Check the clues and answers for your group. Answers stay hidden during live play until the host reveals them.
Round 1
Limits and Continuity
$200
The form 0/0 or infinity/infinity that requires L'Hopital's Rule.
$400
The value that f(x) approaches as x nears a specific point.
$600
The property that a function is continuous on [a,b] if it can be drawn without lifting a pencil.
$800
A type of discontinuity where the limit exists but the function value at that point is different or undefined.
$1000
A theorem stating that if f(x) is between g(x) and h(x) near a point, the limit of f(x) must match the limit of g(x) and h(x).
Derivatives
$200
The derivative of natural log of x.
$400
This rule is used to differentiate functions like x squared times e to the x.
$600
The name of the rule used when differentiating composite functions.
$800
This specific derivative process is used for equations like x squared plus y squared equals 25.
$1000
The fundamental definition of the derivative involves the limit of this fraction.
Integrals
$200
The process of finding the area under a curve.
$400
The constant added when calculating indefinite integrals.
$600
Approximating an integral by using trapezoids instead of rectangles.
$800
The theorem that links differential and integral calculus.
$1000
This technique involves manipulating the integrand by adding and subtracting a constant, often used to transform a quadratic expression to facilitate integration.
Applications of Derivatives
$200
The rate at which distance changes with respect to time.
$400
A point where the concavity changes.
$600
The slope of the line tangent to the graph at a given point.
$800
Where the derivative equals zero, potentially indicating a peak or valley.
$1000
The test used to determine if a critical point is a local maximum or minimum.
Series and Sequences
$200
A sequence where each term is found by adding a constant.
$400
The test that compares a series to 1 over n to the p.
$600
The test used to find the radius of convergence for power series.
$800
A power series representation of a function centered at zero.
$1000
A series where the absolute value of the ratio between terms is less than one.
Parametric/Polar/Vector
$200
Functions defined by x(t) and y(t).
$400
The coordinate system using r and theta.
$600
The total distance traveled by a particle along a path.
$800
The rate of change of a vector function dy/dx is dy/dt divided by this.
$1000
The formula for the area of a polar region involves this trigonometric integral component.
Double Jeopardy
Limits and Continuity
$400
The limit as x approaches zero of sin(x)/x.
$800
The application of the Mean Value Theorem to limits.
$1200
The formal definition of a limit using epsilon and delta.
$1600
Limits that approach infinity as the function grows without bound.
$2000
A point where the limit from the left and right exist but are not equal.
Derivatives
$400
Differentiation technique for functions of the form u to the v.
$800
The slope of the normal line is the negative reciprocal of this.
$1200
The derivative of a function defined by an integral.
$1600
The derivative of a function at a point defines the linear approximation of this.
$2000
Differentiation of inverse trigonometric functions.
Integrals
$400
Finding the volume of a solid by revolving around an axis.
$800
Used when the region being revolved has a hole in the middle.
$1200
The method of approximating volumes using cylindrical shells.
$1600
Integrals that have infinite bounds or vertical asymptotes within the range.
$2000
The technique of rewriting rational functions for integration.
Applications of Derivatives
$400
The rate of change of the rate of change.
$800
Related rates problems often use this theorem to relate variables.
$1200
A theorem stating f prime of c equals the average rate of change.
$1600
Newton's method involves finding roots using this iterative sequence.
$2000
Optimization problems involve finding these extreme values.
Series and Sequences
$400
The general form of a Taylor series about x equals a.
$800
The alternating series error bound is less than the first term of this.
$1200
The range of x values for which a power series converges.
$1600
A series that converges but not absolutely.
$2000
The test that shows a series converges absolutely if the sum of absolute values converges.
Parametric/Polar/Vector
$400
A polar graph shaped like a heart.
$800
The orientation of a curve is indicated by this direction.
$1200
The vector function representing position at time t.
$1600
The formula for the speed of a particle with velocity vector v(t).
$2000
The integral used to find the area of a region between two polar curves.
Final Jeopardy · Calculus History
This scholar is credited alongside Isaac Newton for the independent development of calculus.
