use the squeeze theorem to the limit when 3-x^2

To find the limit of \( 3 - x^2 \) as \( x \to a \) using the **Squeeze Theorem**, we first need to understand how the Squeeze Theorem applies. However, the given function \( f(x) = 3 - x^2 \) is a continuous polynomial, and finding its limit directly doesn't need the Squeeze Theorem. Instead, you would evaluate it by substituting the value of \( x \) into the function.

The **Squeeze Theorem** (also known as the Sandwich Theorem) is typically used when a function is "squeezed" between two other functions, and we know the limits of these other two functions. If \( g(x) \leq f(x) \leq h(x) \) for all \( x \) in some interval around \( a \), and if \( \lim_{x \to a} g(x) = \lim_{x \to a} h(x) = L \), then \( \lim_{x \to a} f(x) = L \).

Now, for your expression \( 3 - x^2 \):

### Direct Calculation of the Limit:
If you want to evaluate \( \lim_{x \to a} (3 - x^2) \), you can do it by direct substitution:
\[
\lim_{x \to a} (3 - x^2) = 3 - a^2
\]
Thus, the limit depends on the value of \( a \).

If you were referring to using the Squeeze Theorem for another related function or a situation where limits are more complex, please clarify and I can assist with that as well.

Would you like to explore a case where the Squeeze Theorem would be applicable?

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Here are 5 related questions:
1. How does the Squeeze Theorem apply to trigonometric limits?
2. Can we use the Squeeze Theorem for absolute value functions?
3. What is an example where the Squeeze Theorem simplifies an indeterminate form?
4. How does continuity affect the application of the Squeeze Theorem?
5. Can the Squeeze Theorem be applied to functions approaching infinity?

**Tip**: When approaching limits for continuous functions, direct substitution is usually the fastest method unless the function leads to an indeterminate form.

Explore how to find the limit of the polynomial function 3 - x^2 using the Squeeze Theorem. Learn about key concepts such as continuity, polynomial functions, and direct substitution. Suitable for high school students in Grades 11-12.

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