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17 Cards in this Set
- Front
- Back
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EVT
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Given: f cont. on [a,b]
∃ Xsub1, Xsub2 ∈ [a,b] : ∀x ∈ [a,b] f(x) ≤ f(Xsub1) max ^ ∀x ∈ [a,b] f(x) ≥ f(Xsub2) min At least one min and at least one max are attained. |
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IVT
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Given: f cont. on [a,b]
∀y ∈ (f(a),f(b))U(f(b),f(a)) ∃x∈(a,b): f(x)=y Every y-value strictly between the endpoints is attained somewhere in the interior. |
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MVT
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Given: f cont. on [a,b] and f differentiable on (a,b)
∃x∈(a,b): d/dx f(x) = (f(b)-f(a))/(b-a) Somewhere in the interior, tangent slope equals secant slope. |
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FTC1
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Given: f cont. on [a,b]
∫ from a to b of f(t)dt = ∫f(b)db-∫f(a)da We have a formula for finding definite integrals. |
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FTC2
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Given: f cont. on [a,b]
d/dx (accum. fcn.) = f(x), the integrand evaluated at x, where accum. fcn. = ∫ from c to x of f(t)dt where c ∈ [a,b] Every continuous function has an antiderivative. |
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Antiderivative
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indefinite integral
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Initial Conditions
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Some information you use in order to specify a member of a family.
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Accumulator Function
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definite integral where the upper endpoint can vary
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Cardinality
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count
"The cardinality of students in this room is 16" |
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Integrability
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If the lower and upper sums for function f on the interval [a,b] have a common limit as ∆x approaches 0, then f is said to be integrable on [a,b].
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Definite Integral
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The definite integral of a function is the common limit defined by its integrability.
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What is the difference between Science and Math?
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Science (theories) are disprovable
Math (theorems) are provable. |
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General Solution
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A solution that still has 1 or more unknown parameters.
A family of possible relations. |
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Particular Solution
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An exact relation that satisfies a general solution.
A diffeq. + initial conditions. |
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Slope Field
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"Directory" of how family curves are changing.
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Diffeq.
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Differential Equation: any equation that includes 1 or more derivatives.
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Also be able to do FTC1 <=> FTC2 (both) and D=>C proofs!
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Also be able to do FTC1 <=> FTC2 (both) and D=>C proofs!
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