CalcNotes0201-page15

CalcNotes0201-page15 - , on which the h function is defined...

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(Section 2.1: An Introduction to Limits) 2.1.14 Suggested solution lim x ± 3 hx () = lim x ± 3 x + 3 () = 3 + 3 = 6 Why is the suggested solution appropriate? We only care about the behavior of the h function in the “immediate vicinity” of x = 3 , excluding x = 3 , itself. The function rule hx () = x + 3 applies to the values of x that are in the “immediate vicinity” of x = 3 , excluding x = 3 , itself. More precisely, we can find an open interval containing 3, say 2.9, 3.1 () or even the entirety of
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Unformatted text preview: , on which the h function is defined using the function rule h x ( ) = x + 3 , except at x = 3 , itself. Therefore, h x ( ) = x + 3 is the only rule that is relevant when we consider approaching x = 3 from the left or from the right. As a consequence, either lim x 3 h x ( ) = lim x 3 x + 3 ( ) , or neither limit exists. We know lim x 3 x + 3 ( ) = 6 , so we can conclude that lim x 3 h x ( ) = 6....
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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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