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Limits
Derivatives
Integrals
100
What is the limit as x approaches 0 of 1 over x?
Does Not Exist EK 1.1A3
100
lim ∆x→0 [(f(x+∆x)-f(x))/∆x]
Definition of a Derivative EK 2.1A1
100
A function F(x) is the antiderivative of a function f(x) if for all x in the domain of f, F'(x)=f(x). ∫ f(x)dx = F(x)+C, where C is a constant.
Indefinite Integrals EK 3.2C1
200
What is the limit as x approaches 0 of 2sinx/(4tanx)?
1/2 EK 1.1B1
200
[g(x)f'(x)-f(x)g'(x)]/[g(x)]2 "Low dee high, minus high dee low, all over the square of whats below."
Quotient rule EK 2.1C3
200
∫ sec^2 x dx
tan x + c EK 3.3B3
300
*DOUBLE JEOPARDY* A function is continuous on the interval [a,b] if there does not exist a c in the interval [a,b] such that:
f(c) is undefined, or the limit from the left of c does not equal the limit from the right, or the limit as x approaches c of f(x) does not equal f(c) Ek 1.2A1
300
d/dx [f(x)g(x)] (Product Rule)
f(x)g'(x)+g(x)f'(x) EK 2.1C3
300
∫ (sin x)dx
-(cos x) + C EK 3.3B4
400
If f(x) is continuous on [a,b], there exists a point "c" between a and b such that f(a) ≤ c ≤ f(b) (what is this?)
IVT (Intermediate Value Theorem) EK 1.1A1
400
If f"(x)>0 for a
The graph of f is concave upward on the interval a
400
If f is continuous on [a,b] and if F' = f, then (a,b)∫ f(x)dx = F(b) - F(a) (what is this?)
The Fundamental Theorem of Calculus EK 3.3A3