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