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Calculus Vocabulary

Word List with 29 words
*By Dictionary.com

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Words in This List

antiderivative
a representation, usually in symbolic form, of any function whose derivative is a given function.
tangent
a line or a plane that touches a curve or a surface at a single point.
chain rule
n
the theorem that defines the method for taking the derivative of a composite function.
concave downward
part of a graph resembling an upside down bowl.
concave upward
part of a graph resembling a right side up bowl.
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continuous
being in immediate connection or spatial relationship.
critical point
point on the graph where the derivative is either 0 or undefined.
cylindrical shell method
technique for finding the volume of a solid of revolution.
definite integral
the representation of the difference in values of a primitive of a given function evaluated at two designated points.
derivative
the change of a function with respect to an infinitesimally small change in the independent variable, or the slope of the point's tangent line.
differentiable
a function whose graph is curve that is smooth and contains no discontinuities or cusps.
disk method
technique for finding the volume of a solid of revolution when integrating along the axis of revolution.
extreme value theorem
noun
guarantees an absolute max and an absolute min
first derivative test
determines whether an inflection point is a minimum, maximum, or neither.
higher order derivatives
any derivatives beyond the first derivative.
implicit differentiation
method for finding the derivative of an implicitly defined function or relation using the chain rule.
indefinite integral
another way of saying antiderivative.
instantaneous rate of change
rate of change at a particular moment.
instantaneous velocity
rate at which an object is moving at a particular moment.
integration by parts
a method of evaluating an integral by use of the formula, ∫udv = uv − ∫vdu.
limit
value that a function approaches as the domain variable approach a specific value.
mean value theorem
the theorem that there is a point in a continuous curve where the derivative is equal to the average derivative of the entire arc.
normal line
line that is at a 90 degree angle, perpendicular to a surface.
point-slope form
form used the most when finding the equation of a line.
riemann sum
method for approximating the definite integral.
second derivative test
determines whether a critical point is a relative minimum or maximum using the value of the second derivative at the point.
u-substitution
integration method that involves using the chain rule in reverse.
trigonometric substitution
substitution of trigonometric functions for other expressions to eliminate radicals in integrals.
washer method
similar to the disk method but using washers instead of disks.

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