Chapter 6: Q. 2 (page 418)

True or False If $x = 3$ is a vertical asymptote of a rational function $R$ , then localid="1646480330211" $\lim_{x \to 3} |R (x)| = \infty$ .

Short Answer

Expert verified

The statement is true.

Step by step solution

Step 1. Concept Used

It is known that as $x$ approaches some number $c$ , the values of $|R (x)| \to \infty$ , then the line $x = c$ is a vertical asymptote of the graph of $R$ .

Step 2. Check whether the statement is true

The notation $\lim_{x \to 3} |R (x)| = \infty$ can be read as $x$ tends to $3$ the value of $R (x)$ tends to $\infty$ .

So using the above information it can be said that the line $x = 3$ is a vertical asymptote of the rational function $R$ .

So the given statement is true.

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.

True or False If $x = 3$ is a vertical asymptote of a rational function $R$ , then localid="1646480330211" $\lim_{x \to 3} |R (x)| = \infty$ .

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Check whether the statement is true

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

True or False If x=3is a vertical asymptote of a rational function R, then localid="1646480330211" limx→3R(x)=∞.

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Check whether the statement is true

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

True or False If $x = 3$ is a vertical asymptote of a rational function $R$ , then localid="1646480330211" $\lim_{x \to 3} |R (x)| = \infty$ .