# Prove using the formal definition of a limit

1. Feb 11, 2012

### LOLItsAJ

1. The problem statement, all variables and given/known data
Prove using the formal definition of a limit that Lim x→4 x2 = 16

2. Relevant equations
|f(x)-L| and |x-c|
Using epsilon/delta definition.

3. The attempt at a solution
I've got that |x2-16| = |x-4||x+4|
I'm also pretty sure only |x-4| matters, since it is the same as |x-c|.
What would delta be? Since there's no coefficient of x to factor out, would delta = epsilon?

Another note: I really have no idea what I'm doing. I've based all my work off of prior examples, I don't understand how to "prove" the limit using the above information.

2. Feb 11, 2012

### tiny-tim

Hi LOLItsAJ!

If eg I specify .001, you have to find a range in which x2 lies between 15.999 and 16.001

3. Feb 11, 2012

### SammyS

Staff Emeritus
You might start by using the formal definition of limit for the case you're working on:
Lim x→4 x2 = 16​

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