CalcNotes0208-page3

CalcNotes0208-page3 - a f x ( ) exists, but 2) f is still...

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(Section 2.8: Continuity) 2.8.3 PART C: CLASSIFYING DISCONTINUITIES We will now consider cases where a function f is discontinuous at a , even though it is defined on an open interval containing a , possibly excluding a itself. We will define removable, jump, and infinite discontinuities. (See Footnote 1 for an example with discontinuities that are none of these.) Removable Discontinuities A function f has a removable discontinuity at a ± 1) lim x ±
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Unformatted text preview: a f x ( ) exists, but 2) f is still discontinuous at a Then, the graph of f has a “hole” at the point a , lim x ± a f x ( ) ( ) . Example 3 (Revisiting Example 9 from Section 2.1) Let g x ( ) = x + 3, x ± 3 ( ) . (Figure 2.8.c) g has a removable discontinuity at 3, because: 1) lim x ± 3 g x ( ) = 6 , but 2) g is still discontinuous at 3; here, g 3 ( ) is undefined. The graph of g has a hole at the point 3, 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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