Theorems
MVT
The limits from the left, right are equal and also equal to the value of the function
What are the requirements for a function to be continuous at a point
The derivative of 2x
What is ln2*2x
Another name for antiderivative
What is integral?
The formula for the area of an equilateral triangle
What is (root 3)/4 times s2
If a function is continuous over [a,b] and f(a) = m and f(b) = n, then there must be some f(c) such that m<f(c)<n
What is intermediate value theorem?
French guy who invented a rule of how to deal with limits which are indeterminate
Who is L'Hopital?
The volume of a sphere
What is 4/3 pi * r3
This kind of Reimann sum overestimates if a function is decreasing
What is a left Reimann sum?
f(a)+integral from a to b of f'(x)
What is f(b)?
Brendon always eats less than or equal to Pakawat, and Pakawat always eats less than or equal to Kevin. If Brendon ate 10 hamburgers, and Kevin ate 10 hamburgers, how many hamburgers did Pakawat eat? (name of theorem)
What is Squeeze Theorem
Type of discontinuity when the limit as x --> a = number / infinity
What is an vertical asymptote or infinite discontinuity
A 4 sided rectangle (e.g. one of the sides is not a wall or a river) always has the greatest area when it has this shape
What is a square
Trapezoidal sum with 3 or 6 intervals - this is closer to the actual value of a definite integral
What is a trapezoidal sum with 6 intervals?
area bounded by the x-axis, sinx and cos x from 0 to pi/2
What is 0.586
The derivative of the integral from 1 to t2 of sinx
What is sin(t2)2t
Identities are useful. Such as this one:
? = 1/2 + cos(2x)/2
What is cos2(x)
type of problem such as.... a 6 foot ladder is sliding down a wall. The top of the ladder contacting the wall is sliding at a rate of 1 ft per second. What is the speed that the bottom of the ladder is moving away from the wall when the top of the ladder is 4 feet from the ground?
What is related rates
For a question like the antiderivative of:
(3x3 - 2x2 - 8)/ (2x2-4x)
this is what you do first.
What is long division?
Name of the technique to find the volume of revolution when there are two functions
What is washer method
A function is defined for all [a,b]. If a function does not a have minimum value in the interval [a,b], then what? (name of Theorem you would use)
What is extreme value theorem
If you take the limit as x --> infinity of some expression and it equals a number, you are finding this
What is a horizontal asymptote?
A cone's height is twice the diameter. This is the volume of the cone in terms of height.
What is 1/48 pi * h3
integral of 1/(xlnx)
What is ln(lnx)+C
Volume of revolution if the area bounded by y=x2 the x-axis and the line y = 1 is rotated around the line y = -2
What is 17.383, or 83/15 pi