To evaluate the limit:

lim x->3 ((9-2x)/3)^(tan(pi.x/6))

First, simplify the expression inside the parentheses:

(9-2x)/3 = (3(3-2x))/3 = 3 - 2x

Now we have:

lim x->3 (3 - 2x)^(tan(pi.x/6))

Plugging in x=3:

(3 - 2(3)) = 3 - 6 = -3

Now we have:

(-3)^(tan(pi))/6

Since tan(pi) is undefined (tan(pi) = 0), we cannot evaluate the limit at x=3. The limit does not exist in this case.