Q.48 - Calculus

Question

Calculate each limit in Exercises 35–80. 

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

Step-by-Step Solution

Answer

The limit does not exist.

Step 1. Given Information:

Given expression: $\underset{x\to 1}{\lim } \frac{x-1}{x^2-2x+1}$

We want to find limit of given expression.

Step 2. Solution:

Make factor of denominator and simplify we get:

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

Now take limit we get

$\underset{x\to 1}{\lim } \frac{1}{x-1}=\frac{1}{1-1}=\frac{1}{0}$

We obtain indermine form solime does not exist.