Find the limits$.$ Is the function continuous at the point being approached?

$\underset{x\frac{5}{16}}{lim}cos(8x-cos(8x))$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The function is continuous at $x=\frac{5}{16}$ because it is a composition of two continuous functions and $\underset{\{\begin{array}{c}\text{:}[]\\ x\frac{5}{16}\end{array}}{lim}{?}^{cos}$

B$.$ The function is not continuous at $x=\frac{5}{16}$ because $cosx$ is not a continuous function.

C$.$ The function is not continuous at $x=\frac{5}{16}$ because $8x$ is not a continuous function.