lim (x,y)→(0,0) x²y (x² + y)²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Directions: Use the Two-Path test to show that the following limits does not exist.
Hint: Use y = x^2
![lim
(x,y) (0,0) (x2 + y)²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa347e917-fa11-4bf5-8fae-5e402bee54cb%2F88349cbf-7ea5-432f-be9e-50f9c97efe62%2Ft0dak6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:lim
(x,y) (0,0) (x2 + y)²
![Theorem (Two-Path Test). Let f be a function defined by z = f(x, y). If f has different.
limits as (x, y) →→ (a, b) along two different paths, then
f(x, y) does not exist.
lim
(x,y)→(a,b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa347e917-fa11-4bf5-8fae-5e402bee54cb%2F88349cbf-7ea5-432f-be9e-50f9c97efe62%2Fqqzvi1t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Theorem (Two-Path Test). Let f be a function defined by z = f(x, y). If f has different.
limits as (x, y) →→ (a, b) along two different paths, then
f(x, y) does not exist.
lim
(x,y)→(a,b)
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