Unit 1 Flashcards
Limit
The value that a function approaches as the input approaches some value.
Continuity
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.
Discontinuity
A point at which a function is not continuous. Types include jump, infinite, and removable discontinuities.
Limit from the Left
The value that a function approaches as the input approaches from the left (negative side) of a point.
Limit from the Right
The value that a function approaches as the input approaches from the right (positive side) of a point.
One-Sided Limit
The limit of a function as the input approaches a value from one side (either from the left or the right).
Infinite Limit
A limit in which the function increases or decreases without bound as the input approaches a particular value.
Limit at Infinity
The value that a function approaches as the input increases or decreases without bound.
Horizontal Asymptote
A horizontal line that the graph of a function approaches as the input either increases or decreases without bound.
Vertical Asymptote
A vertical line where a function’s value becomes unbounded as the input approaches a certain value.
Derivative
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.
Differentiability
A function is differentiable at a point if it has a defined derivative at that point.
Slope of the Tangent Line
The derivative of a function at a specific point, representing the slope of the curve at that point.
Secant Line
A line that intersects a curve at two or more points.
Average Rate of Change
The change in the value of a function divided by the change in the input. Equivalent to the slope of the secant line.
Instantaneous Rate of Change
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.
Continuity at a Point
A function is continuous at a point
𝑐 if its limit equals its function value at that point.
Intermediate Value Theorem
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.
