volume_mute
Match Operations with ∞ to Their Results
publish date: 2026/05/23 22:07:23.176022 UTC
volume_muteMatch each expression to its result (assuming \(x \in \mathbb{R}\) where applicable).
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Expression
x + (+∞), x ∈ ℝ
x − (+∞), x ∈ ℝ
x / (+∞), x ∈ ℝ
(+∞)(−∞)
Result
+∞
−∞
0
−∞
Correct Answer
(1) x + (+∞), x ∈ ℝ,+∞
(2) x − (+∞), x ∈ ℝ,−∞
(3) x / (+∞), x ∈ ℝ,0
(4) (+∞)(−∞),−∞
Explanation
Key rules of the extended real number system: adding \(+\infty\) to any finite number gives \(+\infty\); subtracting \(+\infty\) from any finite number gives \(-\infty\); dividing any finite number by \(\pm\infty\) gives 0; multiplying \(+\infty\) by \(-\infty\) gives \(-\infty\) (opposite signs).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012