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