CalcNotes0208-page4

CalcNotes0208-page4 - The idea is that, in principle, a...

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(Section 2.8: Continuity) 2.8.4 Example 4 (Revisiting Example 10 from Section 2.1) Let hx () = x + 3, x ± 3 7, x = 3 ² ³ ´ (Figure 2.8.d) h has a removable discontinuity at 3, because: 1) lim x ± 3 hx () = 6 , but 2) h is still discontinuous at 3; here, lim x ± 3 hx () ² h 3 () , because h 3 () = 7 . The graph of h also has a hole at the point 3, 6 () . Why are these discontinuities called removable? The term “removable” is a bit of a misnomer here, since we have no business changing the function at hand.
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Unformatted text preview: The idea is that, in principle, a removable discontinuity at a can be removed by defining (or redefining) the function appropriately at a ; then, the modified function will be continuous at a . For example, if we were to define g 3 ( ) = 6 in Example 3 and redefine h 3 ( ) = 6 in Example 4, then we would remove the discontinuity at 3 in both situations. We would obtain this graph: (Figure 2.8.e)...
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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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