{2}$

D

$1$

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