Thumbnail Image | Title | Description | Curriculum Nodes |
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Definition--Calculus Topics--Integral Symbol |
Definition--Calculus Topics--Integral Symbol | Calculus Vocabulary | |
Definition--Calculus Topics--Integrand |
Definition--Calculus Topics--Integrand | Calculus Vocabulary | |
Definition--Calculus Topics--Integration by Substitution |
Definition--Calculus Topics--Integration by Substitution | Calculus Vocabulary | |
Definition--Calculus Topics--Intermediate Value Theorem |
Definition--Calculus Topics--Intermediate Value Theorem | Calculus Vocabulary | |
Definition--Calculus Topics--Inverse Function |
Definition--Calculus Topics--Inverse Function | Calculus Vocabulary | |
Definition--Calculus Topics--L'Hopital's Rule |
Definition--Calculus Topics--L'Hopital's Rule | 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. |
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. |
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. |
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 th |
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. |
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 | |
Definition--Calculus Topics--Rational Function |
Definition--Calculus Topics--Rational Function
A function made up of the ratio of two functions f(x) and g(x). |
Calculus Vocabulary | |
Definition--Calculus Topics--Riemann Sum |
Definition--Calculus Topics--Riemann Sum
An approximation method for estimating the area under a curve and used to approximate the solution to a definite integral. |
Calculus Vocabulary | |
Definition--Calculus Topics--Right-Hand Limit |
Definition--Calculus Topics--Right-Hand Limit
As a function f(x) approaches a specific input value a, for x-values greater than or equal to a, the function may approach a specific limiting value. |
Calculus Vocabulary | |
Definition--Calculus Topics--Rolle's Theorem |
Definition--Calculus Topics--Rolle's Theorem
For function f(x) along an interval [a, b], if f(a) = f(b), then there is a point along the interval where the derivative is zero. |
Calculus Vocabulary | |
Definition--Calculus Topics--Second Derivative |
Definition--Calculus Topics--Second Derivative
For differentiable function f(x), the second derivative is the derivative of f'(x) and denoted as f''(x). |
Calculus Vocabulary | |
Definition--Calculus Topics--Separable Differential Equation |
Definition--Calculus Topics--Separable Differential Equation
A special type of differential equation in which functions f(x) and g(y) can be separated to find the solution to the equation. |
Calculus Vocabulary | |
Definition--Calculus Topics--Sigma Notation |
Definition--Calculus Topics--Sigma Notation
The Greek letter used for summarizing terms of a finite or infinite sequence. |
Calculus Vocabulary | |
Definition--Calculus Topics--Step Function |
Definition--Calculus Topics--Step Function
A discontinuous function whose graph looks like a staircase. A step function can be generated by ceiling or floor functions. |
Calculus Vocabulary | |
Definition--Calculus Topics--Sum Rule |
Definition--Calculus Topics--Sum Rule
For differentiable functions f(x) and g(x) along a given interval, the derivative of the sum f(x) + g(x) is the sum of the individual derivatives f'(x) and g'(x). |
Calculus Vocabulary | |
Definition--Calculus Topics--Tangent to a Curve |
Definition--Calculus Topics--Tangent to a Curve
A line that intersects a curve at a single point and is perpendicular to the curve at that point. |
Calculus Vocabulary | |
Definition--Calculus Topics--Trapezoidal Rule |
Definition--Calculus Topics--Trapezoidal Rule
A technique for approximating a definite integral by adding the areas of trapezoids underneath a curve. |
Calculus Vocabulary | |
Definition--Calculus Topics--Trig Identities |
Definition--Calculus Topics--Trig Identities
Equations that involve trigonmetric functions and are often used to simplify certain trigonometric expressions. |
Calculus Vocabulary | |
Definition--Calculus Topics--Trigonometric Function |
Definition--Calculus Topics--Trigonometric Function
One of six main functions, including sine, cosine, tangent, secant, cosecant, and cotangent. |
Calculus Vocabulary | |
Definition--Calculus Topics--Vector |
Definition--Calculus Topics--Vector
A quantity that has magnitude and direction. Vectors are often used to model real-world phenomena such as force, speed, or acceleration. |
Calculus Vocabulary | |
Definition--Calculus Topics--Velocity |
Definition--Calculus Topics--Velocity
The first derivative, with respect to time, for the displacement function. Velocity is a vector quantity. |
Calculus Vocabulary | |
Definition--Calculus Topics--Vertical Asymptote |
Definition--Calculus Topics--Vertical Asymptote
A vertical line that the graph of a function approaches but does not intersect. The equation of a vertical asymptote is x = c, for some constant c. |
Calculus Vocabulary | |
Definition--Calculus Topics--Zeros of a Function |
Definition--Calculus Topics--Zeros of a Function
Where the graph of a function intersects the x-axis. The solutions to the equation f(x) = 0 for some function f(x). |
Calculus Vocabulary | |
Instructional Resource: Tutorial: What Are Parametric Equations? |
Instructional Resource: Tutorial: What Are Parametric Equations?
In this activity explore the properties of parametric equations. |
Applications of Equations and Inequalities and Applications of Quadratic Functions | |
Instructional Resource: Tutorial: What Are Piecewise Functions? |
Instructional Resource: Tutorial: What Are Piecewise Functions?
In this tutorial students learn about piecewise functions and their properties. —Press PREVIEW to see the tutorial— |
Special Functions |