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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Question
![**Find the limit:**
\[ \lim_{{(x, y) \to (3, 3)}} \frac{4x^4 - 4y^4}{x^2 - y^2} = \]
**Explanation:**
This equation asks for the limit of the function \(\frac{4x^4 - 4y^4}{x^2 - y^2}\) as the point \((x, y)\) approaches \((3, 3)\).
In more detail:
1. **Numerator**: The numerator is \(4x^4 - 4y^4\).
2. **Denominator**: The denominator is \(x^2 - y^2\).
3. We need to find what value this function approaches as \(x\) and \(y\) both get closer to 3.
To solve this, you may need to consider techniques such as factoring, simplifying, or using limit properties and rules.
**Graph Explanation:**
There is no graph or diagram associated with this particular equation. The information provided is purely textual and mathematical in nature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74b6836e-7075-4604-8b7e-b1441272473c%2Fc6d4835c-a555-41f1-8f64-1792baabf5e6%2F7if6rch_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the limit:**
\[ \lim_{{(x, y) \to (3, 3)}} \frac{4x^4 - 4y^4}{x^2 - y^2} = \]
**Explanation:**
This equation asks for the limit of the function \(\frac{4x^4 - 4y^4}{x^2 - y^2}\) as the point \((x, y)\) approaches \((3, 3)\).
In more detail:
1. **Numerator**: The numerator is \(4x^4 - 4y^4\).
2. **Denominator**: The denominator is \(x^2 - y^2\).
3. We need to find what value this function approaches as \(x\) and \(y\) both get closer to 3.
To solve this, you may need to consider techniques such as factoring, simplifying, or using limit properties and rules.
**Graph Explanation:**
There is no graph or diagram associated with this particular equation. The information provided is purely textual and mathematical in nature.
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