Chapter 1: Q. 45 (page 88)

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 2} \frac{3}{4 - 2^{x}}$

Short Answer

Expert verified

The value of the limit does not exist.

Step by step solution

Step 1. Given information.

The given function is $\lim_{x \to 2} \frac{3}{4 - 2^{x}}$

Step 2. Value of the limit.

Consider the table,

$x$	$1.9$	$1.99$	$1.999$	$2$	$2.001$	$2.01$	$2.1$
$\frac{3}{4 - 2^{x}}$	$11.199$	role="math" localid="1648522675095" $108.57$	role="math" localid="1648522644841" $1082.39$		$- 1081.64$	$- 107.82$	$- 10.44$

The value of $\frac{3}{4 - 2^{x}}$ approaches to $\infty, - \infty$ to the left and right respectively.

Therefore, the limit does not exist.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 2} \frac{3}{4 - 2^{x}}$

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

Geometry

Pure Maths

Probability and Statistics

Applied Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.limx→234-2x

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

Geometry

Pure Maths

Probability and Statistics

Applied Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 2} \frac{3}{4 - 2^{x}}$