Solved: Nonexistence of limits Use the Two-Path Test to

Chapter 9, Problem 25E

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QUESTION:

Nonexistence of limits  Use the Two-Path Test to prove that the following limits do not exist.

\(\lim _{(x, y) \rightarrow(0,0)} \frac{x+2 y}{x-2 y}\)

                                       

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QUESTION:

Nonexistence of limits  Use the Two-Path Test to prove that the following limits do not exist.

\(\lim _{(x, y) \rightarrow(0,0)} \frac{x+2 y}{x-2 y}\)

                                       

ANSWER:

Solution 25E

Step 1 :

Given function is

Along the path    x  = 0

       =        

                                           =              

                                           =              

                                           =            -1

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