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Determine whether the limit lim xsin exist, 72 I

Determine whether the limit lim xsin exist, 72 I

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
**Determine whether the limit \(\lim_{x \to 0} x \sin\left(\frac{1}{x^2}\right)\) exists.** In this mathematical expression, the task is to evaluate whether the given limit exists as \(x\) approaches zero. The function involves the product of \(x\) and \(\sin\left(\frac{1}{x^2}\right)\). Understanding how the sine function behaves as its argument tends to infinity, and how it interacts with the linear term \(x\), is crucial to solving the problem.
Transcribed Image Text:**Determine whether the limit \(\lim_{x \to 0} x \sin\left(\frac{1}{x^2}\right)\) exists.** In this mathematical expression, the task is to evaluate whether the given limit exists as \(x\) approaches zero. The function involves the product of \(x\) and \(\sin\left(\frac{1}{x^2}\right)\). Understanding how the sine function behaves as its argument tends to infinity, and how it interacts with the linear term \(x\), is crucial to solving the problem.
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