Question

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

Answer 1

How is that 0?

Answer 2

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

Answer 3

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

Answer 4

substitute 0 for a*

Answer 5

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

Answer 6

Ok. Thanks! :)

Answer 7

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