Explain why f(x, y) must approach a unique number L as (x,

Chapter 9, Problem 2E

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QUESTION:

Explain why f(x, y) must approach L as (x, y) approaches (a, b) along all paths in the domain in order for \(\lim _{(x, y) \rightarrow(a, b)} f(x, y)\) to exist.

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QUESTION:

Explain why f(x, y) must approach L as (x, y) approaches (a, b) along all paths in the domain in order for \(\lim _{(x, y) \rightarrow(a, b)} f(x, y)\) to exist.

ANSWER:

Solution 2E

Step 1:

Given that

f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths in the domain in order for  to exits.

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