Free Taylor, Maclaurin, & Power series challenge Practice Problems • Learn To Be

Let

\displaystyle P\left( x \right)=-3+5\left( x-1 \right)+2{{\left( x-1 \right)}^{2}}

be the second-degree Taylor polynomial for

~g~

centered at

~x=1\,

. Which of the following is the third-degree Taylor polynomial for

~h~

centered at

~x=1~

where

~\displaystyle h\left( x \right)=\int\limits_{1}^{x}{g\left( t \right)\text{ }dt}\,

?

Choose 1 answer:

A
$\displaystyle-3\left( x-1 \right)+\frac{{{5\left( x-1 \right)}^{2}}}{2}+\frac{{{2\left( x-1 \right)}^{3}}}{3}$
B
$\displaystyle-3\left( x-1 \right)+\frac{{{5\left( x-1 \right)}^{2}}}{2\cdot2!}+\frac{{{2\left( x-1 \right)}^{3}}}{3\cdot3!}$
C
$\displaystyle-3x+\frac{{{5\left( x-1 \right)}^{2}}}{2}+\frac{{{2\left( x-1 \right)}^{3}}}{3}$
D
$\displaystyle-3+\frac{{{5\left( x-1 \right)}^{2}}}{2}+\frac{{{2\left( x-1 \right)}^{3}}}{3}$
E
$\displaystyle-3\left( x+1 \right)+\frac{{{5\left( x-1 \right)}^{2}}}{2}+\frac{{{2\left( x-1 \right)}^{3}}}{3}$

Taylor, Maclaurin, & Power series challenge