Terms : Hide Images
| 291693256 | Absolute Maximum | The greatest y-‐value that a function achieves. Occurs either at a local maximum or an endpoint. | |
| 291693257 | Absolute Minimum | The smallest y-value that a function achieves. Occurs either at a local maximum or an endpoint. | |
| 291693258 | Acceleration | The rate of change of the velocity with respect to time. The second derivative of a position function. | |
| 291693259 | Amplitude | In periodic functions, the height of the function at the maximum to the middle line | |
| 291693260 | Antiderivative | An indefinite integral. An arbitrary constant "+C" is included | |
| 291693261 | Antidifferentiation | The process of evaluating an indefinite integral | |
| 291693262 | Approximation | A number which serves as an estimate of a desired number | |
| 291693263 | Arccosine function | The inverse of the cosine function | |
| 291693264 | Arcsine function | The inverse of the sine function | |
| 291693265 | Arctangent function | The inverse of the tangent function | |
| 291693266 | Average rate of change | Slope between two points on a function | |
| 291693267 | Average value | 1/(b−a) ∫ f (x)dx | |
| 291693268 | Axis of rotation | A line around which some body or curve rotates | |
| 291693269 | Axis of symmetry | A line araound which a geometric figure is symmetrical | |
| 291693270 | Base | The number which, raised to the power of a given logarithm, produces a given number | |
| 291693271 | Chain rule | A method of obtaining the derivative of a composite function | |
| 291693272 | Circle | The set of points in a plane that are equidistant from a given point | |
| 291693273 | Closed interval [a,b] | a ≤ x ≤ b | |
| 291693274 | Coefficient | A multiplicative factor in some term of an expression (or of a series); it is usually a number but in any case does not involve any variables of the expression | |
| 291693275 | Concave down | Having a decreasing derivative as the independent variable increases; having a negative second derivative | |
| 291693276 | Concave up | Having an increasing derivative as the independent variable increases; having a positive second derivative | |
| 291693277 | Constant function | A function that is a fixed numerical value for all elements of the domain of the function | |
| 291693278 | Constant of integration | An arbitrary constant term in the expression of the indefinite integral of a function | |
| 291693279 | Continuity at a point | A function that is continuous on both the left and right side at that point | |
| 291693280 | Continuity on an interval | A function that is continuous at every point on the interval | |
| 291693281 | Continuous function | A function such that the following is true: 1. lim f(x ) exists as x approaches a 2. f(a) exists 3. f(a)= limit of f(x) as x approaches a | |
| 291693282 | Cosecant function | The reciprocal of the sine function | |
| 291693283 | Cosine function | The ratio x/r with r being the distance of (x, y) from the origin | |
| 291693284 | Cotangent function | The reciprocal of the tangent function | |
| 291693285 | Critical point | Any ordered pair (x, y) where f ′(x) = 0 or is undefined | |
| 291693286 | Critical value | Any x values where f ′(x) = 0 or is undefined | |
| 291693287 | Cross-sectional area | A plane geometric configuration formed by cutting a given figure with a plane which is at right angles to an axis of the figure | |
| 291693288 | Decreasing function | when x| | |
| 291693289 | Decreasing on an interval | For all x in [a,b], f'x<0 | |
| 291693290 | Definite integral | The expression for the evaluation of the indefinite integral of a positive function between two limits of integration | |
| 291693291 | Derivative | The slope of the tangent line at a point on a curve limit as h approaches 0 of [f (x + h) − f (x)] / h | |
| 291693292 | Differentiability | If a function has a well-defined derivative for each element of the domain | |
| 291693293 | Differentiation | The process of finding the derivative of a function | |
| 291693294 | Discontinuity | A point or value of the independent variable at which the value of a function is not equal to its limit as the value of the independent variable approaches that point, or where it is not defined | |
| 291693295 | Distance (from velocity) | ∫ Iv(t)I (dt) | |
| 291693296 | Distance formula | √[(x2 - x1)^2 + (y2 - y1)^2] | |
| 291693297 | Domain | The set of all values that can be assumed by the independent variable of a function | |
