# Math Help - Another Limit Question

1. ## Another Limit Question

$
\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.

2. Originally Posted by RedBarchetta
$
\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.

3. Limits of Composite Fns