# How do you use the epsilon delta definition to prove that the limit of #2x-4=6# as #x->1#?

##### 1 Answer

May 9, 2017

It cannot be proven. It is false.

#### Explanation:

Proof that

Given

Then for any

# = 2abs(x-1)#

# < 2delta#

# = 2epsilon/2#

# = epsilon#

That is:

We have shown that:

For any

for all

So, by the definition of limit,