Differentials
Integrals
Calculus
Tie-Breaker
100
f'(x)g(x)+f(x)g'(x)
What is Product Rule
100
Method used for approximating the total area underneath a curve on a graph
What is Riemann Sum
100
Used to find the slope (or rate of change) of a function at a certain point
What is the derivative
100
Best AP Calculus teacher anyone could ever have
Who is Ms. Monegan
200
[f'(x)g(x)-f(x)g'(x)]/[g(x)]^2
What is Quotient Rule
200
(integral)[cos(x)dx]=
What is sin(x)+C
200
This is a criterion for determining whether a given critical point of a real function of one variable is a local maximum or a local minimum using the value of the second derivative at the point
What is the Second Derivative Test
300
This theorem states that a function f is continuous on the closed interval [a, b], where a is less than b, and differentiable on the open interval (a, b), then there exists a point c in (a,b) such that f'(c)=[f(b)-f(a)]/[b-a]
What is Mean Value Theorem
300
(int)[sec^2(x)dx]=
What is tan(x)+C
300
This theorem states that, if f is continuous on the closed interval [a,b] and F is the indefinite integral of f on [a,b], then (integral)[f(x)dx)=F(b)-F(a)
What is the First Fundamental Theorem of Calculus
400
This theorem states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero
What is Rolle's Theorem
400
Method used to calculate the volume of a solid of revolution that is hollow about the x-axis (has a hole)
What is Washer Method
400
[u']/[1+u^2]
What is (d/dx)[arctan(u)]
500
This theorem states that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is at least one point in its domain that the function maps to that value
What is Intermediate Value Theorem
500
(int)[sec(x)dx]=
What is ln|sec(x)+tan(x)|+C
500
If f is continuous on [a,b] then (d/dx)*(integral from a to x)[f(t)dt]=f(x)
What is the Second Fundamental Theorem of Calculus
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