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Unformatted text preview: Math 117, F 09 Review Outline for Second Midterm Deﬁnitions.
increasing/decreasing sequence
monotone sequence
limit of a function at an accumulation point of its domain
continuity of a function at a point of its domain
Symbols.
lim f (x)
x→x0 Theorems. This is a list of the major theorems (and corollaries, etc.) that we have
developed in the meantime, with phrases labelling them. You don’t need to memorize the
numbers of these theorems, just the statements. The numbers are just listed here to help
you ﬁnd things in the book.
(1.16) convergence of monotone sequences
(1.17) testing for accumulation points using sequences
(2.1) testing for limits of functions using sequences
(2.3) some boundedness for a function that has a limit
(2.4) limits for sums, products, and quotients of functions
(2.5) limits for functions related by inequalities
(2.6) limits for bounded functions multiplied by functions with limit zero
(no number) automatic continuity for a function at an isolated point of its domain
(3.1) equivalent conditions for a function to be continuous at an accumulation point of
its domain
(3.2) continuity for sums, products, and quotients of functions
(3.3) bounding a continuous function away from zero ...
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 Fall '08
 Akhmedov,A
 Continuity

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