Answer
$\frac{41}{1250}$
Work Step by Step
$P_{4} (x) = x^{2} - x^{3} + \frac{1}{2}x^{4}$
$f(\frac{1}{5})$, so substitute $\frac{1}{5}$ for $x$
$P_{4} (\frac{1}{5}) = (\frac{1}{5})^{2} - (\frac{1}{5})^{3} + \frac{1}{2}(\frac{1}{5})^{4}$
$= \frac{1}{25} - \frac{1}{125} + \frac{1}{1250}$
$= \frac{41}{1250}$
