Check the clues and answers for your group. Answers stay hidden during live play until the host reveals them.
LIMIT CONCEPTS
$200
A line that a graph approaches as the independent variable approaches positive or negative infinity.
$400
Expressions like zero over zero or infinity over infinity are known as this type of form that requires further analysis.
$600
This rigorous method defines a limit using two Greek letters to quantify proximity between inputs and outputs.
$800
This theorem allows for evaluating a limit by bounding a function between two others that converge to the same value.
$1000
This theorem states that a continuous function on a closed interval takes on every value between its endpoints' outputs.
DERIVATIVE RULES
$200
This rule provides the derivative of a fraction of two functions by utilizing the denominator's square.
$400
When a function cannot be explicitly isolated, this technique allows for differentiating both sides with respect to x.
$600
To differentiate x raised to the nth power, one multiplies by the exponent and decreases the power by one.
$800
This technique is essential for differentiating composite functions where one function is nested inside another.
$1000
This rule dictates that the derivative of two functions multiplied together involves adding the derivative of the first times the second to the first times the derivative of the second.
INTEGRAL TECHNIQUES
$200
Also known as the DI method, this shortcut repeatedly applies integration by parts using a structured table.
$400
Often called the inverse of the chain rule, this method simplifies integrals by changing the variable of integration.
$600
This technique uses sine, tangent, or secant substitutions to eliminate radical expressions from integrands.
$800
Derived from the product rule, this technique integrates the product of two functions by splitting them into u and dv.
$1000
This method decomposes a complex rational expression into simpler fractions before integrating.
CALCULUS APPLICATIONS
$200
This object is formed by spinning a function graph around a coordinate axis.
$400
This application uses derivatives to find the maximum or minimum values of a function within a specific context.
$600
This type of problem involves finding the rate at which one quantity changes in relation to another changing quantity.
$800
Representing the geometric center or centroid, this point allows a lamina to be perfectly balanced.
$1000
This integral-based measure represents the distance along a curve between two specific points.
SEQUENCES AND SERIES
$200
This property holds when the sum of the absolute values of a series terms converges.
$400
This convergence test involves checking the limit of the absolute ratio of consecutive terms.
$600
This test determines convergence by comparing the sum of a series to the value of an improper integral.
$800
This type of series is the sum of a sequence where each term is found by multiplying the previous by a constant ratio.
$1000
This type of series features terms that change sign, typically governed by a factor of negative one raised to an integer power.
THEOREMS AND METHODS
$200
This iterative algorithm uses tangent lines to approximate the roots of a function.
$400
A special case of the Mean Value Theorem, this theorem guarantees a point with a zero derivative if the endpoints have equal values.
$600
This theorem guarantees that any continuous function on a closed, bounded interval attains both a maximum and a minimum value.
$800
This theorem ensures there is a point where the instantaneous rate of change equals the average rate of change over an interval.
$1000
This theorem bridges the gap between differential and integral calculus by defining the relationship between antiderivatives and areas.
