Consider the function $f(x) = x \ln(x)$.
Let $T_n$ be the $n^{th}$ degree Taylor approximation of $f(2)$ about $x = 1$.
Find:
$T_{1} =$ $T_{2} =$ $T_{3} =$
Use 3 decimal places in your answer, but make sure you carry all decimals when performing calculations

$T_{3}$ is an (over/under) estimate of $f(2)$.

If $R_{3}$ is the remainder given by the Lagrange Remainder Formula:
$\left|R_{3}\right| \le$