The three conditions which must hold true for a limit to exist
What are the limit from the left must exist, the limit from the right must exist, and both sides must be equal?
100
d/dx 4x^5 - x^-2
What is 20x^4 + 2x^-3?
100
On what interval(s) is the function 4x^2 + 9 increasing
What is (0,∞)?
100
Antiderviative of 6x^2 + 4
What is 2x^3 + 4x?
100
These two men invented calculus.
Who are Leibniz and Newton?
200
lim as x approaches 3 for the function
4x^3 - 5x^2 + 17
What is 80?
200
d/dx (6x^2)(sin(x))
What is 12xsin(x) + 6x^2cos(x)?
200
This point is where the graph of a function changes concavity.
What is a point of inflection?
200
The integral changes from positive to negative when you switch these numbers.
What are the limits of intergration?
200
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 the intermediate value theorem?
300
This is a special type of limit that can be found by using horizontal asymptotes.
What are infinite limits?
300
d/dx (3x)/ln(x)
What is 3/ln(x) - 3/(ln(x))^2?
300
This point is the lowest point of the graph of the function.
What is the absolute minimum?
300
Antidervative of x^2 + sin(3x)
What is (x^3/3) - (cos(3x)/3)?
300
Antiderivative of e^-3x - csc(x) + cot(x)
What is ln(sin(x)) + ln(csc(x)+cot(x)) - (e^-3x)/3?
400
lim as x approaches 2 for the function
(x^2 + x - 6)/(x - 2)
What is 5?
400
d/dx (6x^3 + 7x)^8
What is 8(6x^3 + 7x)^7 * (18x^2 + 7)?
400
If f'(X) = x^2 + 5x + 6, find all relative extrema.
What is x=-3
400
This rule uses parabolas to approximate the area under a curve.
What is Simpson's Rule?
400
This function has the second derivative of 12e^-x
What is 12e^-x
500
lim as x approaches 0 for the function
(1 - cos(x))/(x)
What is 0?
500
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 (the slope of the tangent line to the graph of the function) is zero.
What is Rolle's Theorem?
500
The second derivative test can be used to find this.
What is relative extrema?
500
Antiderivative of tan(x) + e^2x + 9x
What is ln(sec(x)) + (e^2x)/2 + 9x^2/2?
500
This formula is used for finding the volume of a washer.
What is pi∫(R(x))^2 - (r(x))^2 dx? (integral from a to b)