Chapter 2.3, Problem 39E

a.

To determine

To find: $\underset{x\to 1^{-}}{\lim }\frac{1}{x^3-1}$ and $\underset{x\to 1^{+}}{\lim }\frac{1}{x^3-1}$ by evaluating $f\left(x\right)=\frac{1}{x^3-1}$ for values of x that approaches 1 from left and from right.

b.

To determine

To find: $\underset{x\to 1^{-}}{\lim }\frac{1}{x^3-1}$ and $\underset{x\to 1^{+}}{\lim }\frac{1}{x^3-1}$ by reasoning.

c.

To determine

To find: $\underset{x\to 1^{-}}{\lim }\frac{1}{x^3-1}$ and $\underset{x\to 1^{+}}{\lim }\frac{1}{x^3-1}$ by graphing $f\left(x\right)=\frac{1}{x^3-1}$ .