Question

Find the limit L. Then use the ε-δ definition to prove that the limit is L.
Lim (-5)
x->4

Answer 1

What exactly is the limit? Is it just
\[\lim_{x\to4}(-5)~~?\]

Answer 2

If that's the case, it should be clear enough what the limit is, considering \(f(x)=-5\) is a constant function.

To prove this limit, you have to show that for any \(\epsilon>0\), you can find \(\delta\) as a function of \(\epsilon\) such that \(|f(x)-L|=\color{red}{|-5-L|<\epsilon}\) if \(0<|x-4|<\delta\).

The red inequality is the key to the proof. If you can determine \(L\), you're done. An easy proof for an easy limit.