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The line that represents the slope at a certain point on a function tangentline

Derivative of csc x cscxcotx

When the y-value is less than or equal to all the other y-values in the function absolutemin

When the y-value is greater than or equal to all the other y-values in the function absolutemax

uv - ∫ vdu integrationbyparts

the maximum number of a certain object in a logistic equation carryingcapacity

when f'(x)>0, f(x) is ______ increasing

when f'(x)<0, f(x) is ______ decreasing

The test used to see is a number is a max, min, or neither candidatestest

If a quantity is changing it must be represented with a ______ variable

The test that can prove if a series diverges but not if it converges nthtermtest

A way of approximating a definite integral by adding up areas of rectangles riemannsum

If f is continous on [a,b] and differentiable on (a,b), then there is a number c in (a,b) such that f'(c) = f(b)-f(a)/b-a meanvaluetheorem

The graph changes concavity at this point point of inflection

The net change in position displacement

A sequence is _____ if it is nonincreasing/nondecreasing monotonic

dy/dx derivative

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describes the slope of perpendicular lines opposite reciprocals

describes the slope of a line; steepness; incline rate of change

an equation that forms a straight line on the graph linear equation

y=x linear parent function

an inequality that involves a linear function linear inequality

a mathematical sentence that involves two values that are not necessarily equal inequality

> Greater than

< Less than

Any value or values that make an inequality true solution of an inequality

y=mx+b where m is slope and b is the y intercept slope intercept form

Ax+By=C standard form

y-y1=m(x-x1) for any point (x1, y1) point slope form

starting point; the b in a linear function. where x=0 y intercept

the point where the line crosses the x axis; when y=0 xintercept

the set of all the x values domain

the set of all the y values range

The x values; independent; domain input

the y values; dependent; range output

x, input independent variable

y, output dependent variable

the x intercept; when y=0 zero of a function

f(x)=y. y is a function of x function notation

a graph that is represented by a smooth line with no gaps continuous graph

a graph that is represented by set points; not connected discreet graph

a change that occurs on a graph transformation

slide; changing the y intercept translation

creates a mirror image of the graph over a given line or axis reflection

a relation in which each x value (input) has one and only one y value (output) function

a type of graph that uses set points to display information scatterplot

a scatter plot where the points all move in the upward direction positive correlation

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The highest point on a graph, especially over a specified domain. It is the greatest value of f(x) over a defined interval of x, provided y=f(x). ( f'(x)=0 , f''(x)<0 ) Absolute maximum

The lowest point on a graph, especially over a specified domain. It is the least value of f(x) over a defined interval of x, provided y=f(x). (f'(x)=0 , f''(x)>0 ) Absolute Minimum

A line (or curve) that a function approaches without actually reaching the line as the domain either grows unbounded or approaches a limit. Asymptote

when the sum of their expanded terms reaches a boundary or limit. convergence

Let f be defined at c. If f'(c)=0 or if f' is undefined at c, what is c? critical point

A function f has this at (c,f(c)). if f''(c)=0 or f''(c) does not exist and if f'' changes sign from positive to negative or negative to positive at x=c or if f'(x) changes from increasing to decreasing or decreasing to increasing at x=c inflection point

If an object moves along a straight line with position function s(t), then its this is v(t)=s'(t) velocity

If an object moves along a straight line with position function s(t), then its this is |v(t)| speed

If an object moves along a straight line with position function s(t), then its this is a(t)=v'(t)=s''(t) acceleration

s= ∫ sqrt(1+[f'(x)]^2) dx on the bounds of a to b. What is this formula for? arc length

If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f'(c)=(f(b)-f(a))/(b-a) Mean value theorem

If f is continuous on [a,b] and k is any number between f(a) and f(b), then there is at least one number c between a and b such that f(c)=k Intermediate value theorem

In a rational funcion, the graph appears to approach thee horizontal line y=c, as x approaching infinity or negative infinity. In this case, what is y=c? horizontal asymptote

