Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Determining Horizontal Asymptotes Using Limits
**Objective:**
Learn how to determine horizontal asymptotes of a given function by computing the appropriate limits.
---
**Example Problem:**
Determine just one horizontal asymptote of \( f(x) \) by computing an appropriate limit.
\[ f(x) = \frac{\sqrt{4x^4 + 9x - 2}}{x^2} \]
### Steps to Determine the Horizontal Asymptote:
1. Identify the highest degree of \( x \) in both the numerator and the denominator.
2. Simplify the function if necessary, focusing on the terms with the highest degree.
3. Compute the limit of \( f(x) \) as \( x \) approaches infinity or negative infinity.
4. The value obtained is the horizontal asymptote.
**Resource:**
- [Bartleby](https://www.bartleby.com)
---
Note: This is a simplified and specific example for educational purposes, illustrating the process of finding horizontal asymptotes using limits. For deeper understanding, practicing with various types of functions and degrees is recommended.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bcaed0f-2f01-4310-ad37-5698e9f2c4bd%2F29cb30f8-4df5-4c99-80a7-a2301c8be244%2Fllrgmwd_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining Horizontal Asymptotes Using Limits
**Objective:**
Learn how to determine horizontal asymptotes of a given function by computing the appropriate limits.
---
**Example Problem:**
Determine just one horizontal asymptote of \( f(x) \) by computing an appropriate limit.
\[ f(x) = \frac{\sqrt{4x^4 + 9x - 2}}{x^2} \]
### Steps to Determine the Horizontal Asymptote:
1. Identify the highest degree of \( x \) in both the numerator and the denominator.
2. Simplify the function if necessary, focusing on the terms with the highest degree.
3. Compute the limit of \( f(x) \) as \( x \) approaches infinity or negative infinity.
4. The value obtained is the horizontal asymptote.
**Resource:**
- [Bartleby](https://www.bartleby.com)
---
Note: This is a simplified and specific example for educational purposes, illustrating the process of finding horizontal asymptotes using limits. For deeper understanding, practicing with various types of functions and degrees is recommended.
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Find the value for f(x) as x tends to inf.
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