AP Calculus AB – Flashcards

the smallest y-value of the function

a point that represents the maximum value a function assumes over its domain

The distance a number is from zero on a number line

the rate of change of velocity

a function whose dependent variable satisfies a polynomial relationship with one or more independent variables

the height of a wave from the origin to a crest, or from the origin to a trough

an indefinite integral. an arbitrary constant "+c" is included

The process of evaluating an indefinite integral

A number which serves as an estimate of a desired number

The inverse of the cosine function

The inverse of the sine function

The inverse of the tangent function

a line that a graph approaches but never crosses

slope between two points on a function

the total average value of all items

An imaginary line around which rotation occurs

a line that divides a figure into 2 congruent parts

the fixed number we multiply over and over again

the number which, raised to the power of a given logarithm, produces a given number

some number greater than the graph in which the graph may approach but not pass

A set is bounded below if there is an x value greater than or equal to all other x values in the domain

to set limits or bounds to

formed by two perpendicular axes (coordinate axes): the X-axis and the Y-axis.

a method of obtaining the derivative of a composite function

ellipse in which the two axes are of equal length

The six functions sine, cosine, tangent, cosecant, secant, and cotangent.

[a,b] includes all numbers between a and b AND includes a and b

a constant number that serves as a measure of some property or characteristic

a number of the form a+bi where a and b are real numbers and i is the square root of -1

the joining together two different functions

Intervals on which the second derivative is negative

Intervals in which the second derivative is positive

any figure that can be obtained by slicing a double cone

a function that is a fixed numerical value for all elements of the domain of the function

an undetermined constant added to every result of integration (the added +c)

a function that is continuous on both the left and right side at that point

a function that is continuous at every point on the interval

function whose graph has no gaps or breaks

Perpendicular number lines

the reciprocal of the sine function

cos0 = adj/hyp

the reciprocal of the tangent function

the relative maximum and minimum points of the parent function

any x values where f ′(x) = 0 or is undefined

A surface or shape exposed by making a straight cut through something at right angles to the axis

applications where the rate of change of a variable y is proportional to the value of y and is negative

a function with a graph that moves downward as it is followed from left to right

for all x in [a,b], f'(x)<0

the integral of a function over a definite interval

A finite increment in the value of a variable

the result of mathematical differentiation, slope

m=[f(x+h)-f(x)]/h

A function is differentiable at x=a if the f'(a) exists. If a function is differentiable at x=a, it is also continuous at x=a

involving or containing one or more derivatives

an equation that contains the derivative of a function

the mathematical process of obtaining the derivative of a function

lack of connection of continuity

In finding the volume of a solid of revolution, use one of the following depending on the axis of revolution - ∫ π[R(x)]^2 dx for a horizontal axis of revolution, ∫ π[R(y)]^2 dy for a vertical axis of revolution

∫ l v(t) l (dt)

speed X time

the set of values of the independent variable for which a function is defined

A variable occurring in a function, but on which the value of the function does not depend

dy/dx =dy/du*du/dx

the base of the natural system of logarithms

a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it

the behavior of the graph of a function as x approaches positive infinity or negative infinity

when an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined

graph is symmetrical with respect to the y-axis

a function in which an independent variable appears as an exponent

growth pattern in which the individuals in a population reproduce at a constant rate

When an initial amount decreases by the same percent over a given period of time

the local and global maximums and minimums of a function

the product of all the integers up to and including a given integer

accomplishes two things, determines where the function is inc/dec and determines if the CPs are relative max or min

the number of times that a periodic function repeats itself in every unit of the independent variable; the reciprocal of the period of the function

a relation in which each element of the domain is paired with exactly one element of the range

If a function is on the closed interval [a, b] and F is an antiderivative (∫) of f on [a,b] then ∫f(x) dx from a to b is F(b) - F(a)

They help describes how much growth has occurred and how the same can be replicated in the future

the rate of increase in size per unit time

the time required for something to fall to half its initial value (in particular, the time for half the atoms in a radioactive substance to disintegrate)

an open curve formed by a plane that cuts the base of a right circular cone

a number of the form a+bi where a and b are real numbers and i is the square root of -1

is a procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly

any function of a variable whose value increases or is constant as the variable increases

for all x in [a,b], f'(x)>0

the amount by which something increases

the set of functions F(x) + C, where C is any real number, such that F(x) is the integral of f(x)

a limit in which f(x) increases or decreases without bound, as x approaches c

a point where a function changes concavity; also, where the second derivative changes signs

A given value of x and f(x) used to find the constant of integration

problem where you must solve for the variable C

a rectangle whose area lies entirely inside a geometric figure or curve; all vertices of the rectangle lie on the curve.

the rate of change of a function occurring at or associated with a given instant, or as a limit as a time interval approaches zero; the derivative

the speed and direction of an object at a particular instant in time

any of the natural numbers (positive or negative) or zero

a function that possesses a finite integral; the function must be continuous on the interval of integration

the function that is integrated in an integral

an operation used in the calculus whereby the integral of a function is determined

in integrating composite function, either using pattern recognition or change of variables to perform the integration

let f(x) be a function continuous on the closed interval [a,b]. If N is any real number between f(a) and f(b), then there is at least one real number c between a and b such that f(c)=N

a set containing all points (or all real numbers) between two given endpoints

a relation formed by reversing x and y in a function

A non-terminating, non-repeating decimal (π or √2)

c²=a²+b²-2abcosC

sinA/a=sinB/b=sinC/c

the value that a function is approaching as x approaches a given value through values less than x

a rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the left most point of the sub-interval

German mathematician who found and studied calculus at the same time of Newton; Fought with Newton over who was the founder of calculus

the mathematical value toward which a function goes as the independent variable approaches infinity

the value the function approaches as x increases or decreases without bound

either of the endpoints of an interval over which a definite integral is to be evaluated

f(x)≈f(a)+f'(a)(x-a)

a function whose graph is a straight line

the set of all local maxima and minima points on the graph of a function

that the more you zoom in on a point on the graph of the function (with equal scaling horizontally and vertically), the more the graph will look like a straight line

zooming in at a point on the graph of a function until the function approaches the tangent line at that point

The inverse of an exponential function

logb mn=logb m+logb n logb m/n = logbm - logbn logb m^n = nlogbm logb(b) =1 logb1 = 0

a function is bounded below on a given domain if there is a number "m" such that "m" is less than or equal to f(x) for all "x" in the domain

the largest possible quantity

an average of n numbers computed by adding some function of the numbers and dividing by some function of n

(x₁+x₂)/2, (y₁+y₂)/2

the smallest possible quantity

A sequence is non decreasing or its non increasing

the act of changing location from one place to another

English mathematician and scientist who invented differential calculus and formulated the theory of universal gravitation

a point of discontinuity that is not removable. it represents a break in the graph of f where you cannot redefine f to make the graph continuous

perpendicular to tangent line

an approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(−x)=−f(x)

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graph is symmetrical with respect to the origin; f(-x)=-f(x)

1. A function where each element of the range is paired with exactly one element of the domain. 2. A function whose inverse is a function.

x such that a < x < b

is the process of making a system as effective as possible

if y is a function of x, y′ = dy is the first order, or first, derivative of y with dx respect to x

the point of intersection of coordinate axes

the graph of a quadratic function

in a plane, curves that differ from one another by a vertical translation or shift

any factor that defines a system and determines (or limits) its performance

dividing an interval into n sub-intervals

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