This theorem says that if f is continuous on [a,b] and differentiable on (a,b), then there exists a number c such that: f'(c)= f(b)-f(a)/b-a
What is Mean Value Theorem
100
d/dx x^3
What is 3x^2
100
The integral of f(x) dx = F(x) +c is the definition of what?
What is Definition of Integrals
100
A= 4/3 pi r^3 is the formula for the area of what geometric figure?
What is sphere
100
This rule can be used to find the limit of a quotient if the form is indeterminate.
What is L'Hopital's Rule
200
This theorem says that the definite integral of a rate of change is the total change in the original function. Also modeled by the integral from a to b of f(x) dx= F(a)- F(b)
What is Fundamental Theorem of Calculus Part 2
200
d/dx sec(x)
What is sec(x) tan(x)
200
f(c)= this equation when finding the average value of a function.
What is 1/b-a times the integral from a to b of f(x) dx
200
Pi times the integral from a to b of [f(x)]^2 dx is the formula for what method of finding the volume of a region?
What is the Disk Method
200
d^2y/dx^2 is another way to express what?
What is second derivative
300
Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)= f(b) then there is at least one number c on (a,b) such that f'(c)=0.
What is Rolle's Theorem
300
These numbers occur where the derivative of a function is zero or undefined.
What is Critical Numbers
300
What method of integration would be easiest to use to solve this problem? Solve the problem.
The integral from 0 to 2 of xe^3x2 dx= ____
What is U-substitution, and 1/6e^12-1/6
300
1/2h (b1+b2) is the formula used to find the area of what shape?
What is trapezoid
300
Name one of the three ways that a function is not differentiable.
What is (1). cusp (2). corner (3). anywhere it is not continuous
400
If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k.
What is Intermediate Value Theorem.
400
If f'(x) changes from negative to positive at c, c is a local __________.
If f'(x) changes from positive to negative at c, c is a local __________.
What is Local minimum and local maximum
400
What is the antiderivative of 1/x?
What is ln x+c
400
This method of finding the volume of a region uses the outer radius squared minus the inner radius squared.
What is Washer Method
400
Name one of the three places that functions are not continuous.
What is (1). Gaps (2). Holes (3). Jumps
500
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occurs at critical points in the interval or at the endpoints of the interval.
What is Extreme Value Theorem.
500
lim as h approaches 0 of f(x+h)-f(x)/h
What is Definition of a Derivative
500
What method of integration is used to find the antiderivative of products?
What is Integration by parts
500
This method of finding the volume of a region can be used when the region is revolved about the y axis without changing the equations if they are in respect to x.