Nonexistence of limits Use the Two-Path Test

Chapter 9, Problem 30E

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QUESTION:

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

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

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QUESTION:

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

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

ANSWER:

Step 1 of 2

A function is said to be continuous at a point of its domain, it the right hand limit and the left hand limit at that point coincide with the functional value at that point.

 

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