volume_mute
Sort These Expressions: Defined or Indeterminate?
publish date: 2026/05/23 22:07:24.033675 UTC
volume_muteClassify each expression as Defined (has a determinate value) or Indeterminate (cannot be determined from the form alone).
drag and drop the selected option to the right place
Correct Answer
(1) 5 + ∞,Defined
(2) 3 / ∞,Defined
(3) ∞ / ∞,Indeterminate
(4) ∞ − ∞,Indeterminate
(5) 0 × ∞,Indeterminate
(6) ∞⁰,Indeterminate
Explanation
Defined: \(5 + \infty = +\infty\) (finite + infinity); \(3/\infty = 0\) (finite ÷ infinity). Indeterminate: \(\infty/\infty, \infty-\infty, 0 \times \infty, \infty^0\) — these require more context (a limiting process) to evaluate. Different sequences or functions approaching these forms can give different limiting values. They are resolved using L'Hôpital's Rule or algebraic manipulation.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012