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,

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- May 12th 2009, 06:09 AMpberardilimit 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, - May 12th 2009, 06:23 AMCalculus26
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 - May 12th 2009, 06:25 AMpberardi
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. - May 12th 2009, 06:26 AMCalculus26
you got it--