To use the Squeeze Theorem and show that a limit exists, follow these simple steps:

1. Identify the Functions: First, let’s say you have a function called $f(x)$ that you want to find the limit for as $x$ gets close to a number $a$.

   You need to find two other functions, $g(x)$ and $h(x)$, such that: $g(x) \leq f(x) \leq h(x)$ for all $x$ in a range around $a$, except maybe at $a$ itself.

2. Evaluate Limits: Next, you need to figure out what happens to $g(x)$ and $h(x)$ as $x$ approaches $a$. In simple math language, you will find: $\lim_{x \to a} g(x) = L$ $\lim_{x \to a} h(x) = L$

3. Apply the Squeeze Theorem: If both limits end up being the same thing, $L$, then according to the Squeeze Theorem, you can say: $\lim_{x \to a} f(x) = L$

Example: Let’s look at the limit $\lim_{x \to 0} x^2 \sin(\frac{1}{x})$.

We know that $-1 \leq \sin(\frac{1}{x}) \leq 1$.

So, we can say: $-x^2 \leq x^2 \sin(\frac{1}{x}) \leq x^2$

As $x$ gets closer to $0$, both $-x^2$ and $x^2$ get closer to $0$.

This shows that: $\lim_{x \to 0} x^2 \sin(\frac{1}{x}) = 0$

And that's it! You've used the Squeeze Theorem to find the limit.