Solution Found!
Answer: Nonexistence of limits Use the Two-Path Test to
Chapter 9, Problem 27E(choose chapter or problem)
QUESTION:
Nonexistence of limits Use the Two-Path Test to prove that the following limits do not exist.
\(\lim _{(x, y) \rightarrow(0,0)} \frac{y^{4}-2 x^{2}}{y^{4}+x^{2}}\)
Questions & Answers
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.