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Calculus Theorems and Inequalities

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Questions and Answers

What type of interval has finite real numbers as end points?

Half-closed interval

Finite interval (correct)

Infinite interval

Half-open interval

Which of the following intervals is considered closed?

(−∞, b]

[a, + ∞] (correct)

[a, + ∞)

(a, − ∞)

What is the set of all solutions of an inequality called?

Unknown set

Solution set (correct)

Variable set

Inequality set

What operation should not be performed on both sides of an inequality?

Multiplication by zero Signup and view all the answers

What is the solution set of the inequality x < 5?

(-∞, 5) Signup and view all the answers

Which of the following is a solution of the inequality x < 5?

x = 1 Signup and view all the answers

What is the type of interval that has no endpoints?

Infinite interval Signup and view all the answers

What is special about the intervals (a, − ∞) and (−∞, b)?

They are both open and closed Signup and view all the answers

What is the purpose of the theorem mentioned in the passage?

To perform operations on inequalities without changing the solution set Signup and view all the answers

What is the purpose of the pause in the passage?

To allow the reader to digest the information Signup and view all the answers