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 [ $\lim_{n \to \infty} (\frac{cos~x}{x})$ ]

~Apply the theorem

Note that [ $-1 \leq cos~x \leq 1$ ] and [ $\lim_{n \to \infty} (-\frac{1}{x})\leq \lim_{n \to \infty} (\frac{cos~x}{x})\leq \lim_{n \to \infty} (\frac{1}{x})$ ]

~Apply the infinity property to every side but the middle

$\lim_{n \to \infty} (-\frac{1}{x}) = 0$

$\lim_{n \to \infty} (\frac{1}{x}) = 0$

So... $\lim_{n \to \infty} (\frac{cos~x}{x})=0$

Best of Luck!