Unit 1 Flashcards

1
Q

Limit

A

The value that a function approaches as the input approaches some value.

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2
Q

Continuity

A

A function is continuous at a point if the limit exists at that point, the function value exists, and the limit equals the function value.

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3
Q

Discontinuity

A

A point at which a function is not continuous. Types include jump, infinite, and removable discontinuities.

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4
Q

Limit from the Left

A

The value that a function approaches as the input approaches from the left (negative side) of a point.

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5
Q

Limit from the Right

A

The value that a function approaches as the input approaches from the right (positive side) of a point.

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6
Q

One-Sided Limit

A

The limit of a function as the input approaches a value from one side (either from the left or the right).

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7
Q

Infinite Limit

A

A limit in which the function increases or decreases without bound as the input approaches a particular value.

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8
Q

Limit at Infinity

A

The value that a function approaches as the input increases or decreases without bound.

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9
Q

Horizontal Asymptote

A

A horizontal line that the graph of a function approaches as the input either increases or decreases without bound.

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10
Q

Vertical Asymptote

A

A vertical line where a function’s value becomes unbounded as the input approaches a certain value.

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11
Q

Derivative

A

A measure of how a function’s output changes as its input changes. Represented as the slope of the tangent line at any point on the function.

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12
Q

Differentiability

A

A function is differentiable at a point if it has a defined derivative at that point.

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13
Q

Slope of the Tangent Line

A

The derivative of a function at a specific point, representing the slope of the curve at that point.

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14
Q

Secant Line

A

A line that intersects a curve at two or more points.

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15
Q

Average Rate of Change

A

The change in the value of a function divided by the change in the input. Equivalent to the slope of the secant line.

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16
Q

Instantaneous Rate of Change

A

The derivative at a particular point, representing the slope of the tangent line and the rate at which the function is changing at that instant.

17
Q

Continuity at a Point

A

A function is continuous at a point
𝑐 if its limit equals its function value at that point.

18
Q

Intermediate Value Theorem

A

If a function is continuous on the interval
[𝑎,𝑏] and f(a) does not equal f(b),
then the function takes on every value between f(a) and f(b) at least once in the interval.