# Question #b7690

${\lim}_{x \to \infty} {x}^{2} \cos \left(\frac{1}{x}\right) = + \infty$
Substitute $y = \frac{1}{x}$. When $x \to \infty$, $y \to {0}^{+}$, so:
${\lim}_{x \to \infty} {x}^{2} \cos \left(\frac{1}{x}\right) = {\lim}_{y \to {0}^{+}} \cos \frac{y}{y} ^ 2 = \infty$