Q. 57 - Calculus

Question

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits. 

$\underset{x\to 1}{\lim }\frac{x-1}{x^2-1}$

Step-by-Step Solution

Answer

The value of $\underset{x\to 1}{\lim }\frac{x-1}{x^2-1}=\frac{1}{2}$and graph is

Step 1. Given information.

The given function is $\underset{x\to 1}{\lim }\frac{x-1}{x^2-1}.$

Step 2. Graph of the equation.

The graph of the function is,

$$\begin{gathered} As x\to 1, f\left(x\right)=\frac{1}{2} \\ Therefore, \\ \underset{x\to 1}{\lim }\frac{x-1}{x^2-1}=\frac{1}{2} \end{gathered}$$