Chapter 4: Q. 47 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$T (x) = \frac{x^{3}}{x^{4} - 1}$

Short Answer

Expert verified

$y = 0$ is the horizontal asymptote for given rational expression.

Step by step solution

Step 1. Given information

Given rational expression:

$T (x) = \frac{x^{3}}{x^{4} - 1}$

Step 2. Write the concept

If $n < m$ (the degree of the numerator is less than the degree of the denominator), then R is a proper rational

function, and the graph of R will have the horizontal asymptote y = 0 (the x-axis).

Step 3. Calculation

Here, $n = 3, m = 4$

Now,

$c o n s i d e r P (x) = \frac{x^{3}}{x^{4} - 1} = l i m_{x \to \infty} \frac{x^{3}}{x^{4} (1 - \frac{1}{x^{4}})} = 0$

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.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$T (x) = \frac{x^{3}}{x^{4} - 1}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Discrete Mathematics

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.T(x)=x3x4-1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Discrete Mathematics

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$T (x) = \frac{x^{3}}{x^{4} - 1}$