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# Squeeze Theorem

Course Topic(s): One-Variable Calculus | Infinite Limits, Function Values and Integrals | Continuity and Limits

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

Publisher:
Wolfram Demonstrations Project

This review was published on February 07, 2011