Lect9 - One-Sided Limits Definitions Right-Hand Limit lim f...

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92.131 Lecture 9 1 of 8 Ronald Brent © 2009 All rights reserved. One-Sided Limits Definitions: Right-Hand Limit L x f a x = + ) ( lim means that L x f ) ( as a x from the right. That is a x , and a x > . Left-Hand Limit L x f a x = ) ( lim means that L x f ) ( a s a x from the left. That is a x , and a x < . The ordinary limit exists iff both the left and right hand limits exist and are equal. L x f a x = ) ( lim L x f a x = ) ( lim AND L x f a x = + ) ( lim
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92.131 Lecture 9 2 of 8 Ronald Brent © 2009 All rights reserved. x -2 -1 0 1 2 0 1 2 y 2 3 ) ( lim 1 = x f x and 1 ) ( lim 1 = + x f x Since ) ( lim ) ( lim 1 1 x f x f x x + , we say ) ( lim 1 x f x does not exist.
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92.131 Lecture 9 3 of 8 Ronald Brent © 2009 All rights reserved. x -2 -1 0 1 2 1 2 f ( x ) 2 1 ) ( lim 1 = x f x and 2 1 ) ( lim 1 = + x f x Since 2 1 ) ( lim ) ( lim 1 1 = = + x f x f x x , we say 2 1 ) ( lim 1 = x f x .
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92.131
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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Lect9 - One-Sided Limits Definitions Right-Hand Limit lim f...

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