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Indeterminate Forms Involving ∞

publish date: 2026/05/23 22:07:22.901123 UTC

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Expressions involving \(\infty\) that are not defined and cannot be determined without further analysis are called indeterminate forms. Which of the following are indeterminate forms? (Select all that apply.)

\(\infty - \infty\)

\(\infty / \infty\)

\(\infty^0\)

\(x + \infty\) for \(x \in \mathbb{R}\)

\(0 \cdot \infty\)

Correct Answer

(1) \(\infty - \infty\)

(2) \(\infty / \infty\)

(3) \(\infty^0\)

(4) \(0 \cdot \infty\)

Explanation

Indeterminate forms are expressions where the result cannot be determined from the form alone — different limiting processes can give different results. \(\infty - \infty, \infty/\infty, \infty^0, 0 \cdot \infty\) are all indeterminate. In contrast, \(x + \infty = +\infty\) for finite \(x\) is determinate — it always equals \(+\infty\). Indeterminate forms are resolved using L'Hôpital's Rule or algebraic techniques.

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

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