Unit 1 Limits

removable discontinuties

holes

nonremovable discontinuities

vertical asymptotes, jump discontinuities

continuity conditions

i. f(c) is defined

ii. the limit of f(x) as x approaches c exists

iii. the limit of f(x) as x approaches c is equal to f(c)

intermediate value theorem

since f(x) is continuous on [a,b], there must be a value c such that f(c) = __, since f(a) ≤ f(c) ≤ f(b)