This may be a stupid question thats gonna easily be proved but i just wondered at which step is this wrong. This is taken from a proof in my uni class that limit x->3 (7x) = 21 but just changing one number. why is it wrong and where does it go wrong?

Prove using the

definition of a limit that

(was originally 21 of course)

Rough Work:

|f(x) - L| = |7x - 28| = 7|x - 4|

|x - p| we can control with

If

, then

Proof.

Let

be given. Choose

, then if

=>

From the

definition of a limit,

Can somebody point out the mistake in that? surely there must be some step thats wrong!