Find the largest δ so that

Question

Let f(x)=−5x+(−5).
Find the largest δ so that |f(x)−f(a)|<ϵ when |x−a|<δ.

 

δ=________

Answer 1

The way this works is, GIVEN epsilon, you find the delta.  In this case it will be (1/5) of ϵ.

 

This is because |f(a+h) - f(a)| < ϵ

|5h| < ϵ