Answer
Please see below.
Work Step by Step
We want to prove that $$\lim_{x \to c}b=b$$ by using $\epsilon - \delta$ definition; that is, we must show that for each $\epsilon >0$, there exists a $\delta >0$ such that $|b-b|< \epsilon$ whenever $|x-c|< \delta$.
But, the inequality $|b-b|=0$.