In a rational function, this asymptote occurs when a factor remains in the denominator. vertical

In a rational function, this asymptote occurs when the power of x in the numerator is greater than the power of x in the denominator. slant

this of the function f(x) at x=a is defined as f'(a)= lim(h approaching to 0) (f(a+h)-f(a))/h derivative

The derivative using this rule is (d/dx)x^n=nx^(n-1) where n is any real number power rule

suppose that f and g are differentiable at x. then (d/dx)[f(x)g(x)]= f'(x)g(x)+f(x)g'(X). what is this rule's name? product rule

suppose that f and g are differentiable at x and g(x) is not equal to 0. Then (d/dx)[f(x)/g(x)]= (f'(x)g(x)-f(x)g'(x))/(g(x))^2. What's this rule's name? quotient rule

When f(x)>=g(x) on the interval [a,b], then the ? between these two curves in the given interval is ∫ [f(x)-g(x)]dx (bounded a to b) area

When V= ∫ pi[(outer radius)^2-(inner radius)^2]dx (bounded a to b) What method is this? Washer

S= 2pi∫ f(x){sqrt(1+[f'(x)]^2)} dx on the bounds of a to b. What is this formula for? surface area

A situation where population growth levels off and approaches a limiting number M ( the carrying capacity) because of limited resources is called this. logistic growth

graphical approach, also called 'direction fields'. Pick several points (x,y) and sketch a tiny segment with slope as specified by dy/dx. It shows the general shape of all solutions. slope fields

Numerical approximation to the solution to a differential equation. Arithmetic way of following the lines in a slope field. Use the point slope form to find an approximation value. Given an initial value, and an indicated step size, along with the DE, we can solve for the solution. What method is this? Euler's method

the process of finding the greatest or least value of a function for some constraint, which must be true regardless of the solution. This finds the most suitable value for a function within a given domain. Optimization

If the limit does not exist, we say that the improper integral ____. diverge

This coordinate system is a two-dimensional system where each point is represented as a distance r from the origin (sometimes called the pole) and an angle θ from the positive horizontal axis. polar

This series diverges if |r|>=1. If |r|<1, the series converges to the sum S=a/(1-r). _____ series. geometric

This series is a series whose terms are alternately positive and negative. ____ series. alternating

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the opposite of distributing factoring

Ax^2+Bx+C quadratic equation

b^2-4ac =0 one real solution

b^2-4ac>0 two real solutions

b^2-4ac<0 no real solution

used to find the zeros(roots,x-intercepts,solutions)to a quadratic equation. Quadratic Formula

roots, x-intercepts and solutions zeros

b^2 -4ac discriminant

Ax^2+Bx+C=0 Standard form

numbers that is multiplied by a variable coefficients

the shape of the graph of a quadratic function parabola

the peak in the curve vertex

where a<0 maximum

where a>0 minimum

when the discriminant is negative complex number

when the squared number is a negatve imaginary unit

where the parabola hits x-intercept

when Ax^2+Bx+C does not equal 0 quadratic function

cannot change in equation constant

line of symmetry of a parabola axis of symmetry

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Slope of line tangent to point on graph of f(x). Derivative

Where f(x) is the biggest or smallest value for a while. Extremum

At a point of ____, the derivative's slope changes sign. Inflection

f(x) is ____ at point x=a if a derivative exists at point x=a. Differentiable

f(x) is ____ over a closed interval [a,b] if you can draw the graph without lifting your pen. Continuous

A function is ____ over an interval [a,b] if it is constantly increasing or constantly decreasing. Monotonic

For the ____ sum, the lowest value in each subinterval is chosen. Lower

For the ____ sum, the greater value in each subinterval is chosen. Upper

The net overall change in distance. Integral

You can isolate y on one side of the equation in ____ functions. Explicit

You cannot isolate y on one side of the equation in ____ functions. Implicit

In ____ intervals, the endpoints are not taken into consideration. Open

In ____ intervals, the endpoints are included. Closed

The ____ value theorum states that if a function is continuous over a closed interval [a, b], there is a maximum and a minumum value in that interval. Extreme

