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LimitsOfFunctions10F

# LimitsOfFunctions10F - Limits of Functions Denition of a...

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Limits of Functions Definition of a Function f : D Y Let D and Y be nonempty sets. A rule f that assigns to each member of D a unique member of Y is a function from D to Y . We write the relationship between a member x of D and the member y of Y that f assigns to x as y = f ( x ) . The set D is the domain of f , denoted by D f . The members of Y are the possible values of f . The range of f is defined by range of f := { f ( x ): x D } ⊂ Y . Set-up for rest of Handout f : D f Y is a function with D f R and Y R . x 0 R and a can be x 0 , x + 0 , x - 0 , or ±∞ . L b R := R ∪ {±∞} . Overview Loosely speaking, we say that the limit of y = f ( x ) as x appoaches a is L , and we write lim x a f ( x ) = L , provided that the value of f ( x ) can be made as close to L as we wish by taking x sufficiently close to, but not equal to , a . We now need to make this concept precise! This is where the topology we learned comes in!! What does it mean to be close ? Well, that it is in a basic neighborhood . Let’s look at some of these (deleted)

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LimitsOfFunctions10F - Limits of Functions Denition of a...

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