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
(-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.
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.