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# Calculus Words

### Calculus Vocabulary

To put all the like terms in a mathematical sentence together. simplify
A mathematical sentence without an equals sign. expression
The number in front of a variable. coefficient
A fixed value that does not change. constant
A letter of symbol that represents a number. variable
A number form that uses various roots of a number. radical
A number that when multiplied by itself equals a given number. square root
A number that when multiplied three times equals a given number. cube root
A number that tells how many times a factor is to be multiplied. exponent
The solution to a subtraction problem. difference
The answer to a multiplication problem. product
The solution to a division problem. quotient
Rules followed to simplify expressions in the proper sequence. order of operations
The distance a number or point is from zero. absolute value
To find an answer to a particular problem. solve
A mathematical sentence with an equals sign. equation
An equation with at most one solution. linear
An equation with at most two solutions. quadratic
The shape of the graph usually formed by a quadratic equation. parabola
An equation with at most three solutions cubic
An equation with at most four solutions. quartic
The acronym used to identify the basic trigonometric rations. SOHCAHTOA
The trigonometric ratio for an angle made up of the ratio of the opposite side and the hypotenuse. sine
The trigonometric ratio for an angle made up of the ratio of the adjacent side and the hypotenuse. cosine
The trigonometric ratio for an angle made up of the ratio of the opposite side and the adjacent side. tangent
The reciprocal of the sine function or the ratio of the hypotenuse to the opposite side of an angle in a right triangle. cosecant
The reciprocal of the cosine function or the ratio of the hypotenuse to the adjacent side of an angle in a right triangle. secant
The reciprocal of the tangent function or the ratio of the adjacent side to the opposite side of an angle in a right triangle. cotangent
a rule used to prove three segment lengths make a right triangle or a²+b²=c². Pythagorean Theorem
The horizontal number line on the coordinate plane. x-axis
The vertical number line on a the coordinate plane. y-axis
The intersection of the horizontal and vertical number lines on the coordinate plane. origin
Two numbers that name a specific location on the coordinate plane. ordered pair
One of the four sections on the coordinate plane. quadrant
Values where a line or curve crosses the horizontal axis. x-intercept(zeroes)
The place on the coordinate plane where a line or curve crosses the vertical axis. y-intercept
The quality of having balance or exact parts of a figure on either side of an axis. symmetry
The name for any function whose graph is symmetric with the y-axis. even function
The name for any function whose graph is symmetric with the origin. odd function
A set of equations with two or more variables. system of equations
The property shown if a=b and b+a=d, then b+b=d. substitution
The rate of change or the rise over run of a line. slope
y=mx+b. slope-intercept form
A set of ordered pairs. relation
A relationship in which each independent variable matches with exactly one dependent variable. function
A method used to determine if a relation is a function. vertical line test
The independent variable of a function. domain
The dependent variable of a function. range
The process of combining two or more functions. composition
A method for determining if a relationship exists between two variables. regression analysis
A numerical value indicated by 'r' that includes and is between -1 and 1 which measures the strength of the relationship between two variables. correlation coefficient
A numerical value indicated by 'r²' that includes and is between 0 and 1 which measures the percentage of data that is closest to the line of best fit helping to indicate the strength of a relationship. coefficient of determination
A line that intersects a curve only once in a given area whose slope represents the rate of change. tangent line
A line that connects any two points on a curve. secant line
A definite set of numbers between two endpoints. interval
The space inside a two-dimensional figure. area
Types of rectangles put on the inside of a function's graph. inscribed
Types of rectangles put on the outside of a function's graph. circumscribed
√((x1-x2)²+(y1-y2)²) given (x1,y1) and (x2,y2) distance formula
A value that a function or any situation approaches. limit
A method used to evaluate limits by using a table of values. numerical
A method used to evaluate limits by using the picture of the function on the coordinate plane. graphical
Methods associated with evaluating limits using various algebraic techniques. analytical
An analytical method of finding limits where a common factor in the numerator and in the denominator of a rational function can be removed. cancellation
An analytical method of finding limits where radical parts of expressions are eliminated without changing the value of the entire expression. rationalization
The rule stating that if a function is between two functions and those two functions have the same limit at a given x value, the function in between also has the same limit. Squeeze Theorem
A rule stating that on a closed interval [a,b] with a given value k between f(a) and f(b), there exists a number c in [a,b] such that f(c)=k. Intermediate Value Theorem
Any break in a function's graph. discontinuity
A discontinuity resulting in a hole in a graph that can be redefined at one point making the continuous. removable
It's what a removable discontinuity creates a graph. hole
