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Squeeze Theorem  

Students investigate the limits of the functions \(x^n \sin(^1/_x)\) as \(x \to 0\) for \( n = 0, 1, 2\) and \(3\). They see the graphs of the function and its bounds \(|x|^n\) and \(-|x|^n\) and zoom in toward \(0\). They can see that the functions with \(n = 1, 2\) and \(3\) have a limit of \(0\) while the function with \(n = 0\) does not have a limit. This would make an excellent classroom demo.

Resource URL: http://demonstrations.wolfram.com/SqueezeTheorem/

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Subject classification(s): Limits | Single Variable Calculus | Calculus

Creator(s): Bruce Atwood (Beloit College) and Selwyn Hollis (Armstrong Atlantic State University)

Contributor(s): Wolfram Demonstrations Project

This resource was cataloged by Philip Yasskin

Related Resources

• Investigating Limits Numerically
• Finite Limits at Infinity
• Infinite Limits at Infinity
• Finite Limits at a Finite Point
• L'Hospital's Rule for 0/0 Forms

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