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# Calculus Words

### Calculus Vocabulary

Question | Answer |
---|---|

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 answer to an addition problem. | sum |

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 |

x=(-b±√(b²-4ac))/2a given ax²+bx+c=0. | quadratic formula |

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 |