Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
17 Cards in this Set
- Front
- Back
EVT
|
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. |
|
IVT
|
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. |
|
MVT
|
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. |
|
FTC1
|
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. |
|
FTC2
|
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. |
|
Antiderivative
|
indefinite integral
|
|
Initial Conditions
|
Some information you use in order to specify a member of a family.
|
|
Accumulator Function
|
definite integral where the upper endpoint can vary
|
|
Cardinality
|
count
"The cardinality of students in this room is 16" |
|
Integrability
|
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].
|
|
Definite Integral
|
The definite integral of a function is the common limit defined by its integrability.
|
|
What is the difference between Science and Math?
|
Science (theories) are disprovable
Math (theorems) are provable. |
|
General Solution
|
A solution that still has 1 or more unknown parameters.
A family of possible relations. |
|
Particular Solution
|
An exact relation that satisfies a general solution.
A diffeq. + initial conditions. |
|
Slope Field
|
"Directory" of how family curves are changing.
|
|
Diffeq.
|
Differential Equation: any equation that includes 1 or more derivatives.
|
|
Also be able to do FTC1 <=> FTC2 (both) and D=>C proofs!
|
Also be able to do FTC1 <=> FTC2 (both) and D=>C proofs!
|