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
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 $\displaystyle u = x + a \Rightarrow x = u - a$ into $\displaystyle \lim_{x \rightarrow 0} f(x)$:
$\displaystyle \lim_{u - a \rightarrow 0} f(u - a)$
$\displaystyle \Rightarrow \lim_{u \rightarrow a} f(u - a)$.
But u is just a dummy variable so you can re-brand it as x ......