Provide an Appropriate Response $- x \leq x \cos \left( \frac { 1 } { x } \right) \leq x$

Multiple Choice

Provide an appropriate response.
-It can be shown that the inequalities $- x \leq x \cos \left( \frac { 1 } { x } \right) \leq x$ hold for all values of $x \geq 0$ . Find $\lim _ { x \rightarrow 0 } x \cos \left( \frac { 1 } { x } \right)$ if it exists.

A) does not exist
B) $0.0007$
C) 1
D) 0