A discontinuity that can not be redefined at one point to make a graph continuous. nonremovable
The line x=c that a function approaches if the function approaches ∞ or -∞ as x nears c from either side. vertical asymptote
A function that is always defined and has a limit at every given x value thus making the graph unbroken. continuous
A function or other idea that approaches a certain limit is doing this. converge
A "step" function which gives back the largest positive, neutral, or negative of a value. greatest integer function
The foundational equation for the derivative or slope of the tangent line or the limit as the ⌂x approaches 0 of (f(x+⌂)-f(x))/⌂x difference quotient
The process of finding the rate of change of a function. differentiation
An equation used to determine the location of an object relative to time. position function
The beginning speed at which an object starts. initial velocity
The change in position divided by the change in time. average velocity
The change in position of an object at a specified time. instantaneous velocity
The change in speed or velocity of an object. acceleration
f'(x)g(x)+f(x)g'(x) product rule
(f'(x)g(x)-f(x)g'(x))/(g(x))² quotient rule
A rule used to differentiate a function inside a function. chain rule
Finding the derivative of a function that is written as "y=" a function in terms of x such as y=4x³=2x-1. explicit differentiation
Finding the derivative of a function that ca not be written as "y=" a function only in terms of x such as y²=2xy=4x². implicit differentiation
A maximum or minimum over a closed interval. absolute extrema
A maximum or minimum on an open interval. relative extrema
A value where the derivative is equal to zero or is undefined. critical number
A rule stating that a function has both a minimum and a maximum on a closed interval if the function is continuous. Extreme Value Theorem
A rule stating that instantaneous velocity equals average velocity using derivatives. With integrals, there exists a rectangle whose area is the same as that under the curve. Mean Value Theorem
The rule stating that if a function has two x values with the same y value and is differentiable between those two x values, then there exists a value in between where the derivative is equal to zero. Rolle's Theorem
It's what a function is doing if x1<x2 and f(x1)<f(x2). increasing.
It's what a function is doing if x1<x2 and f(x1)>f(x2). decreasing
The line y=d that a function approaches as the function's x values near ∞ or -∞. horizontal asymptote
A place where the concavity of a function's graph changes. point of inflection
The type of direction or shape of a graph that can be determined through the second derivative. concavity
Applications involved in determining a minimum or maximum value. optimization
The main equation or formula that is to be optimized. primary equation
An equation or formula that is substituted into an equation that is to be optimized. secondary equation
The distance around a polygon. perimeter
The distance around a circle. circumference
A difference in measurements that when computer into other equations or formulas leads to this type of error. propogated error
The ratio of the propagated error and the actual result of a given situation. relative error
An error formed by moving the decimal twice to the right on the relative error. percent error
A technique used for approximating the real zeroes of a function by using numerous iterations after having an initial guess. Newton's Method
A repetition of process. iteration
An equation involving a derivative and its variables which can be solved by integration methods. differential equation
The process of finding a function given derivative. integration
The general function of a differential equation whose constant is not readily known. indefinite integral
The result of finding the unknown constant to an indefinite integral. particular solution
Σ or summation. sigma
Archimedes method for determining the area of a region with sums rather integrals by squeezing the region between two polygons whose number of sides increase. exhaustion method
A method used to approximate area or an integral using summation. Riemann Sums
The numerical limit of Riemann Sums on an interval. definite integral
Given the integral of f(x)dx bounded by [c, d], it's the rule that allows F(d) - F(c) Fundamental Theorem of Calculus
Approximation techniques used to evaluate a definite integral. Simpson's & Trapezoid Rules
An alternate way to express a number using exponents and a variety of numerical bases, of which 10 is the most common. logarithm
An alternate way to express a number using exponents and a base of 'e'. natural logarithm
An equation formed by interchanging the domain and the range. inverse
Any function that is either entirely increasing or entirely decreasing. monotonic
A method used to determine if a function has an inverse. horizontal line test
A number that increases or decreases another quantity at a set rate over time. proportionality constant
A process of a substance becoming larger or more numerous. growth
The gradual reduction of the quantity of a substance often associated with chemical elements and radioactivity. decay
A three-dimensional figure formed by rotating a curve about an axis. solid of revolution
A line that a curve rotates around in the creation of a solid. axis of revolution
The amount of space inside a solid. volume
A method of finding the volume of a solid of revolution. disk method
A method of finding the volume of a solid of revolution with a hole in it. washer method
The shape taken by something flexible suspended from two points. catenary
The amount of material needed to make the outside of a geometric solid. surface area
Created by: mbarnard

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