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The image shows a mathematical problem related to the Squeeze Theorem (Teorema Squeeze in Indonesian) for limits. Here's the problem breakdown:

You are asked to sketch three functions:
1. \( u(x) = 1 \)
2. \( l(x) = 1 - x^2 \)
3. \( f(x) = \cos^2(x) \)

Then, you are instructed to use these graphs and apply the Squeeze Theorem to determine the limit:

\[
\lim_{x \to 0} f(x)
\]

### Applying the Squeeze Theorem

The Squeeze Theorem states that if:
\[
l(x) \leq f(x) \leq u(x)
\]
for all \(x\) near some point (except possibly at the point itself), and if:
\[
\lim_{x \to 0} l(x) = \lim_{x \to 0} u(x) = L,
\]
then:
\[
\lim_{x \to 0} f(x) = L.
\]

#### Step-by-Step:
1. **Upper Bound**: \( u(x) = 1 \) is constant, and \(\lim_{x \to 0} u(x) = 1\).
   
2. **Lower Bound**: \( l(x) = 1 - x^2 \) approaches 1 as \(x \to 0\), i.e., \(\lim_{x \to 0} l(x) = 1\).
   
3. **Function**: \( f(x) = \cos^2(x) \). At \(x = 0\), \(\cos^2(0) = 1\), so \(\lim_{x \to 0} f(x) = 1\).

Since both the upper and lower bounds converge to 1 as \(x \to 0\), by the Squeeze Theorem:
\[
\lim_{x \to 0} \cos^2(x) = 1.
\]

### Conclusion:
\[
\lim_{x \to 0} f(x) = 1.
\]

Would you like to see more details on the graph or how to apply the Squeeze Theorem in other scenarios? Here are a few related questions to deepen your understanding:

1. Can you visualize the graphs of \(u(x)\), \(l(x)\), and \(f(x)\) to confirm the bounds?
2. How does the Squeeze Theorem apply when the limits are not equal at a point?
3. Can we use the Squeeze Theorem for limits approaching infinity?
4. What happens if \(f(x)\) does not lie between \(u(x)\) and \(l(x)\)?
5. How would the result change if we were considering \(\lim_{x \to \infty} f(x)\)?

**Tip**: The Squeeze Theorem is especially useful for functions that are difficult to evaluate directly but can be bounded by simpler ones.

Sketsakan fungsi u(x), l(x), dan f(x), yaitu u(x) = 1, l(x) = 1 - x^2, dan f(x) = cos^2(x). Gunakan grafik ini menggunakan Teorema Squeeze untuk menentukan lim f(x) saat x → 0.

Learn how to apply the Squeeze Theorem to determine the limit of f(x) = cos^2(x) as x approaches 0. The functions u(x) = 1 and l(x) = 1 - x^2 are used to bound f(x). Understand the application of limits and the Squeeze Theorem in trigonometric contexts.

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