Chapter 11.3, Problem 71E

Solution

To find: The value of the limit $\underset{x\to 1}{{\displaystyle \lim }}\frac{x^2+1}{x-1}$ .

The value of $\underset{x\to 1}{{\displaystyle \lim }}\frac{x^2+1}{x-1}$ is undefined.

Given information:

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

Calculation:

  $\begin{array}{l}\underset{x\to 1}{{\displaystyle \lim }}\frac{x^2+1}{x-1}\\ \underset{x\to 1^{-}}{{\displaystyle \lim }}\ne \underset{x\to 1^{+}}{{\displaystyle \lim }}\end{array}$

Therefore, the limit is undefined.