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AP® Calculus AB-BC

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Moderate

Writing a Third Degree Taylor Polynomial

APCALC-ISPLEU

Find the $3^{rd}$ degree Taylor polynomial for $f(x)=\cfrac{1}{x}$ centered at $x = 1$.

A

$1-( x-1 ) +\cfrac{( x-1 ) ^{ 2 }}{2}-\cfrac{( x-1 ) ^{ 3 }}{6}$

B

$1+( x-1 ) -( x-1 ) ^{ 2 }+( x-1 ) ^{ 3 }$

C

$1-( x-1 ) +( x-1 ) ^{ 2 }-( x-1 ) ^{ 3 }$

D

$1+( x+1 ) -( x+1 ) ^{ 2 }+( x+1 ) ^{ 3 }$