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lim (x,y)→(0,0) x²y (x² + y)²

lim (x,y)→(0,0) x²y (x² + y)²

Advanced Engineering Mathematics
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
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)
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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