CalcNotes0207-page3 - (Section 2.7: Precise Definitions of...

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(Section 2.7: Precise Definitions of Limits) 2.7.3 Where Do We Look For Winners? We only care about players that are “close” to x = a (here, x = 4 ). We ignore a itself, and we say in this context that a is not “close” to itself. In particular, we only care about players that are strictly between 0 and ± units of a , where > 0 . Like , the Greek letter (“delta”) often represents a small positive quantity. Here, we can think of as the half-width of a “symmetric punctured interval” that is symmetric about x = a , though we delete a itself as a “puncture.” Symbolically: Player x is "close" to a ± a ² ³ < x < a + x ´ a () Subtract a from all three parts. ± ² < x ² a < x ´ a ± 0 < x ² a < This makes sense, because x ± a represents the distance between Player
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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