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15 Cards in this Set
- Front
- Back
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First condition for continuity at a point |
Function is defined at that point (function has a value at that point)
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Second condition for continuity at a point |
Limit exists at that point (RHS Limit = LHS Limit) |
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Third condition for continuity at a point |
Limit value = function value |
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Types of Continuity |
Point Discontinuity Jump Discontinuity Infinite Discontinuity Oscillating Discontinuity |
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Removable Discontinuities |
Point Discontinuity |
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Nonremovable discontinuities |
Jump Discontinuity Infinite Discontinuity Oscillating Discontinuity |
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f(x) + g(x) (Properties of cont. fns) |
Will be continuous |
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f(x) - g(x) (Properties of cont. fns) |
Will be continuous |
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f(x) * g(x) (Properties of cont. fns) |
Will be continuous |
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f(x) / g(x) (Properties of cont. fns) |
Will be continuous given g(x) does not = 0 |
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a * f(x) (Properties of cont. fns) |
Will be continuous |
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Two conditions that must be satisfied for Extreme Value Theorem |
i) f(x) must be continuous ii) interval must be closed |
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Extreme Value Theorem |
The function has a maximum and minimum
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Two conditions that must be satisfied for Intermediate Value Theorem (IVT) |
i) f(x) must be continuous ii) interval must be closed |
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Intermediate Value Theorem (IVT) |
If f(a) ≤ M ≤ f(b), then there is at least one point a ≤ c ≤ b so that f(c) = M |
