# B Proof of a limit rule

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1. Dec 19, 2017

### shihab-kol

Hello, I would like to begin by saying that this does not fall into any homework or course work for me. It is just my interest.
I need to prove that limit of a constant gives the constant it self. Can some one provide a link? I have exams or I would have searched myself but unfortunately I don't have time. So, I had to post this thread.

2. Dec 19, 2017

### Staff: Mentor

3. Dec 19, 2017

### Staff: Mentor

This is one of the easiest of limits to prove, using the definition of a limit to prove it. If f(x) = k, a constant, can you show that $|f(x) - f(a)| < \epsilon$ when $|x - a| < \delta$?

4. Dec 22, 2017

### shihab-kol

If I take f(a) =k for some interval around x , then |f(x) - f(a)| =0 <E since by definition E >0.
But will this work?

5. Dec 22, 2017

### Staff: Mentor

It will work, but you need to say more.
Someone gives you a value of $\epsilon > 0$. Can you specify a number $\delta > 0$ so that when $|x - a| < \delta$, then $|f(x) - f(a)| < \epsilon$?