The ____ value theorum states that for a closed interval [a, b], is f(x) is continuous, it takes (at some point) every value between f(a) and f(b). Intermediate

In the ____ value theorum, there is some point c between points a and b such that the slope of the line tangent to c is equal to the slope of the secant between point a and b. Mean

____ maxima or minima are the biggest or smallest values in the whole graph. Absolute

____ maxima or minima are the biggest or smallest values in a certain range. Relative

x=c is a ____ value if the derivative of c is zero or undefined. critical

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It is the greatest value of f(x) over a defined interval of x, provided y=f(x). Absolute Maximum

It is the least value of f(x) over a defined interval of x, provided y=f(x). Absolute Minimum

The original function of a derivative. Anti-derivative

A line (or curve) that a function approaches without actually reaching the line. Asymptote

It is the second letter of the Greek alphabet. Beta

A basic rule in calculus to find the derivative of a composite function. Chain Rule

If a graph has no gaps, no holes, no steps, or discontinuities it is... Continuous

An integral between limits of integration is a... Definite Integral

It is the fourth letter of the Greek alphabet. Delta

It is the slope of the line tangent to a function. Derivative

A function that is continuous is... Differentiable

When a function is not continuous it has... Discontinuity

An integral with no limits of integration. Indefinite Integral

When a curve changes direction. Point of Inflection

Speed and direction is also... Velocity

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The number D = b2 – 4ac determined from the coefficients of the equation ax2 + bx + c = 0. Discriminant

a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. squareroot

also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x) = 0. zero

the formula for determining theroots of a quadratic equation from its coefficients: . quadratic formula

value of a function is the place where the graph has a vertex at its lowest point minimum

the common point to join the two line segments vertex form

where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis x-intercept

an important process in algebra which is used to simplify expressions, simplify fractions, and solve equations. factoring

if you square any Real Number you always get a positive, or zero, result. For example 2×2=4, and (-2)×(-2)=4 as well imaginary unit

a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number constant

a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. standard form

the highest exponent of this function is 2. The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0 quadratic equation

it "discriminates" between the possible solutions one real solution

6z means 6 times z, and "z" is a variable, so 6 coefficients

First, Outer, Inner, Last. First means multiply the terms which occur first in each binomia foil

(√) symbol radical

a technique used to solve quadratic equations, graph quadratic functions, and evaluate integrals completing the square

In 8^2 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64. In words: 82 could be called "8 to the power 2" or "8 to the second power squared exponent

a quantity of the form v + iw, where v and w are real numbers complex number

a corner or a point where lines meet. vertex

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The set of the first numbers of the ordered pairs domain

Minus Subtraction

Please Excuse My Dear Aunt Sally orderofoperations

Sum addition

The ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) slope

A mathematical sentence that contains an equal sign equation

A relation between input and output FUNCTION

Symbol used to represent unknown numbers or values variable

The form of a linear equation Ax + By = C, with a graph that is a straight line standard

The set of second numbers of the ordered pairs range

To find the value of an expression evaluate

The vertical number line on a coordinate plane yaxis

A comparison of two numbers by division ratio

To draw or lot the oints named by certain numbers or ordered pairs on a number line or coordinate plane graph

The numbers that correspond to a point on a coordinate system coordinates

A point where the graph intersects an axis intercept

The horizontal number line on a coordinate plane xaxis

The point (0,0) origin

The answer when multiplying product

A polynomial with two terms binomial

Distance around the outside perimeter

To shift a graph vertically or horizontally translation

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approaches a definite limit converges

point(s) at which the derivative equals zero critical

point of ______; curve changes concavity inflection

area under a curve integral

slope or rate of change of a function derivative

differentiation by separating variables implicit

increases to infinity diverges

sum of terms in a sequence series

list of numbers written in a specific order sequence

a curve that is uninterrupted continuous

method of finding volume using cylindrical layers shell

an equation of a curve in terms of r and Θ polar

a function that uses two equations to describe a curve parametric

highest or lowest point on the graph; ______ max/min absolute

method of finding volume by subtracting the volume of the outer solid minus the volume of the inner solid washer

