Chapter 1: Q. 44 (page 88)

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 5} \frac{x - 5}{x^{2} - 25}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

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

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,

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

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Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 5} \frac{x - 5}{x^{2} - 25}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the limit.

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Use tables of values to make educated guesses for each of the limits in Exercises 39–52.limx→5x-5x2-25

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the limit.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 5} \frac{x - 5}{x^{2} - 25}$