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

Chapter 9, Problem 27E

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QUESTION:

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

\(\lim _{(x, y) \rightarrow(0,0)} \frac{y^{4}-2 x^{2}}{y^{4}+x^{2}}\)

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QUESTION:

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

\(\lim _{(x, y) \rightarrow(0,0)} \frac{y^{4}-2 x^{2}}{y^{4}+x^{2}}\)

ANSWER:

Step 1 of 2

Consider the limit,

.

Assume .

The domain of the function is , therefore the limit is at a boundary point outside the domain.

Approach the originalong two paths the linesand.

 

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