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Limits and Continuity
$200The value approached by a function as the input gets arbitrarily close to a number.
$400The type of discontinuity that can be removed by defining the function at a specific point.
$600The horizontal asymptote of a function is determined by taking this limit as x approaches positive or negative infinity.
$800The condition stating that a function is continuous at a point if the limit equals the function value.
$1000The theorem that guarantees a continuous function takes on every value between its endpoints on a closed interval.
Derivative Rules
$200The rule used to differentiate a function raised to a power.
$400The method required to find the derivative of the product of two functions.
$600The rule applied when finding the derivative of a function composed within another.
$800The derivative of the natural logarithm function ln(x).
$1000The slope of the tangent line to a curve defined implicitly at a specific point.
Applications of Derivatives
$200The instantaneous rate of change of position with respect to time.
$400The value of the derivative at a local maximum or minimum of a smooth function.
$600The rate at which velocity changes over time.
$800The line that approximates a function near a point of tangency.
$1000The concept used to solve problems where variables change relative to time.
Definite Integrals
$200The visual interpretation of a definite integral on a graph.
$400The sum used to approximate the area under a curve using rectangles.
$600The theorem that links the concept of differentiation and integration.
$800The property that allows splitting an integral over the sum of two intervals.
$1000A method to approximate integrals using trapezoids instead of rectangles.
Indefinite Integrals
$200The constant added to the result of an indefinite integral.
$400The indefinite integral of e to the x.
$600The integral of cosine x with respect to x.
$800The process of integration that is the reverse of the chain rule.
$1000The antiderivative of the function one over the square root of 1 minus x squared.
Differential Equations
$200A graphical representation of the slopes of a differential equation.
$400The process of solving a differential equation by grouping x and y terms.
$600A solution to a differential equation containing arbitrary constants.
$800The specific solution that satisfies a given initial condition.
$1000A differential equation where the rate of change is proportional to the current amount.