how would i go about doing this problem?
lim_(x->0^+) (tan(3 x))^x
I am thinking of using lim_(x->0^+) y =?
lny = xln(tan(3x))
lntan(3x)/ (x^-1)
3(sec(3x)^2 / (-x^-2)
am i on the right path?
Yes, You are!... if You consider a more general complex variable z You have...
(1)
... and from (1) You derive...
(2)
Now from (2) is easy to derive that is...
(3)
... so that...
(4)
It is remarkable the fact that the limit (3) and (4) are independent from how z tends to 0...
Kind regards