| 291693298 | dy/dx (Leibniz notation) | Notation used for the first derivative of a function | |
| 291693299 | Exponent laws | x^a * x^b =x^a+b (x^a)^b = x^ab x^a/x^b = x^a−b x^1 = x x^0 =1 | |
| 291693300 | Exponential function | Any function closely related to the exponential function, and in particular y = ax , for any a | |
| 291693301 | Extremum | The local and global maximums and minimums of a function | |
| 291693302 | First derivative test | When testing critical values, if the first derivative changes from negative to zero to positive, then that critical value is a local minimum of the function. If the first derivative changes from positive to zero of negative, then that critical value is a local maximum of the function | |
| 291693303 | Fundamental theorem of calculus | Expresses the relationship between integration and differentiation, namely that if the integral ∫ f (x)dx exists, and a function F(x) also exists for which F'(x)=f(x) in [a,b], then ∫f(x)dx=F(b)−F(a) | |
| 291693304 | Implicit differentiation | The differentiation of an implicit function with respect to the independent variable | |
| 291693305 | Increasing on an interval | For all x in [a,b], f'x>0 | |
| 291693306 | Indefinite integral | An integral without any specific limits, whose solution includes an undetermined constant c; antiderivative | |
| 291693307 | Inflection point | A point where a function changes concavity; also, where the second derivative changes signs | |
| 291693308 | Instantaneous rate of change | 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 | |
| 291693309 | Instantaneous velocity | The rate of change of the position function occurring as a limit as a time interval approaches zero; the derivative of the position function | |
| 291693310 | Integrable function | A function that possesses a finite integral; the function must be continuous on the interval of integration | |
| 291693311 | Integrand | The function that is integrated in an integral | |
| 291693312 | Integration | The process by which an antiderivative is calculated | |
| 291693313 | Integration by substitution | In integrating composite function, either using pattern recognition or change of variables to perform the integration | |
| 291693314 | Left-hand limit | The value that a function is approaching as x approaches a given value through values less than x limit as x approaches c- of f(x) | |
| 291693315 | Left-hand sum | 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 | |
| 291693316 | Limit of integration | Either of the endpoints of an interval over which a definite integral is to be evaluated | |
| 291693317 | Limit | The value that the function is approaching as x approaches the given value; the left and right-hand limits must agree | |
| 291693318 | Linear function | A function that can be expressed in the form f(x) = mx + b | |
| 291693319 | Linear approximation | Approximating the value of a function by using the equation of the tangent line at a point close to the desired point | |
| 291693320 | Local linearization | Zooming in at a point on the graph of a function until the function approaches the tangent line at that point | |
| 291693321 | Local extrema | Local maximums and minimums of a function | |
| 291693322 | Logarithmic function | The function y=logax that is the inverse of the function y=a^x | |
| 291693323 | Maximum | The highest value of a function for each value of the domain | |
| 291693324 | Mean value of f(x) | 1/(b-a)∫(b/a) f(x)dx | |
| 291693325 | Mean value theorem for definite integrals | If f is continuous on [a, b], then at some point,c in [a, b], f(c) = 1/(b-a)∫(b/a) f(x)dx | |
| 291693326 | Mean value theorem for derivatives | If y=f(x) is continuous at every point of the close interval [a,b] and differentiable at every point of its interior (a,b), then there is at least one point c in (a,b) at which f'(c)= [f(b)-f(a)]/(b-a) | |
| 291693327 | Middle sum | 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 midpoint of the sub-interval | |
| 291693328 | Minimum | The smallest value of a function for each value of the domain | |
| 291693329 | Natural logarithm | The function y=lnx is the inverse of the exponential function y=e^x | |
| 291693330 | Normal line | A line perpendicular to a tangent line at the point of tangency | |
| 291693331 | Odd function | f(-x)=-f(x) | |
