Mathematical Analysis Fundamentals

Furthermore, take any $r>0$ in part (b). Fix $z\in \mathbb{R}$ satisfying $r<\mid z-c\mid$. Then for every $x\in [c-r\text{,}c+r]$, we have

$\mid a_n{(x-c)}^n\mid \le \mid a_n{r}^n\mid \le \mid a_n{(z-c)}^n\mid \text{,}$

where $\mid a_n{(}^{}$