Solved: Limit proof Use the formal definition of a limit

Chapter 9, Problem 68AE

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QUESTION:

Limit proof  Use the formal definition of a limit to prove that \(\lim _{(x, y) \rightarrow(a, b)} y=b\) (Hint: Take \(\delta=\varepsilon\).)

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QUESTION:

Limit proof  Use the formal definition of a limit to prove that \(\lim _{(x, y) \rightarrow(a, b)} y=b\) (Hint: Take \(\delta=\varepsilon\).)

ANSWER:

Solution 68AE

Step 1: 

Limit proof  Use the formal definition of a limit to prove that

 (Hint: Take δ = ℇ.)

Definition:  Let us  consider the function with two variables f(x,y)=L there must be function ,call ( such that the all >0

| f(x,y)- L| <

 |(x,y)-(a,b)| <( 

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