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?

<p>Multiplication by zero (B)</p> Signup and view all the answers

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

<p>(-∞, 5) (D)</p> Signup and view all the answers

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

<p>x = 1 (D)</p> Signup and view all the answers

What is the type of interval that has no endpoints?

<p>Infinite interval (B)</p> Signup and view all the answers

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

<p>They are both open and closed (D)</p> Signup and view all the answers

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

<p>To perform operations on inequalities without changing the solution set (A)</p> Signup and view all the answers

What is the purpose of the pause in the passage?

<p>To allow the reader to digest the information (A)</p> Signup and view all the answers

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