a line or curve that a function approaches without ever reaching asymptote

the derivative of velocity acceleration

rule used to differentiate composite functions chain

rule to differentiate a function composed of a function divided by another function quotient

rule to differentiate a function that contains multiplication of two other functions product

series shown by harmonic

rule used to evaluate indefinite forms of limits lhopital

a value that a function approaches as an input approaches some value limit

integral of velocity position

test to determine convergence of a power series pseries

a vector of length one along an axis unit

the derivative of position velocity

approximation of the area of a function using rectangles under the curve riemann sum

theorem stating that a differentiable function that has equal values at point a and point b must have point c with a slope of zero rolles

theorem stating if f(x) is defined, continuous, and differentiable on interval [a,b], then there is a c such that a<c<b mean value

a line that touches a curve at a point without crossing it tangent

a straight line joining two points on a function's curve secant

a form of integration using the chain rule in reverse u substitution

a quantity with magnitude and direction vector

a series of a function represented as an infinite sum of terms taylor

a Taylor Series centered around zero maclaurin

how fast a function is increasing or decreasing slope

can be found using Disk/Washer/Shell methods volume

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any number that can be written in the form of a+bi complex number

a unit of angular measure equal to 1/180th of a straight angle degree

a relation that associates each value in the domain with exactly one value in the range funtion

a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. logarithm

the Greek word for “measurement of triangles.” trigonometry

adjacent/hypotenuse cosine

a central angle that intercepts an arc s equal in length to the radius r of the circle. radian

when a real number that can be written as a simple fraction rational

a value f(c) that is greater than or equal to all range values of f on some open interval containing c local maximum

for any two points in the interval a positive change in x results in a zero change in f(x) constant

a value that, when multiplied by itself, produces a specified quantity square root

An expression that can have constants, variables and exponents, that can be combined using addition, subtraction, multiplication and division polynomial

ax2 + bx + c = 0 quadratic formula

in the xy- plane defines y as a function of x if and only if no vertical line intersects the graph in more than one point vertical line test

A general term meaning "written down in the way most commonly accepted" standard form

A number made by squaring a whole number. perfect square

Interest calculated as a percent of the original loan simple interest

first, outside, inner, last FOIL

A line with a start point but no end point (it goes to infinity) ray

Opposite in effect inverse

hypotenuse/opposite cosecant

How far a number is from zero absolute value

a quantity representing the power to which a given number or expression is to be raised exponent

a positive change between size or quantity increase

this is formed by the intersection of a plane with two equal cones on opposites of the same vertex. hyperbola

Where interest is calculated on both the amount borrowed and any previous interest. compound interest

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one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. Quadratic Function

2. a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line Parabola

simplify expressions, simplify fractions, and solve equations Factoring

4. an equation containing a single variable of degree 2 quadratic equation

5. is a number used to multiply a variabl Coefficient

6. number is a value that, when multiplied by itself, gives the number Square root

7.a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit Complex number

8.the highest or lowest point, also known as the maximum or minimum of a parabola. Vertex

9.the point at which the graph of an equation crosses the x-axis. X-intercept

10. A line through a shape so that each side is a mirror image. Axis of symmetry

11. A mathematical expression that is the sum of three monomials Trinomial

12. An expression that has a square root, cube root, etc. Radical

13. one that when squared gives a negative result Imaginary Unit

14. where you change the sign in the middle of two terms Conjugates

15. a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number Constant

16.a technique used to solve quadratic equations, graph quadratic functions, and evaluate integrals Completing the square

17. another way of writing the equation of a line. Standard form

18. the value of a function at a certain point in its domain, which is greater than or equal to the values at all other points in the immediate vicinity of the point Maximum

19. the place where the graph has a vertex at its lowest point Minimum

20. members x of the domain of f such that f(x) vanishes at x Zeros