I see you’ve uploaded an image of a series of limit problems for a math class (Mat TL Kelas XII). Let’s go through these problems one by one.

Problem 1

$\lim_{x \to 3} \frac{\sqrt{10 - 2x}}{3x}$

Problem 2

$\lim_{x \to 3} \frac{x^2 + 5x + 6}{x + 3}$

Problem 3

$\lim_{x \to 1} \frac{x + 3}{x - 1}$

Problem 4

$\lim_{x \to 0} \frac{6x^2}{3x^2 - 8}$

Problem 5

$\lim_{x \to \infty} \frac{x^3 + 3x^2 - \sqrt{4x^5 - 5}}{x^3}$

Problem 6

$\lim_{x \to 0} \frac{(x + 4)(x - 6)}{\sin(x) + \cos(x)}$

Problem 7

$\lim_{x \to \frac{\pi}{2}} \frac{\sin\left(\frac{x}{2}\right)}{\sin(x)}$

Problem 8

$\lim_{x \to 0} \frac{\tan(x)}{3\sin(x)}$

Problem 9

$\lim_{x \to 0} \frac{1 - \cos(4x)}{x^2}$

Problem 10

$\lim_{x \to \infty} \left[\frac{\tan\left(\frac{\pi}{6} + \cos\left(\frac{1}{x}\right)\right)}{\tan\left(\frac{5x}{6}\right)} \cdot \frac{\sin\left(\frac{1}{4x}\right)}{\sin\left(\frac{1}{4x}\right)}\right]$

Would you like to begin solving these limits one by one or have me focus on a specific problem?

5 Follow-up Questions:

1. Are you familiar with L'Hôpital's rule for solving indeterminate limits?
2. Would you like me to go through the basic properties of limits before solving?
3. Do you need detailed steps on any particular problem from the list?
4. Do you need help identifying indeterminate forms (like 0/0 or ∞/∞)?
5. Are you comfortable with trigonometric limits, or should I review them?

Tip:

For limits involving $\infty$, comparing the degrees of polynomials (for large $x$) is a quick way to solve them.