limit refresher

Could some please explain how to take this limit?

lim x ->2/3 1/(3x-2)^3

and a similar one

lim x ->2/3 7/(3x-2)^2

Thanks,

lim x ->2/3 1/(3x-2)^3 yields 1/0 so the limit could be inf,-inf or DNE

So consider onesided limits

lim x ->2/3+ ( 1/(3x-2)^3) = infinity since if x > 2/3 3x-2 > 0 and
(3x-2)^3 > 0

lim x ->2/3- (1/(3x-2)^3) = neg infinity since if x < 2/3 3x-2 < 0 and

(3x-2)^3 < 0

Therefore lim x ->2/3 1/(3x-2)^3 DNE

Note if we had (3x-2)^2 then both limits would be infinity and the limit would be infinity

And the second one is infinity from both sides so the limit is positive infinity correct?
Ooops just saw the last line of your post. Thanks.

you got it--