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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 |
Created by:
mbarnard
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