$\displaystyle

\mathop {\lim }\limits_{x \to \infty } \sin \left( {\tfrac{\pi }

{2} + \tfrac{1}

{x}} \right) = \sin \left( {\mathop {\lim }\limits_{x \to \infty } \tfrac{\pi }

{2} + \tfrac{1}

{x}} \right)

$

What limit property allows you to do this? I've looked through my textbook and found no real answer. Would anyone care to elaborate?

Thank you.