
means to say that for any given
, we can find
such that anytime
(i.e. the whenever
is "close enough" to 5), we can guarantee that
(i.e. the value of
is "close enough" to the limit value).
What we want to end up with is

Dividing both sides by 3 gives

which suggests
is a sufficient threshold.
The proof itself is essentially the reverse of this analysis: Let
be given. Then if

and so the limit is 7. QED
Thank you for posting your answer, but I don't think this answer is possible to solve, because of its lack of information.
You cant determine "u" if there is no "equal" sign with an answer following
But if you were looking to simplify the expression
The answer would be