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Derivatives
Formulas/Theorems
Integrals
Rules
Limits
100
The derivative of y = 3x^2 + 4x - 7
What is 6x + 4 ?
100
The formula for finding the volume of a right circular cylinder.
What is (PI) r^2 h
100
It is the result when you get when you integrate 1 dx
What is x + C ?
100

fg' + f'g

What is the product rule ?

100
The limit as x approaches infinity of 1/x
What is 0 ?
200
The derivative of f(x) = cos x
What is -sin x ?
200

What's the area of an equilateral triangle?

A = sqrt(3)/4 * s^2

200
It is the result when you get when you integrate e^x dx
What is e^x + C ?
200

(gf' - fg')/g^2

What is the quotient rule?

200
The limit as x approaches 0 of (cos x - 1) / x
What is 0 ?
300
The derivative of y = sec x
What is sec x tan x ?
300

if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].

What is the Mean Value Theorem?

300
It is the result when you get when you integrate 1/x dx
What is ln |x| + C ?
300

f'(g(x)) * g'(x)

What is the chain rule?

300
The limit as x approaches 0 of (sin x) / x
What is 1 ?
400
The derivative of f(x) = a^x
What is (ln a) a^x ?
400

The definite integral (from a to b) gives us the area under the curve between x=a and x=b.

What is the Fundamental Theorem of Calculus?
400
It is the result when you get when you integrate sec^2 x dx
What is tan x + C ?
400
The rule that we use for limits if we get 0/0 or infinity/infinity

What is L'hospital's rule?

400
The limit as h approaches 0 of (e^h - 1) / h
What is 1 ?
500
The derivative of f(x) = arctan x
What is 1 / (1 + x^2) ?
500

If a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval.

What is the Extreme Value Theorem?

500

It is the result when you get when you integrate 4x*SQRT(16-x^2)dx

What is -4/3 (16-x^2)^3/2 + C?

500

We use this when we need to integrate with chain rule.

What is u-substitution?

500
The limit as x approaches infinity of (1 + (1/x))^x
What is e ?