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5. Let f(x, y) = 3 xy³ x² + y6 (a) 0 (b) 1 (c) -1 (d) 1/2 (e) Does not exist. Find lim f(x,y). (x,y) →(0,0)

5. Let f(x, y) = 3 xy³ x² + y6 (a) 0 (b) 1 (c) -1 (d) 1/2 (e) Does not exist. Find lim f(x,y). (x,y) →(0,0)

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...
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correct answer is DNE right? please explain

5. Let f(x, y) = 3 xy³ x² + y6 (a) 0 (b) 1 (c) -1 (d) 1/2 (e) Does not exist. Find lim f(x,y). (x,y) →(0,0)
Transcribed Image Text:5. Let f(x, y) = 3 xy³ x² + y6 (a) 0 (b) 1 (c) -1 (d) 1/2 (e) Does not exist. Find lim f(x,y). (x,y) →(0,0)
Expert Solution
Step 1

The point (0,0) can be reached along so many different paths. If each path results in a different limit value then we say the limit do not exist.

For instance the (0,0) can be reached by any straight line of the form y=mx. For different values of m.

If each of these lines given a different limiting value we say limit do not exist.

We can also approach the point (0,0) along any curve not just straight lines.

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