6.

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

𝑥 0

lim

→

𝑓(𝑥).

To solve this problem, we need to use the **Squeeze Theorem** and analyze the given functions to find the limit of \( f(x) \) as \( x \to 0 \). The functions provided are:

- \( u(x) = 1 \)
- \( l(x) = 1 - x^2 \)
- \( f(x) = \cos^2(x) \)

### 1. Squeeze Theorem Concept:
The **Squeeze Theorem** states that if we have three functions \( l(x) \leq f(x) \leq u(x) \) for all \( x \) near a certain point (in this case, as \( x \to 0 \)), and if both the upper bound \( u(x) \) and lower bound \( l(x) \) converge to the same limit, then \( f(x) \) will also converge to that same limit.

### 2. Check the bounds at \( x = 0 \):
We need to check the limits of the upper and lower bounds as \( x \to 0 \).

- For \( u(x) = 1 \):
  \[
  \lim_{x \to 0} u(x) = \lim_{x \to 0} 1 = 1
  \]

- For \( l(x)

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.

This problem uses the Squeeze Theorem to determine the limit of cos^2(x) as x approaches 0. Learn how to apply the theorem with functions u(x) = 1, l(x) = 1 − x^2, and f(x) = cos^2(x). Suitable for high school calculus students.

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