# lecture7 - Lecture 7 Limits(Chapter 2 Sec 1 2 Recall the...

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Lecture 7: Limits (Chapter 2, Sec. 1, 2) Recall the deﬂnition: For a given function f ( x ), we say that lim x ! a f ( x ) = L if we can make the values of f ( x ) as close to L as we want by choosing x suf- ﬂciently close to a on either side but not equal to a . ex. If f ( x ) = x if x 6 = 1 3 if x = 1 , ﬂnd lim x ! 1 f ( x ). 6 - ? ± ex. If g ( x ) = 3 if x 0 ¡ 1 if x > 0 , ﬂnd lim x ! 0 g ( x ). 6 - ? ±

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Def. One-Sided Limits We say that a function f ( x ) : R ! R has limit L as x approaches the number a from the right if we can make every value of f ( x ) as close to L as we want by choosing x su–ciently close to a but x > a . In other words, given a small number ² , we can make the distance j f ( x ) ¡ L j < ² by choosing x > a so that the distance j x ¡ a j is as small as necessary. We write this right-hand limit lim x ! a + f ( x ) = L Similarly, we say that a function f ( x ) : R ! R has limit L as x approaches the number a from the left if we can make every value of f ( x ) as close to L as we want by choosing x su–ciently close to a but x < a .
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## This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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lecture7 - Lecture 7 Limits(Chapter 2 Sec 1 2 Recall the...

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