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It looks like you've uploaded a photo with a math problem related to limits. The problem visible in the image asks to "Determine the limit of the following functions" (in Indonesian: "Tentukan nilai limit fungsi berikut") and focuses on the first limit:

\[
\lim_{{x \to \infty}} \frac{4x + 3}{x + \cos{x}}
\]

### Solution:
To solve this limit as \( x \to \infty \), we can begin by dividing both the numerator and the denominator by \( x \), which is the highest degree of \( x \) in the expression:

\[
\lim_{{x \to \infty}} \frac{\frac{4x + 3}{x}}{\frac{x + \cos{x}}{x}} = \lim_{{x \to \infty}} \frac{4 + \frac{3}{x}}{1 + \frac{\cos{x}}{x}}
\]

As \( x \to \infty \):
- \( \frac{3}{x} \to 0 \)
- \( \frac{\cos{x}}{x} \to 0 \) (since \( \cos{x} \) is bounded between -1 and 1)

Thus, the limit simplifies to:

\[
\lim_{{x \to \infty}} \frac{4 + 0}{1 + 0} = 4
\]

### Final Answer:
\[
\lim_{{x \to \infty}} \frac{4x + 3}{x + \cos{x}} = 4
\]

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Would you like further details on this solution or clarification of any step?

Here are some follow-up questions to expand your understanding:
1. What happens if \( \cos{x} \) in the denominator was replaced by a different trigonometric function like \( \sin{x} \)?
2. How would the limit change if we were asked to find it as \( x \to -\infty \)?
3. Can you explain why dividing by \( x \) is necessary in this problem?
4. How would the answer change if \( \lim_{{x \to 0}} \) was asked instead of \( \infty \)?
5. What is the effect of \( \cos{x} \) approaching infinity compared to just a constant?

**Tip**: When solving limits as \( x \to \infty \), try to simplify expressions by focusing on the highest powers of \( x \). This often makes the calculation easier.

Tentukan nilai limit fungsi berikut: lim(x -> ∞) (4x + 3) / (x + cos(x))

Learn how to solve the limit of (4x + 3)/(x + cos(x)) as x approaches infinity. This problem involves dividing by the highest power of x and understanding the behavior of trigonometric functions at large values of x. Suitable for students in Grades 10-12.

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