Approaching Without Ever Getting There
Change this Instant!
What's under my function?
Move it!
Miscellaneous
100
A function has a two-sided limit at a point if and only if these two values are equal.
What are the left-hand limit and the right-hand limit?
100
The derivative of a function at a point gives the slope of this at that point.
What is the tangent line?
100
The integral of a function from x=a to x=b is defined as the area bounded by the function and this.
What is the x-axis?
100
Let x(t) represent the position of an object. Then this quantity is represented by x'(t)
What is velocity?
100
sin frac{2pi}{3}
What is
frac{sqrt{3}}{2}?
200
The existence of a limit at a point guarantees that the function behaves predictably near that point, but it does not guarantee this property.
What is continuity?
200
For a function to be differentiable at a point, it must also be this.
What is continuous at that point?
200
A left Riemann Sum used to approximate the value of a definite integral will overestimate the true value if the function is this
What is decreasing?
200
|v(t)|
What is speed?
200
The area of a trapezoid.
What is
A=frac{b_1+b_2}{2}cdot h?
300
A function can have an infinite limit at a finite value of x, meaning the function exhibits this type of behavior at that point.
What is a vertical asymptote?
300
A function f has a critical point at x=c and its second derivative at c is negative. Then at x=c, the graph of f has this feature.
What is a maximum?
300
int_a^bf(x) dx=F(b)-F(a)
What is the fundamental theorem of calculus?
300
intv(t)dt
What is displacement?
300
The rule used to simplify the process of evaluating indeterminate limits.
What is L'Hopital's Rule?
400
A function has a finite left-hand limit and a finite right-hand limit at x = c, but they are not equal. What type of discontinuity does this create, and how does it appear on the graph?
What is a jump discontinuity?
400
The derivative at x=0.
What is undefined?
400
The value of the integral shown below.
What is 0?
400
An object with v<0 and a<0 is described as this.
What is speeding up in the negative direction?
400
frac{1}{b-a}int f(x)dx
What is the average value of
f?
500
The Intermediate Value Theorem guarantees that there is at least one value c in (a,b) such that f(c)=0 provided that this is true.
What is f is continuous and f(a) and f(b) are different signs?
500
The conditions needed to apply the Mean Value Theorem.
What are continuous on a closed interval, and differentiable on an open interval?
500
The formula will calculate the volume of a solid generated by revolving an area around a vertical axis.
What is
pi int_a^bR^2dy?
500
A moving object reaches it maximum position. At this instant, the velocity is this.
What is 0?
500
The date of the AP exam this year.
What is May 12?