Chapter 1.4, Problem 57ES

(a) Find the largest open interval, centered at the origin on the $x\text{-axis}$ , such that for each $x$ in the interval, other than the center, the values of $f\left(x\right)=1/x^2$ are greater than $100$ .

(b) Find the largest open interval, centered at $x=1,$ such that for each $x$ in the interval, other than the center, the values of the function $f\left(x\right)=1/\left|x-1\right|$ are greater than $1000$ .

(c) Find the largest open interval, centered at $x=3,$ such that for each $x$ in the interval, other than the center, the values of the function $f\left(x\right)=1/{\left(x-3\right)}^2$ are greater than $-1000$ .

(d) Find the largest open interval, centered at the origin on the $x\text{-axis}$ , such that for each $x$ in the interval, other than the center, the values of $f\left(x\right)=1/x^4$ are greater than $-10,000$ .