Q. 44 - Calculus

Question

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

$\underset{x\to 5}{\lim }\frac{x-5}{x^2-25}$

Step-by-Step Solution

Answer

The value of $\underset{x\to 5}{\lim }\frac{x-5}{x^2-25}$ is $0.1$ .

Step 1. Given information.

The given function is $\underset{x\to 5}{\lim }\frac{x-5}{x^2-25}$.

Step 2. Value of the limit.

Consider the table,

$x$	$4.9$	$4.99$	$4.999$	$5$	$5.001$	$5.01$	$5.1$
$\frac{x-5}{x^2-25}$	$0.101$	$0.1001$	$0.10001$	-	$0.0999$	$0.0999$	$0.099$

Hence, the value approaches to $0.1$ to the left and right.

Therefore,

$\underset{x\to 5}{\lim }\frac{x-5}{x^2-25}=0.1\text{ or }\frac{1}{10}$.