Chapter 1.4, Problem 1ES

(a) Find the largest open interval, centered at the origin on the $x\text{-axis}$ , such that for each $x$ in the interval the value of the function $f\left(x\right)=x+2$ is within $0.1$ unit of the number $f\left(0\right)=2.$

(b) Find the largest open interval, centered at $x=3,$ such that for each $x$ in the interval the value of the function $f\left(x\right)=4x-5$ is within $0.01$ unit of the number $f\left(3\right)=7$ .

(c) Find the largest open interval, centered at $x=4,$ such that for each $x$ in the interval the value of the function $f\left(x\right)=x^2$ is within $0.001$ unit of the number $f\left(4\right)=16$ .