Answer
$\frac{\pi^{2}}{16}$
Work Step by Step
tan(θ) is continuous within its domain, and $tan(\pi /4)$ is defined under its range
$\lim\limits_{x \to \pi/4} x^{2} tan x = (\pi/4)^{2} tan (\pi/4)$
$\lim\limits_{x \to \pi/4} x^{2} tan x = (\frac{\pi^{2}}{16} (1))$
$\lim\limits_{x \to \pi/4} x^{2} tan x = \frac{\pi^{2}}{16}$
