## Zenmo one year ago Very small question (will probably take a second), help me understand this textbook example. ~Calculus Limits & Derivatives.

1. Zenmo

How is that 0?

2. thomas5267

Why is $$\lim_{x\to a}(x-a)\neq 0$$? $$a-a=0$$.

3. Zenmo

So, substitute 0 in $\lim_{x \rightarrow a}(x-a)$ to get a-a=0?

4. Zenmo

substitute 0 for a*

5. thomas5267

Since $$f(x)=x-a$$ is continuous you can do that.

6. Zenmo

Ok. Thanks! :)

7. thomas5267

Continuity of $$f(x)=x-a$$ can be proven using $$\epsilon\text{-}\delta$$ definition of limit.