Q. 55 - 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. 

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

Step-by-Step Solution

Answer

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

Step 1. Given information.

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

Step 2. Graph of the solution.

The graph of the function is,

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