Prove using the formal definition of a limit

[LOLItsAJ]

Homework Statement

Prove using the formal definition of a limit that Lim _x→4 x² = 16

Homework Equations

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

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.

 

[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

 

[SammyS]

Homework Statement

Prove using the formal definition of a limit that Lim _x→4 x² = 16

Homework Equations

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

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.

You might start by using the formal definition of limit for the case you're working on:

Lim _x→4 x² = 16​