Unformatted text preview: say that f is continuous at a if . That is, if: for every ϵ > 0, there is a δ > 0 (that depends on f, a, and ϵ ) such that f(x)  f(a) < ϵ whenever x satisfies x – a < δ . Pg 15 Theorem 1.18  Let f be a realvalued function defined in some neighborhood of a ϵ R. Then, the following are equivalent: (i) f is continuous at a (by the ϵδ definition); (ii) whenever ; (iii) converges (to something) whenever . (iv) f(a) and f(a+) both exist, and both are equal to f(a). Pg 15 Rightcontinuous at a – if f(a+) exists and equals f(a); Jump Discontinuity at a – if f(a) and f(a+) both exist but at least one is different from f(a)....
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This note was uploaded on 11/10/2011 for the course MATH 511 taught by Professor Higdon during the Spring '11 term at Oregon State.
 Spring '11
 Higdon
 Continuity, Limits

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