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

1. anonymous

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

2. anonymous

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.