Show:
Limits
Derivatives
Integration
Calculus Potpourri
1st and 2nd Derivative Test
100
This function characteristic will cause an infinite limit.
What is asymptote (or vertical asymptote)?
100
If f(x) = cos x, then f '(x) equals this.
What is -sin x?
100
If y=f'(x), then the integral of y equals this.
What is f(x)?
100
The limit as x approaches infinity of y = (3x^2 - 5x)/(2x^2 + 7).
What is 3/2?
100
This indicates that a function is increasing.
What is a positive first derivative value?
200
This type of discontinuity has a limit.
What is removable discontinuity (or hole)?
200
The rule or rules required to find the derivative of y = sin(2x).
What is the chain rule?
200
This is the antiderivative of cos x.
What is sin x (+c)?
200
These are points where f '(x) = 0 but they are not a max or min.
What plateau points?
200
These three are the criteria of a critical point.
What is a. derivative equal to zero, b. derivative undefined, or c. endpoint values?
300
The type of discontinuity that will cause a one-sided limit.
What is jump (or step) discontinuity?
300
The rule or rules required to find the derivative of y = x^x. (Not tested on the AP Calculus AB test)
What is logarithmic differentiation?
300
"+C" must be included when evaluating these.
What are indefinite integrals?
300
These are points on a function where concavity changes.
What are inflection points?
300
This is indicated by a negative value for the second derivative.
What is negative concavity (concave down)?
400
If a function has a limit from above that equals C and a limit from below that equals C, then it has this.
What is a limit at C?
400
The rule or rules required to find the derivative of y = (3-2x)/(4x+1).
What is the quotient rule?
400
This method is required to find the integral of y = x sin(x^2).
What is substitution (or u-substitution)?
400
The antiderivative of 1/(x^2+1).
What is arctan(x)?
400
This type of behavior is identified by the second derivative test.
What is extrema?
500
If a function has a limit at x=c and f(x)=c then the function is said to be this.
What is continuous at c?
500
The method required to find the derivative of xy=sin(2xy).
What is implicit differentiation?
500
The derivative of this function is 1/x.
What is ln x?
500
The integral of (sin x)^2 + (cos x)^2.
What is x?
500
This behavior occurs when a critical point has negative values of f ' to the left and positive values of f ' to the right.
What is a minimum?