7x2 – 3y2 EXAMPLE 1 Show that lim does not exist. (x, Y)- (0, 0) x2 + y2 SOLUTION Let f(x, y) = (7x2 – 3y2)/(x² + y2). First, let's approach (0, 0) along the x-axis. Then y = gives f(x, 0) = 7x²/x² = for all x + 0, so f(x, y) - as (x, y) – (0, 0) along the x-axis. We now approach along the y-axis by putting x = f(0, y) = -3y2/y? =| Then for all y + 0, so f(x, y) → as (x, y) – (0, 0) along the y-axis. Since f has two different limits along two different lines, the given limit does not exist.
7x2 – 3y2 EXAMPLE 1 Show that lim does not exist. (x, Y)- (0, 0) x2 + y2 SOLUTION Let f(x, y) = (7x2 – 3y2)/(x² + y2). First, let's approach (0, 0) along the x-axis. Then y = gives f(x, 0) = 7x²/x² = for all x + 0, so f(x, y) - as (x, y) – (0, 0) along the x-axis. We now approach along the y-axis by putting x = f(0, y) = -3y2/y? =| Then for all y + 0, so f(x, y) → as (x, y) – (0, 0) along the y-axis. Since f has two different limits along two different lines, the given limit does not exist.
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...
Related questions
Question
![7x2 – 3y2
EXAMPLE 1 Show that
lim
does not exist.
(x, Y)- (0, 0) x2 + y2
SOLUTION Let f(x, y) = (7x² – 3y2)/(x² + y2). First, let's approach (0, 0) along the
x-axis. Then y =
gives f(x, 0) = 7x²/x² =
for all x + 0, so
f(x, y) →
as (x, y) – (0, 0) along the x-axis.
We now approach along the y-axis by putting x =
f(0, y) = -3y2/y? =|
Then
for all y + 0, so
f(x, y) →
as (x, y) → (0, 0) along the y-axis.
Since f has two different limits along two different lines, the given limit does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11116739-cb46-40a0-8159-7a3629791d30%2Fb6ee2df8-76a6-43a2-8725-a17d8c8197aa%2Fzgl36wq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7x2 – 3y2
EXAMPLE 1 Show that
lim
does not exist.
(x, Y)- (0, 0) x2 + y2
SOLUTION Let f(x, y) = (7x² – 3y2)/(x² + y2). First, let's approach (0, 0) along the
x-axis. Then y =
gives f(x, 0) = 7x²/x² =
for all x + 0, so
f(x, y) →
as (x, y) – (0, 0) along the x-axis.
We now approach along the y-axis by putting x =
f(0, y) = -3y2/y? =|
Then
for all y + 0, so
f(x, y) →
as (x, y) → (0, 0) along the y-axis.
Since f has two different limits along two different lines, the given limit does not exist.
![7x2 – 3y2
EXAMPLE 1 Show that
lim
does not exist.
(x, Y)- (0, 0) x2 + y2
SOLUTION Let f(x, y) = (7x² – 3y2)/(x² + y2). First, let's approach (0, 0) along the
x-axis. Then y =
gives f(x, 0) = 7x²/x² =
for all x + 0, so
f(x, y) →
as (x, y) – (0, 0) along the x-axis.
We now approach along the y-axis by putting x =
f(0, y) = -3y2/y? =|
Then
for all y + 0, so
f(x, y) →
as (x, y) → (0, 0) along the y-axis.
Since f has two different limits along two different lines, the given limit does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11116739-cb46-40a0-8159-7a3629791d30%2Fb6ee2df8-76a6-43a2-8725-a17d8c8197aa%2F17ek0o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7x2 – 3y2
EXAMPLE 1 Show that
lim
does not exist.
(x, Y)- (0, 0) x2 + y2
SOLUTION Let f(x, y) = (7x² – 3y2)/(x² + y2). First, let's approach (0, 0) along the
x-axis. Then y =
gives f(x, 0) = 7x²/x² =
for all x + 0, so
f(x, y) →
as (x, y) – (0, 0) along the x-axis.
We now approach along the y-axis by putting x =
f(0, y) = -3y2/y? =|
Then
for all y + 0, so
f(x, y) →
as (x, y) → (0, 0) along the y-axis.
Since f has two different limits along two different lines, the given limit does not exist.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning