Limits
Derivatives
f/f'/f''
Theorems
Integrals
100
limit of x^2 as x approaches 10
What is 100?
100
d/dx of e^2
What is 0?
100
As a particle moves left, its direction is considered to be moving this direction
What is negative?
100
if a function is continuous on [a, b], and if y is any number between f(a) and f(b), then there must be a value, x = c, where a < c < b, such that f(c) = y
What is the Intermediate Value Theorem (IVT)?
100
Integral of x^2 dx
What is 1/3 x^3 + C?
200
limit of ln(x) as x approaches 0 from the positive direction
What is negative infinity?
200
d/dx of ln(x)
What is 1/x?
200
The absolute value of the derivative of position
What is speed?
200
If f is differentiable for all values of x in [a,b] and f is continuous and differentiable on (a,b), then there exists at least one value x=c in (a, b) such that f'(c) = (f(b) - f(a)) / b-a
What is the Mean Value Theorem(MVT)?
200
Integral from 0 to 2 of 4x^3 + 8x^2 + 2 dx
What is 124/3?
300
What is l'hopital's rule?
300
d/dx of cot(x)
What is -1/(1+x^2)?
300
Speed is this when velocity is increasing and acceleration is decreasing
What is decreasing?
300
If a function is continuous on a closed interval [a,b], then the function contains a maximum and a minimum value on that interval.
What is the Extreme Value Theorem(EVT)?
300
∫u v dx = u∫v dx −∫u' (∫v dx) dx
What is integration by parts?
400
limit of [x^2 - 1]/[x+1] as x approaches -1
What is -2?
400
d/dx of sin(x)/cos(x)
What is sec^2(x)?
400
The second integral at this value equaling 0 indicates the possibility of this
What is a critical point?
400
If f is continuous on a closed interval [a,b] then
What is the First Fundemental Theorem of Calculus?
400
Integral from 0 to π of sec^2(x) dx
What is 0?
500
f'(x) = lim h->0 of [f(x+h) - f(x)]/h
What is the definition of a derivative?
500
d/dx of sin(2x)*cos(x)
2cos(x)cos(2x) - sin(x)sin(2x)
500
The tangent line to the graph at this point lies below the graph to the right, indicating this graph is this at the section.
What is concave up?
500
What is the Second Fundamental Theorem of Calculus?
500
Integral of sec(x)tan(x) - cot^2(x) dx
What is sec(x) + cot(x) + C?