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LIMITS AND CONTINUITY
$200A function is this if there is no break or jump in its graph at a given point.
$400The vertical value that a function approaches as x gets closer to a specific point without reaching it.
$600The specific type of discontinuity that occurs when a limit exists but the function value at that point does not.
$800The theorem that identifies the existence of a value between two bounds by squeezing a function.
$1000The term describing a point where a function grows without bound as it approaches a vertical asymptote.
DIFFERENTIATION RULES
$200The rule used to find the slope of a power function like x raised to the fifth power.
$400The differentiation technique applied when calculating the slope of a product of two functions.
$600The method for finding the derivative of a function nested within another function.
$800This rule determines the rate of change for a ratio of two differentiable functions.
$1000This involves differentiating both sides of an equation with respect to x when y is not isolated.
INTEGRATION BASICS
$200The constant added when calculating an indefinite integral to represent all possible antiderivatives.
$400The geometric interpretation of the definite integral of a positive function on a closed interval.
$600The process of evaluating an integral by reversing the chain rule using a substitution variable.
$800The fundamental result relating the definite integral to the evaluation of the antiderivative at the endpoints.
$1000The technique of using rectangles with heights determined by the midpoint of subintervals to approximate area.
APPLICATIONS OF DERIVATIVES
$200The instantaneous rate of change of position with respect to time.
$400A point where the derivative is undefined or equals null, often serving as a candidate for a maximum or minimum.
$600The second derivative helps determine this property of a curve, indicating if it bends upward or downward.
$800Problems that use derivatives to find the most efficient dimensions for a physical object.
$1000The point where a curve switches from concave up to concave down.
SEQUENCES AND SERIES
$200An ordered list of numbers following a specific pattern.
$400The summation of the terms of a sequence.
$600A test for convergence that compares the limit of a series to a known geometric series.
$800A series that alternates signs between positive and negative terms.
$1000The power series representation of a function centered at zero.
CALCULUS HISTORY
$200The English polymath often credited with inventing calculus alongside Leibniz.
$400The German mathematician who independently developed calculus and standard notation.
$600The French mathematician known for the mean value theorem, a cornerstone of calculus.
$800The Swiss mathematician who made vast contributions to calculus and invented the symbol for summation.
$1000This mathematician formulated the rigorous definition of a limit using epsilon and delta.