Mathematics: Describe the Squeeze Theorem as simply as possible.

Describe the Squeeze Theorem as simply as possible.

Ответ:

001035783

05.02.2022

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!

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Ответ:

mariafsoriano928

08.02.2021

Mathematics

For the first pair it's (1, 4) and the next is (1.5, 6), and the last is (6, 6)

Step-by-step explanation:

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Describe the Squeeze Theorem as simply as possible.

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