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Show that the limit below does not exist. Note that the function is not continuous at (0, 0), so we cannot simply evaluate the limit by plugging in (0, 0). Instead, approach (0,0) from two different paths. First try approaching along the x-axis (when y = 0), and then try approaching along the line y = x. What can you conclude about this limit? x²y² lim (x,y) (0,0) x4 + 3y4

Show that the limit below does not exist. Note that the function is not continuous at (0, 0), so we cannot simply evaluate the limit by plugging in (0, 0). Instead, approach (0,0) from two different paths. First try approaching along the x-axis (when y = 0), and then try approaching along the line y = x. What can you conclude about this limit? x²y² lim (x,y) (0,0) x4 + 3y4

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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Show that the limit below does not exist. Note that the function is not continuous at (0, 0), so we cannot simply evaluate the limit by plugging in (0, 0). Instead, approach (0,0) from two different paths. First try approaching along the x-axis (when y = 0), and then try approaching along the line y = x. What can you conclude about this limit? x²y² lim (x,y) (0,0) x4 + 3y4
Transcribed Image Text:Show that the limit below does not exist. Note that the function is not continuous at (0, 0), so we cannot simply evaluate the limit by plugging in (0, 0). Instead, approach (0,0) from two different paths. First try approaching along the x-axis (when y = 0), and then try approaching along the line y = x. What can you conclude about this limit? x²y² lim (x,y) (0,0) x4 + 3y4
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