Chapter 14.1, Problem 45AYU

In Problems 43-48, use a graphing utility to find the indicated limit rounded to two decimal places.

$\underset{x\to 2}{\lim }\frac{x^3-\text{ 2}{x}^2+\text{ 4}x-8}{x^2+x-6}$

To determine

To find: The indicated limit rounded to two decimal places by using graphing utility.

Answer to Problem 45AYU

Solution:

$1.6$

Explanation of Solution

Given:

$\underset{x \to 2}{\text{lim}}\frac{x^2 - 2x^2 + 4x - 8}{x^2 + x - 6}$

$x$	$\underset{x \to 1}{\text{lim}}\frac{x^3 - 2x^2 + 4x - 8}{x^2 + x - 6}$
$1.999$	$1.6$
$1.99$	$1.6$
$2.01$	$1.6$
$2.001$	$1.6$

$\underset{x \to 2}{\text{lim}}\frac{x^3 - 2x^2 + 4x - 8}{x^2 + x - 6} = 1.6$