Thank you for uploading the image! I will analyze and solve the mathematical problems step-by-step. Here's the breakdown of the problems:

1. Limit Calculations

$\text{a. } \lim_{x \to 2} (3x^2 - x - 8)$
$\text{b. } \lim_{x \to -1} (3x^3 - x - 6)$

2. Limit Calculations with Fractions

$\text{a. } \lim_{n \to 2} \frac{x^2 - 2x - 15}{x + 3}$
$\text{b. } \lim_{n \to -1} \frac{x^3 - 3x - 13}{x + 1}$

3. Transpose of Matrix

Matrix $A = \begin{bmatrix} 2 & 3 & 0 \\ 3 & -1 & 4 \end{bmatrix}$, find $A^T$.

4. Limit with Roots

$\text{a. } \lim_{x \to 2} \sqrt{\frac{1}{5x - 1}}$
$\text{b. } \lim_{x \to 2} \sqrt{\frac{1}{5x - 6}}$

5. Derivatives

$\text{a. If } y = 3x^2 - x, \text{ find } \frac{dy}{dx}.$
$\text{b. If } y = 3x^2 + x^3, \text{ find } \frac{dy}{dx}.$
$\text{c. If } y = 4x^2 \cdot x^2, \text{ find } \frac{dy}{dx}.$

6. Matrix Multiplication

Matrix $A = \begin{bmatrix} 1 & 2 \\ 1 & 3 \\ 0 & 1 \end{bmatrix}$
Matrix $B = \begin{bmatrix} 3 & 1 & 4 \\ 2 & 1 & 0 \end{bmatrix}$,
find $A \times B$.

Would you like a full solution to each question or focus on any specific section? Let me know!