Solved: Nonexistence of limits Show that lim does not

Chapter 9, Problem 62AE

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QUESTION:

Nonexistence of limits  Show that \(\lim _{(x, y) \rightarrow(0.0)} \frac{a x^{2(p-n)} y^{n}}{b x^{2 p}+c y^{p}}\) does not exist when a, b, and c are nonzero real numbers and n and p are positive integers with \(p \geq n\).

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QUESTION:

Nonexistence of limits  Show that \(\lim _{(x, y) \rightarrow(0.0)} \frac{a x^{2(p-n)} y^{n}}{b x^{2 p}+c y^{p}}\) does not exist when a, b, and c are nonzero real numbers and n and p are positive integers with \(p \geq n\).

ANSWER:

Solution 62AE

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