Find the following limit using $\underset{0}{lim}\frac{sin}{}=1.$

$\underset{x0}{lim}\frac{tan4x}{sin9x}$

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

A$.\underset{x0}{lim}\frac{tan4x}{sin9x}=\frac{4}{9}($Type an integer or a simplified fraction$)$

B$.$ The limit does not exist