# Math Help - A "trivial" limit proof

1. ## A "trivial" limit proof

I'm just clueless of how to prove this;

Prove that lim f(x) = lim f(x-a)
x->0 x->a

I can see that making x to approach 0 is the same as making x approach a in (x-a), since both things go near zero. Well, I hope that you can help me

2. Originally Posted by akolman
I'm just clueless of how to prove this;

Prove that lim f(x) = lim f(x-a)
x->0 x->a

I can see that making x to approach 0 is the same as making x approach a in (x-a), since both things go near zero. Well, I hope that you can help me
Substitute $u = x + a \Rightarrow x = u - a$ into $\lim_{x \rightarrow 0} f(x)$:

$\lim_{u - a \rightarrow 0} f(u - a)$

$\Rightarrow \lim_{u \rightarrow a} f(u - a)$.

But u is just a dummy variable so you can re-brand it as x ......

3. wow, that was fast!

Thanks.