Chapter 14.2, Problem 29AYU

To determine

To find: The value of limit $\underset{x\to 2}{\lim }\frac{x^2-4}{x^2-2x}$ .

Answer to Problem 29AYU

The value of limit $\underset{x\to 2}{\lim }\frac{x^2-4}{x^2-2x}$ is 2.

Explanation of Solution

Given:

The function is $\underset{x\to 2}{\lim }\frac{x^2-4}{x^2-2x}$ .

Calculation:

Simplify the expression as follows.

  $\begin{array}{c}\underset{x\to 2}{\lim }\frac{x^2-4}{x^2-2x}=\underset{x\to 2}{\lim }\frac{\left(x+2\right)\left(x-2\right)}{x\left(x-2\right)}\\ =\underset{x\to 2}{\lim }\frac{x+2}{x}\\ =\frac{2+2}{2}\\ =2\end{array}$

Hence, the value of limit $\underset{x\to 2}{\lim }\frac{x^2-4}{x^2-2x}$ is 2.