| 291693332 | Optimization | In an application, maximizing or minimizing some aspect of the system being modeled | |
| 291693333 | Origin | The point (0,0) in the Cartesian coordinate plane | |
| 291693334 | Piecewise-defined function | A function that is defined by applying different formulas to different parts of its domain | |
| 291693335 | Polynomial | An expression in the form y = an x^n + an−1x^n−1 + ...+ a1x + a0 | |
| 291693336 | Position function | A function f that gives the position f(t) of a body on a coordinate axis at time t | |
| 291693337 | Prime notation | If y=f(x), then both y' and f'(x) denote the derivative of the function with respect to x | |
| 291693338 | Product rule | If h(x)=f(x)*g(x) then h'(x)=f(x)*g'(x)+g(x)*f'(x) | |
| 291693339 | Quotient rule | If h(x)= f(x)/g(x) then h'(x)= [g(x)f'(x)-f(x)g'(x)]/[g(x)]^2 | |
| 291693340 | Radius of a circle | A segment from a the center of the circle to a point on the circle | |
| 291693341 | Rate of change | The amount of change divided by the time it takes | |
| 291693342 | Region (in a plane) | A connected subset of two-dimensional space, such as the set of points (x,y) enclosed by equations of function and boundary points | |
| 291693343 | Related rates | An equation involving two or more variables that are differentiable functions of time can be used to find an equation that relates the corresponding rates | |
| 291693344 | Relative maximum | Where the derivative changes signs from positive to zero to negative | |
| 291693345 | Relative minimum | Where the derivative changes signs from negative to zero to positive | |
| 291693346 | Right-hand limit | The limit of f as x approaches c from the right | |
| 291693347 | Right-hand sum | 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 right-most point of the sub-interval | |
| 291693348 | Root of an equation | Zero of a function; A solution of the equation f(x)=0 is a zero of the function f or a root of the equation of a x-intercept of the graph | |
| 291693349 | Secant function | THe reciprocal of the cosine function | |
| 291693350 | Secant line | A line through two points on the curve | |
| 291693351 | Second derivative | The derivative of the first derivative | |
| 291693352 | Second derivative test | If f'(c)=0 and f"(c)>0, then f has a local maximum at x=c. If f'(c)=0 and f"(c)<0, then f has a local minimum at x=c | |
| 291693353 | Separable differential equation | A differential equation y'=f(x,y) in which f can be expressed as a product of a function of x and a function of y | |
| 291693354 | Sine function | The trigonometric function that is equal in a right-angled triangle to the ratio of the side opposite the given angle to the hypotenuse | |
| 291693355 | Slope | The steepness of a line; the ratio of the rise of a line divided by the run of a line between any two points; the tangent of the angle between the direction of the line and the x-axis | |
| 291693356 | Solid of revolution | The solid figure generated by revolving a plane region around a line | |
| 291693357 | Speed | The absolute value or magnitude of velocity | |
| 291693358 | Tangent function | A trigonometric function that in a right-angles triangle is the ratio of the length of the side opposite the given angle to that of the adjacent angle side | |
| 291693359 | Tangent line | To the graph of a function y=f(x) at a point x=a where exists, the line through (a, f(a)) with slope f'(a) | |
| 291693360 | Trapezoidal rule | A method of approximating to an intergral as the limit of a sum of areas of trapezoids. Can be done by averaging a left hand sum and a right hand sum | |
| 291693361 | u-substitution | A method of intergration in which ∫f(g(x))*g'(x)dx is rewritten as ∫f(u)du by substituting u=g(x) and du=g'(x)dx | |
| 291693362 | Velocity | The rate of change of position with respect to time | |
| 291693363 | Volume by slicing | A method for finding the volume of a solid by evaluating A(x)dx where A(x) (assumed intergrable) is the solid cross section at area x | |
| 291693364 | x-axis | The horizontal axis of the cartesian coordinate system | |
| 291693365 | x-intercept | The x-coordinate of the point where a curve intersects the x-axis | |
| 291693366 | y-axis | The vertical axis of the cartesian coordinate system | |
| 291693367 | y-intercept | The y-coordinate of the point where a curve intersects the y-axis | |
| 291693368 | Zero of a function | A solution of the equation f(x)=0; a root of the equation |
