Calculus Terms & Flashcards

Calculus Terms & Flashcards
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Domain (of a function)
The domain of a function is the set of values the input variable can take. For a function f(x), the domain is all the values x can take in which f(x) is defined.
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Variable
A variable is a quantity that may change or vary. Consider the function f(x) = x + 2, where x is the input variable. As the input x changes or varies, so does the output of the function.
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Function
A function is a defined relationship that gives an output corresponding to inputs from a variable. The function f(x) = x + 2 (where x is the input variable), for example, represents a line.
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Continuous (function)
A function f(x) is said to be continuous over a given interval a,b if for every point k on a,b, the limit as x approaches k is f(k) (the limit from the left equals the limit from the right).
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Tangent line
A straight line that is adjacent to a function at one single point. The slope of this line is equal to the instantaneous rate of change, or the derivative, of the function at that point.
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Derivative
Derivative is the instantaneous rate of change at a given point; it is equal to the slope of the line tangent to the function at that point.
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Slope
The average rate of change over an interval.
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Limit

The limit is the value a function approaches as its variable approaches some number.

Let f(x) be a function. If f(x) = x, then the limit of f(x) as x approaches 3 is 3.

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17 cards in set

Flashcard Content Overview

This flashcard set touches on the major concepts of Calculus I. The set covers concepts like the limit, derivative, and integral, and it also defines the major theorems of Calculus. Some examples are given to help understand the major concepts and theorems.

Front
Back
Limit

The limit is the value a function approaches as its variable approaches some number.

Let f(x) be a function. If f(x) = x, then the limit of f(x) as x approaches 3 is 3.

Slope
The average rate of change over an interval.
Derivative
Derivative is the instantaneous rate of change at a given point; it is equal to the slope of the line tangent to the function at that point.
Tangent line
A straight line that is adjacent to a function at one single point. The slope of this line is equal to the instantaneous rate of change, or the derivative, of the function at that point.
Continuous (function)
A function f(x) is said to be continuous over a given interval a,b if for every point k on a,b, the limit as x approaches k is f(k) (the limit from the left equals the limit from the right).
Function
A function is a defined relationship that gives an output corresponding to inputs from a variable. The function f(x) = x + 2 (where x is the input variable), for example, represents a line.
Variable
A variable is a quantity that may change or vary. Consider the function f(x) = x + 2, where x is the input variable. As the input x changes or varies, so does the output of the function.
Domain (of a function)
The domain of a function is the set of values the input variable can take. For a function f(x), the domain is all the values x can take in which f(x) is defined.
Range (of a function)
The range of a function is the set of all values the output can take. For a function f(x), the range is all of the values f(x) takes for all x in the domain.
Differentiable (function)
A function is said to be differentiable if the derivative of the function exists.
L'Hôpital's Rule
A rule used to find the limit of a function.
Integral
An integral is used to find the exact area underneath a curve between two points. This is useful, for example, because taking the integral of velocity determines how far one has traveled.
Riemann Sum
The riemann sum is an approximation for an integral, or area under the curve. The riemann sum works by adding together rectangles under the curve.
Fundamental Theorem of Calculus
Let f(x) and F(x) be functions where F'(x) = f(x). If f(x) is continuous from x=a to x=b, then the Fundamental Theorem of Calculus says that the integral of f(x) from a to b equals F(b) - F(a).
Mean Value Theorem
This theorem states that if f(x) is continuous and differentiable over an interval a,b, then there must be a point m in the interval such that f'(m) is equal to the slope of f(x) from a to b.
Intermediate Value Theorem
The theorem states that if a function f(x) is continuous over an interval from x=a to x=b, then f(x) must contain every value between f(a) and f(b) on that interval.
Squeeze/Sandwich Theorem
Let a(x), b(x), and c(x) be functions where a(x) <= b(x) <= c(x). This theorem states that if the limit of a(x) = the limit of c(x), then the limit of b(x) equals the limit of a(x) and c(x).

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