Proof of Limit Law 3 Use the formal definition of a limit

Chapter 9, Problem 71AE

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QUESTION:

Proof of Limit Law 3  Use the formal definition of a limit to prove that \(\lim _{(x, y) \rightarrow(a b)}[c f(x, y)]=c \lim _{(x, y) \rightarrow(a, b)} f(x, y)\).

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QUESTION:

Proof of Limit Law 3  Use the formal definition of a limit to prove that \(\lim _{(x, y) \rightarrow(a b)}[c f(x, y)]=c \lim _{(x, y) \rightarrow(a, b)} f(x, y)\).

ANSWER:

Solution 71AE
Step 1 of 3:

We have to prove that

We know that limit property

So finally we need to prove that

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