Term
| Conditions for continuity at a point |
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Definition
Function exists
Limit exists
Limit is equal to function |
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Term
| Conditions where a function is not differentiable |
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Definition
Corners / Cusps
Vertical tangents
Discontinuities |
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Term
| Definition of a corner or cusp |
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Definition
| Slope from left does not equal slope from right |
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Term
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Definition
(First)*(derivative of second)+(second)*(derivative of first)
or
uv'+vu' |
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Term
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Definition
| (bottom)(derivative of top) - (top)(derivative of bottom) all over (bottom)2 |
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Term
| Intermediate value theorem -- functions |
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Definition
if f(x) is continuous on (a,b)
Then f(x) will pass through every value between f(a) and f(b) at least once on the interval (a,b) |
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Term
| Intermediate value theorem -- derivatives |
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Definition
if f(x) is differentiable on (a,b)
then f'(x) takes every value between f'(a) and f(b) at least once on the interval (a,b) |
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Term
| If it's differentiable... |
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Definition
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