Title | Description | Thumbnail Image | Curriculum Topics |
---|---|---|---|
Definition--Calculus Topics--Inflection Point |
Definition--Calculus Topics--Inflection Point
The point on a curve where the curvature changes. This is often indicated by a change in the slopes of tangents to the curve. |
Calculus Vocabulary | |
Definition--Calculus Topics--Instantaneous Rate of Change |
Definition--Calculus Topics--Instantaneous Rate of Change
Another way of describing the slope of the line tangent to a given curve at a given point. |
Calculus Vocabulary | |
Definition--Calculus Topics--Integral |
Definition--Calculus Topics--Integral
A method for finding the area of a curve along an interval. In calculus, integrating a function f(x) involves finding the antiderivative of f(x). |
Calculus Vocabulary | |
Definition--Calculus Topics--Integral Symbol |
Definition--Calculus Topics--Integral Symbol
The mathematical symbol used to denote the process of integration. The symbol is an elongated S, which indcates the infinitesimal sums that make up the area under a curve. |
Calculus Vocabulary | |
Definition--Calculus Topics--Integrand |
Definition--Calculus Topics--Integrand
In the process of integration, it is the function that is being integrated. |
Calculus Vocabulary | |
Definition--Calculus Topics--Integration by Substitution |
Definition--Calculus Topics--Integration by Substitution
Replacing the integrand with a simpler expression to make the process of integration easier. |
Calculus Vocabulary | |
Definition--Calculus Topics--Intermediate Value Theorem |
Definition--Calculus Topics--Intermediate Value Theorem
For continuous function f(x) along interval [a, b] there are values between f(a) and f(b). |
Calculus Vocabulary | |
Definition--Calculus Topics--Inverse Function |
Definition--Calculus Topics--Inverse Function
For function f(x), the inverse function f-1(x), if it exists, undoes the mapping of the original function. |
Calculus Vocabulary | |
Definition--Calculus Topics--L'Hopital's Rule |
Definition--Calculus Topics--L'Hopital's Rule
For function f(x)/g(x), where f(x) and g(x) are two functions, along an interval [a, b], if there is a point c in the interval such that g(x) = 0, then L'Hopital's Rule can be used to find the limit as x approaches c by taking the ratio of the derivatives of the two functions. |
Calculus Vocabulary | |
Definition--Calculus Topics--Left-Hand Limit |
Definition--Calculus Topics--Left-Hand Limit
As a function f(x) approaches a specific input value a, for x-values less than or equal to a, the function may approach a specific limiting value. This limit may or may not exist. |
Calculus Vocabulary | |
Definition--Calculus Topics--Limit |
Definition--Calculus Topics--Limit
As a function f(x) approaches a specific input value a, the function may approach a specific limiting value. This limit may or may not exist. |
Calculus Vocabulary | |
Definition--Calculus Topics--Limits at Infinity |
Definition--Calculus Topics--Limits at Infinity
Finding the limiting value for function f(x) as the input value x approaches infinity. This limit may or may not exist. |
Calculus Vocabulary | |
Definition--Calculus Topics--Linear Approximation |
Definition--Calculus Topics--Linear Approximation
For differentiable function f(x), the linear approximation at x = a, for some real number a, is the equation of the line tangent to f(x) at a. |
Calculus Vocabulary | |
Definition--Calculus Topics--Local Maximum |
Definition--Calculus Topics--Local Maximum
When a function takes an input value, a, for some region in the domain, such that f(a) ≥ f(x), for all x in that region. A function can have more than one local maximum. |
Calculus Vocabulary | |
Definition--Calculus Topics--Local Minimum |
Definition--Calculus Topics--Local Minimum
When a function takes an input value, a, for some region in the domain, such that f(a) ≤ f(x), for all x in that region. A function can have more than one local minimum. |
Calculus Vocabulary | |
Definition--Calculus Topics--Matrix Representations of Vectors |
Definition--Calculus Topics--Matrix Representations of Vectors
A vector quantity can be represented by a matrix. |
Calculus Vocabulary | |
Definition--Calculus Topics--Mean Value Theorem |
Definition--Calculus Topics--Mean Value Theorem
For differentiable function f(x) along the closed interval [a, b] there is a value c within that interval such that f'(c) is parallel to the secant formed by the line connecting the endpoints of the interval. |
Calculus Vocabulary | |
Definition--Calculus Topics--Oblique Asymptote |
Definition--Calculus Topics--Oblique Asymptote
A slanted line that the graph of a function approaches but does not intersect. The equation of an oblique asymptote is y = mx + b, for some constants m and b. |
Calculus Vocabulary | |
Definition--Calculus Topics--Odd Function |
Definition--Calculus Topics--Odd Function
A function whose graph has point symmetry about the origin. |
Calculus Vocabulary | |
Definition--Calculus Topics--One-Sided Limits |
Definition--Calculus Topics--One-Sided Limits
Restricting the limit of a function for values approaching the limiting value from one side. |
Calculus Vocabulary | |
Definition--Calculus Topics--Parametric Equations |
Definition--Calculus Topics--Parametric Equations
A set of equations where each variable, x and y, is a function of a third variable, t. Graphs of parametric equations are sometimes not functions. |
Calculus Vocabulary | |
Definition--Calculus Topics--Piecewise Function |
Definition--Calculus Topics--Piecewise Function
A function made up of separate functions, each with its own interval. |
Calculus Vocabulary | |
Definition--Calculus Topics--Power Function |
Definition--Calculus Topics--Power Function
A function with a single term that consists of a variable base raised to a real number power. The variable can also have a real number coefficient. |
Calculus Vocabulary | |
Definition--Calculus Topics--Power Rule |
Definition--Calculus Topics--Power Rule
The process of finding the derivative of a power function. |
Calculus Vocabulary | |
Definition--Calculus Topics--Quotient Rule |
Definition--Calculus Topics--Quotient Rule
The rule for finding the derivative of a function made up of the ratios of two functions f(x) and g(x). |
Calculus Vocabulary |