Find the limit: lim (z,y) → (3,3) 4x4 - 4y¹ x² - y²

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...
icon
Related questions
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.
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.
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning