The Squeeze Theorem states that if three functions [itex]f(x)[/itex], [itex]g(x)[/itex], and [itex]h(x)[/itex] exist, and [itex]f(x) \leq g(x) \leq h(x)[/itex], and if [itex] \lim_{x \rightarrow a} f(x) = L[/itex] and [itex] \lim_{x \rightarrow a} h(x) = L[/itex], then [itex] \lim_{x \rightarrow a} g(x)[/itex] must exist and its value must be L.(adsbygoogle = window.adsbygoogle || []).push({});

Here is something I don't understand about the Squeeze Theorem: what does it mean for a function to be less than or greater than a another function? It doesn't make sense to me because depending on the input values of the function, sometimes the value of the function can be greater than the value of a different function, and sometimes the value of the function to be less than the value of the other function, and sometimes the value of the two functions could be equal. How does one know if a function is less than or greater than another function? Can you determine it mathematically, or do you have to look at a table or a graph?

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Squeeze Theorem: What does it mean for a function to be less than or greater than a another function

**Physics Forums | Science Articles, Homework Help, Discussion**