Gevraagd: \eqalign{\mathop {\lim }\limits_{x \to 0} \sqrt x \cos ^2 \left( {\frac{1} {x}} \right)}

\eqalign{ & \mathop {\lim }\limits_{x \to 0} \sqrt x \cos ^2 \left( {\frac{1} {x}} \right) \cr & 0 \leq \sqrt x \cos ^2 \left( {\frac{1} {x}} \right) \leq \sqrt x \cr & \mathop {\lim }\limits_{x \to 0} 0 = 0\,\,en\,\,\mathop {\lim }\limits_{x \to 0} \sqrt x = 0 \cr & \mathop {\lim }\limits_{x \to 0} \sqrt x \cos ^2 \left( {\frac{1} {x}} \right) = 0 \cr}