Thread: Simple Limit Proof/Reasoning

Hey all, thanks again for all help in the past! Here's a limit question that I am unsure if I am overthinking, or if it's as simple as it looks.

It states:

Prove:
lim f(x) as x-->a is equal to lim f(a+h) as h-->0 (this is really just an exercise in understanding what the terms are)

Now the easiest way would just to pop in the values and boom, lim f(a) = lim f(a). But I think he is looking for a different reasoning. My attempt was to kind of define the statements like so:

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LHS: f can be made to be as close to a limit L as desired by making x sufficiently close to a.

RHS: f can be made to be as close to a limit L as desired by making h sufficiently close to zero.

And in this example, it just so happens when h is made to go to zero we are left with the respective equations L's equal to each other.
______

I don't think I've really "proved" anything though, have I?

Thanks again!

It depends on whether and are continuous at and respectively, and if you are allowed to use the result that if is continuous at .

If so, your reasoning is fine.

If not, you will need to use an proof.