Chapter 1.4, Problem 39ES

(a) Find the smallest positive number $N$ such that for each $x$ in the interval $\left(N,+\infty \right)$ , the value of the function $f\left(x\right)=1/x^2$ is within $0.1$ unit of $L=0$ .

(b) Find the smallest positive number $N$ such that for each $x$ in the interval $\left(N,+\infty \right)$ , the value of $f\left(x\right)=x/\left(x+1\right)$ is within $0.01$ unit of $L=1$ .

(c) Find the largest negative number $N$ such that for each $x$ in the interval $\left(-\infty ,N\right)$ , the value of the function $f\left(x\right)=1/x^3$ is within $0.001$ unit of $L=0$ .

(d) Find the largest negative number $N$ such that for each $x$ in the interval $\left(-\infty ,N\right)$ , the value of the function $f\left(x\right)=x/\left(x+1\right)$ is within $0.01$ unit of $L=1$ .