Go on. Explore!

lvl 0 • 0 xp

lvl 1

Home Market Decks Interests

AP Calculus AB Vocab Review

memorize.ai (lvl 286)

(0)

50 cards

()

Section 1

Preview this deck

Interval

Front

1 / 50

Calculus Math

0.0

0 reviews

5			0
4			0
3			0
2			0
1			0

Active users

All-time users

Favorites

Last updated

6 years ago

Date created

Mar 1, 2020

Cards (50)

Section 1

(50 cards)

Interval

Front

The set of all real numbers between two given numbers. The two numbers on the ends are the endpoints.

Back

Derivative

Front

A function which gives the slope of a curve; that is, the slope of the line tangent to a function. The derivative of a function f at a point x is commonly written f '(x).

Back

Discontinuity

Front

A point at which the graph of a relation or function is not connected. Discontinuities can be classified as either removable or essential. There are several kinds of essential discontinuities, one of which is the step discontinuity.

Back

Implicit Differentiation

Front

A method for finding the derivative of an implicitly defined function or relation. Implicit Differentiation is used to find dy/dx.

Back

Inflection Point

Front

A point at which a curve changes from concave up to concave down, or vice-versa.

Back

Calculus

Front

The branch of mathematics dealing with limits, derivatives, definite integrals, indefinite integrals, and power series.

Back

Unit Circle

Front

A circle with a radius of one. It is used to understand sines and cosines of angles found in right triangles.

Back

Instantaneous Acceleration

Front

The rate at which an object's instantaneous velocity is changing at a particular moment. This is found by taking the derivative of the velocity function.

Back

Absolute Maximum

Front

The highest point over the entire domain of a function or relation.

Back

Absolute Minimum

Front

The lowest point over the entire domain of a function or relation.

Back

Composition

Front

Combining two functions by substituting one function's formula in place of each x in the other function's formula.

Back

Chain Rule

Front

A method for finding the derivative of a composition of functions. The formula is . Another form of the chain rule is .

Back

Volume

Front

The total amount of space enclosed in a solid.

Back

Differential Equation

Front

An equation showing a relationship between a function and its derivative(s). For example, is a differential equation with solutions y = Ce-x.

Back

Normal Line

Front

The line that is perpendicular to the tangent line at the point of tangency. Because the slopes of perpendicular lines (neither of which is vertical) are negative reciprocals of one another, the slope of the normal line to the graph of f(x) is −1/ f′(x).

Back

Riemann Sum

Front

an approximation that takes the form Σ f(x)*Δx. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations.

Back

Rolle's Theorem

Front

A theorem of calculus that ensures the existence of a critical point between any two points on a "nice" function that has the same y-value. It essentially states that any real-valued differentiable function that attains equal values at two distinct points must have a stationary point somewhere between them—that is, a point where the first derivative is zero.

Back

Cusp

Front

A point at which two branches of a curve meet such that the tangents of each branch are equal.

Back

Displacement

Front

A net change in position.

Back

Second Derivative

Front

The derivative of a derivative. Usually written f"(x), , or y".

Back

Integration

Front

The inverse of differentiation, since integrating a given function results in a function whose derivative is the given function. It is used in the calculation of such things as the areas and volumes of irregular shapes and solids.

Back

Secant Line

Front

A line which passes through at least two points of a curve. It is a straight line joining two points on a function.

Back

First Derivative Test

Front

Uses the first derivative of a function to determine whether a given critical point of a function is a local maximum, a local minimum, an inflection point, or neither.

Back

Area under a Curve

Front

The area between the graph of y = f(x) and the x-axis is given by the definite integral below. This formula gives a positive result for a graph above the x-axis, and a negative result for a graph below the x-axis.

Back

Related Rates

Front

A class of problems in which rates of change are related by means of differentiation. Standard examples include water dripping from a cone-shaped tank and a man's shadow lengthening as he walks away from a street lamp.

Back

Washer Method

Front

A technique for finding the volume of a solid of revolution. It is a means of calculating the volume of a solid of revolution of a solid-state material when integrating along the axis of revolution.

Back

Mean Value Theorem

Front

A major theorem of calculus that relates values of a function to a value of its derivative. Essentially the theorem states that for a "nice" function, there is a tangent line parallel to any secant line.

Back

Trapezoid Rule

Front

A method for approximating a definite integral using linear approximations of f. The trapezoids are drawn as shown below. The bases are vertical lines.

Back

Concavity

Front

A shape or solid which has an indentation or "cave". The second derivative of a function may also be used to determine the general shape of its graph on selected intervals.

Back

Product Rule

Front

A formula for the derivative of the product of two functions. (xy)' =x'y+xy'

Back

Velocity

Front

The rate of change of the position of an object. For motion in one dimension, such as along the number line, velocity is a scalar.

Back

Infinity

Front

A "number" which indicates a quantity, size, or magnitude that is larger than any real number. The number infinity is written as a sideways eight: ∞. Negative infinity is written -∞.

Back

Asymptote

Front

A line that continually approaches a given curve but does not meet it at any finite distance.

Back

Slope

Front

A number that describes both the direction and the steepness of the line.

Back

Natural Logarithm

Front

a logarithm to the base e (2.71828...).

Back

Quotient Rule

Front

A formula for the derivative of the quotient of two functions. (x/y)' =x'y-xy'/y^2

Back

Curve Sketching

Front

The process of using the first derivative and second derivative to graph a function or relation. As a result the coordinates of all discontinuities, extrema, and inflection points can be accurately plotted.

Back

Tangent Line

Front

A line that touches a curve at a point without crossing over. Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line.

Back

U-Substitution

Front

An integration method that essentially involves using the chain rule in reverse.

Back

Critical Point

Front

A point (x, y) on the graph of a function at which the derivative is either 0 or undefined. A critical point will often be a minimum or maximum, but it may be neither.

Back

Power Rule

Front

The formula for finding the derivative of a power of a variable.

Back

Explicit Differentiation

Front

The process of finding the derivative of an explicit function. For example, the explicit function y = x^2 - 7x + 1 has derivative y' = 2x - 7.

Back

Limit

Front

The value that a function or expression approaches as the domain variable(s) approach a specific value. They are written in the form .

Back

Definite Integral

Front

An integral which is evaluated over an interval. A definite integral is written . Definite integrals are used to find the area between the graph of a function and the x-axis. There are many other applications.

Back

Extreme Value Theorem

Front

A theorem which guarantees the existence of an absolute max and an absolute min for any continuous function over a closed interval.

Back

Instantaneous Rate of Change

Front

The rate of change at a particular moment. Same as the value of the derivative at a particular point. For a function, the instantaneous rate of change at a point is the same as the slope of the tangent line. That is, it's the slope of a curve.

Back

Acceleration

Front

The rate of change of velocity over time.

Back

Instantaneous Velocity

Front

The rate at which an object is moving at a particular moment. Same as the derivative of the function describing the position of the object at a particular time.

Back

Disk Method

Front

A technique for finding the volume of a solid of revolution. This method is a specific case of volume by parallel cross-sections.

Back

Continuity

Front

A function is continuous on an interval if we can draw the graph from start to finish without ever once picking up our pencil.

Back