Question

Describe the Squeeze Theorem as simply as possible.​

Answer 1

Hey there,

The squeeze theorem shows if
`f(x)\leq g(x)\leq h(x)` for all real numbers
`(-\infty,~\infty)` then f(x) = h(x) but g(x) has to equal that as well.

Let's say we have [
`\lim_(n \to \infty) ((cos~x)/(x))` ]

~Apply the theorem

Note that [
`-1 \leq cos~x \leq 1` ] and [
`\lim_(n \to \infty) (-(1)/(x))\leq \lim_(n \to \infty) ((cos~x)/(x))\leq \lim_(n \to \infty) ((1)/(x))` ]

~Apply the infinity property to every side but the middle

`\lim_(n \to \infty) (-(1)/(x)) = 0`

`\lim_(n \to \infty) ((1)/(x)) = 0`

So...
`\lim_(n \to \infty) ((cos~x)/(x))=0`

Best of Luck!