# 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.
Identifier:
http://demonstrations.wolfram.com/SqueezeTheorem/
Rating:
Creator(s):
Bruce Atwood (Beloit College) and Selwyn Hollis (Armstrong Atlantic State University)
Cataloger:
Philip Yasskin
Publisher:
Wolfram Demonstrations Project
Rights:
Wolfram Demonstrations Project