Closed Interval
Definition
A closed interval is a set of real numbers that includes both of its endpoints. It is denoted by square brackets [ ].
Analogy
Think of a closed box with both ends sealed shut. All the numbers within the closed interval are trapped inside just like objects inside the box.
Related terms
Open Interval: A set of real numbers that does not include its endpoints. It is denoted by parentheses ( ).
Half-Closed Interval: An interval that includes one endpoint but not the other. It can be either left-closed and right-open or left-open and right-closed.
Bounded Set: A set where all elements are contained within some finite range.
"Closed Interval" appears in:
Subjects (1)
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Practice Questions (6)
Which condition is required to confirm continuity over a closed interval [a, b]?
Is f(x) = sqrt(x + 4) continuous over the closed interval [-4, 6]?
Is s(x) = 2x^2 - 3x + 1 continuous over the closed interval [0, 2]?
Is q(x) = e^(3x) continuous over the closed interval [1, 4]?
Is h(x) = cos(2x) continuous over the closed interval [0, π]?
If a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), which of the following statements is true?
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