Homework Help is Here – Start Your Trial Now!
Math
Calculus
3. Determine the domain of the following function, then sketch it: 1 f(x, y) = V² + y? – 9

3. Determine the domain of the following function, then sketch it: 1 f(x, y) = V² + y? – 9

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
**Question 3:** Determine the domain of the following function, then sketch it: \[ f(x, y) = \frac{1}{\sqrt{x^2 + y^2 - 9}} \] **Explanation:** The function \( f(x, y) \) is defined as \( \frac{1}{\sqrt{x^2 + y^2 - 9}} \). The domain of this function is determined by the values of \( (x, y) \) for which the expression inside the square root is positive, since the square root and division by zero are undefined for non-positive numbers. Thus, for \( f(x, y) \) to be defined, the condition is: \[ x^2 + y^2 - 9 > 0 \] This implies: \[ x^2 + y^2 > 9 \] The domain includes all points \((x, y)\) that are outside the circle defined by the equation \( x^2 + y^2 = 9 \), which is a circle with radius 3, centered at the origin \((0,0)\).
Transcribed Image Text:**Question 3:** Determine the domain of the following function, then sketch it: \[ f(x, y) = \frac{1}{\sqrt{x^2 + y^2 - 9}} \] **Explanation:** The function \( f(x, y) \) is defined as \( \frac{1}{\sqrt{x^2 + y^2 - 9}} \). The domain of this function is determined by the values of \( (x, y) \) for which the expression inside the square root is positive, since the square root and division by zero are undefined for non-positive numbers. Thus, for \( f(x, y) \) to be defined, the condition is: \[ x^2 + y^2 - 9 > 0 \] This implies: \[ x^2 + y^2 > 9 \] The domain includes all points \((x, y)\) that are outside the circle defined by the equation \( x^2 + y^2 = 9 \), which is a circle with radius 3, centered at the origin \((0,0)\).
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
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
SEE MORE TEXTBOOKS