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The image you have uploaded contains a set of 14 limit problems under the title "Latihan Soal." Let me provide solutions to a few of these problems with detailed steps.

### Problem 1:
\[
\lim_{x \to 0} \frac{\cos x}{x + 1}
\]

### Solution:
1. As \(x \to 0\), \(\cos x \to \cos 0 = 1\) and \(x + 1 \to 1\).
   
Thus, the limit is:
\[
\lim_{x \to 0} \frac{\cos 0}{0 + 1} = \frac{1}{1} = 1
\]

### Problem 2:
\[
\lim_{\theta \to \frac{\pi}{2}} \theta \cos \theta
\]

### Solution:
1. As \(\theta \to \frac{\pi}{2}\), \(\cos \theta \to \cos \frac{\pi}{2} = 0\).
   
Thus, the limit is:
\[
\lim_{\theta \to \frac{\pi}{2}} \theta \cos \theta = \frac{\pi}{2} \cdot 0 = 0
\]

### Problem 3:
\[
\lim_{t \to 0} \frac{\cos^2 t}{1 + \sin t}
\]

### Solution:
1. As \(t \to 0\), \(\cos^2 t \to \cos^2(0) = 1\) and \(\sin t \to 0\), so \(1 + \sin t \to 1\).
   
Thus, the limit is:
\[
\lim_{t \to 0} \frac{\cos^2 0}{1 + \sin 0} = \frac{1}{1} = 1
\]

### Problem 4:
\[
\lim_{x \to 0} \frac{\sin x}{3x \tan x}
\]

### Solution:
1. Use the fact that \(\lim_{x \to 0} \frac{\sin x}{x} = 1\) and \(\lim_{x \to 0} \frac{\tan x}{x} = 1\).

Thus, the limit becomes:
\[
\lim_{x \to 0} \frac{\frac{\sin x}{x}}{3 \frac{\tan x}{x}} = \frac{1}{3} = \frac{1}{3}
\]

### Problem 5:
\[
\lim_{x \to 0} \frac{\sin x}{2x}
\]

### Solution:
1. Again, use \(\lim_{x \to 0} \frac{\sin x}{x} = 1\).

Thus, the limit becomes:
\[
\lim_{x \to 0} \frac{\sin x}{2x} = \frac{1}{2}
\]

---

Do you want further explanations or solutions to more of these problems? Here are some relative questions for you:

1. How do you evaluate limits when the function involves a trigonometric identity?
2. What are common limit rules used in calculus, especially for trigonometric limits?
3. How does L'Hôpital's Rule apply to limits with indeterminate forms like \(0/0\)?
4. What is the small-angle approximation for trigonometric functions, and how is it useful in limits?
5. Can limits always be calculated directly, or do you sometimes need additional techniques (like series expansions)?

**Tip:** When dealing with trigonometric limits, remembering that \(\lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1\) and \(\lim_{\theta \to 0} \frac{\tan \theta}{\theta} = 1\) simplifies many problems.

The image contains 14 limit problems involving trigonometric and algebraic functions.

Explore 14 limit problems involving trigonometric and algebraic functions, including solutions for cos(x), sin(x), tan(x), and other limits. Detailed step-by-step solutions provided. Ideal for students studying Calculus I in Grades 11-12.

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