Q. 43 - Calculus

Question

Use tables of values to make educated guesses for each of the limits in Exercises 39–52. 

$\underset{x\to 3}{\lim }\frac{x-3}{\left(x^2-2\right)(x-3)}$

Step-by-Step Solution

Answer

The value is $0.413 .$

Step 1. Given information.

The given function is $\underset{x\to 3}{\lim }\frac{x-3}{\left(x^2-2\right)(x-3)}.$

Step 2. Table of values.

Consider the table,

$x$	$2.9$	$2.99$	$2.999$	$3$	$3.001$	$3.01$	$3.1$
$\frac{x-3}{\left(x^2-2\right)(x-3)}$	$0.156$	$0.144$	$0.143$	*	$0.143$	$0.143$	$0.131$

The value of $\frac{x-3}{\left(x^2-2\right)(x-3)}$ approaches to $0.143$ to the left and right.

Therefore, $\underset{x\to 3}{\lim }\frac{x-3}{\left(x^2-2\right)(x-3)}=0.143$