Differentiation
f'(x) of x2
What is 2x?
The variable that follows an integral
What is C?
This test is used to find concavity of a graph.
What is the Second Derivative Test?
This is the limit of (x-2) as x approaches infinite.
What is ∞?
This uses the derivative of the function to describe the limits.
What is L' Hopital's Rule?
f''(x) of x3 + x2
What is 6x +2?
This the integral of 4x3.
What is x4 + C?
The Fundamental Theorem of Calculus.
What is ∫ab f(x)dx = F(b) - F(a) where F'(x) = f(x)?
This is the limit of (x11-1)/(x4-1) as x approaches 1
This method is used to find the volume under the curve when it is connected to the y and/or x axis.
What is the Disk Method?
This helps find the possible relative max. or min. of the original function.
What is the First Derivative Test?
∫-22 (x3 + 4x)dx
What is 0?
This is what the Intermediate Value Theorem is.
What is if the function f(x) is continous on [a,b], and y is a number between f(a) and f(b), then there exists at least one number x=c in the open interval (a,b) such that f(c)=y?
What is the limit of (x2-2x-3)/(x-3) as x approaches 3
What is zero?
This is the second derivative of distance.
What is acceleration?
f'(x) of (x3 - 2)2
What is 6x2(x3 - 2)?
dy/dx = (√x) * y
What is y= Ce(2/3)x^3/2?
This equation is if f(x) is continuous on [a,b], and the first derivative exists on the interval (a,b), which means there is at least one number x=c in (a,b).
What is f'(c) = [f(b) - f(a)] / (b - a)?
MVT
What is the limit of ((arcsin(x))/x) as x approaches 0.
What is 1?
This method is used to find the volume under two curves when it is not connected to the y and/or x axis.
What is the Washer Method?
f3(x) of -sin(u)cos(u)
What is 4cos2(x)−4sin2(x)
or
−4(sin2(x)−cos2(x))
These are the lengths and widths of a rectangle that give it it's maximum area when bounded by the x-axis and the semi-circle y = √(25-x2).
What are a width of (5√2)/2 and a length of 5√2?
If the function f(x) is continous on [a,b], and the frist derivative exists on the inerval (a,b), and f(a) = f(b), then there is at least one number x=c in (a,b) such that f'(c) = 0.
What is Rolle's Theorem?
What is ∞?
When the limit is to infinity, and the exponents are the same both in the numerator and denominator, this is the part of the function you look at to find the limit.
What are the coefficients?