Evaluate the following limit or state that if does not exist. $($Hint: Identify the given limit as the derivative of a function $f$ at a point a$.)$

$\underset{x3\frac{x}{2}}{lim}\frac{cosx}{x-3\frac{x}{2}}$

BB$.f(x)=cosx,a=\frac{3x}{2}$

c$.f(x)=sinx,a=-\frac{3}{2}$

D$.f(x)=sinx,a=\frac{3}{2}$

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

A$.\underset{x3\frac{x}{2}}{lim}\frac{cosx}{x-3\frac{x}{2}}=$

$$ B$.$ The imit does not exist.