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A Function Is Continuous When...
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Intermediate Value Theorem
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BC Calc - Unit 1

QuestionAnswer
A Function Is Continuous When... f(c) exists, limit as x->c exists, limit as x->c = f(c)
Intermediate Value Theorem if f(x) is continuous on the interval [a,b] with f(a)≠f(b), then if d is any number between f(a) and f(b), there is a least one c between a and b such a that f(c)=d
Extreme Value Theorem if f(x) is continuous on the interval [a,b], then f(x) has both an absolute maximum and absolute minimum value on {a,b}
Infinite Limit also known as a vertical asymptote, it's a limit that when evaluated, is increasing without bound to +∞ or decreasing without a bound to -∞
Limit At Infinity a limit where x is approaching +∞ or -∞
Horizontal Asymptote Rules top heavy = none, bottom heavy = 0, equal = coefficient/coefficient
A Jump Discontinuity Occurs When... the limit from the right does not equal the limit from the left (non-removable)
A Point Discontinuity Occurs When... limit f(x) does not equal f(x) (removable)
Special Trig Limits sin(0) / 0 = 1
The Squeeze Theorem if h(x)≤f(x)≤g(x) for all x in an open interval containing c, except possibly c itself, and if limit x->c h(x) = L = limit x->c g(x), then limit x->c f(x) exists and is equal to L
Limit a limit is what happens near a point, not at a point
Created by: abievans
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