suplecture1 - Supplemental Lecture 1 Continuity and Limits...

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Unformatted text preview: Supplemental Lecture 1 Continuity and Limits I - 2 Functions • Let X and Y be sets, and let f ⊆ X × Y . – That means that f is a set of ordered pairs ( x , y ) such that x ∈ X and y ∈ Y . • If f also satisfies the property that for all x ∈ X there exists a unique y ∈ Y such that ( x , y ) ∈ f , then f is a function . I - 3 Function Notation • We write f : X → Y . • X is called the domain of f , and Y is called the range of f . • If ( x , y ) ∈ f , then we write y = f ( x ) and y is called the image of x under f . I - 4 The Absolute Value Function • The absolute value function |·| : R → R + = [0, ∞ ) will play an essential role. • For x ∈ R , • Properties of absolute value: a) | xy | = | x || y | b) | |x | - | y || ≤ |x + y | ≤ | x | + | y | (Triangle Inequality) . <- ≥ = x x x x x-1-0.5 0.5 1 0.2 0.4 0.6 0.8 1 I - 5 Definition of Continuity in One Dimension • Let x ∈ D and y = f ( x )....
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.

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suplecture1 - Supplemental Lecture 1 Continuity and Limits...

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